mechanical design of the next generation turtlemate.tue.nl/mate/pdfs/11360.pdf · tech united is...

R.J.G. Alaerds

CST 2010.005

Mechanical design of the nextgeneration Tech United Turtle

Master’s thesis

Coach: Dr.ir. P.C.J.N. Rosielle

Supervisor: Prof.dr.ir. M. Steinbuch

Commission members: Dr. D. KosticDr.ir. M.J.G. v.d. Molengraft

Technische Universiteit EindhovenDepartment of Mechanical EngineeringControl Systems Technology Group

Eindhoven, January, 2010

Abstract

RoboCup is an international research and education initiative. Its goal is to foster artificialintelligence and robotics research by providing a standard problem where a wide rangeof technologies can be examined and integrated. For this purpose the game of soccer ischosen, which is played in different leagues.The middle size league is one of them. In this league, teams of five autonomous robotsplay against each other. Tech United is the RoboCup team of the Eindhoven University ofTechnology that competes in this league. To fulfill their goal of becoming world champion,Tech United is constantly developing their software and hardware. Their current robots,which are called Turtles, face deformation problems, as a result of collisions. Due tothe deformation the Turtle starts to rock when driving around. An omnivision unit ontop produces images with are used to determine the position of the Turtle on the field.When the Turtle rocks, the position cannot be determined accurately. To overcome theseproblems, a new mechanical design for the Turtle has been made.The wheel configuration determines the basic shape of the Turtle’s frame. Different wheelconfigurations are compared on top speed, acceleration, cornering speed and maneuver-ability. A configuration with four omniwheels at the corners of a 500 mm x 500 mmsquare is chosen. The axes of the wheels are along the diagonals of the square. Thewheel configuration has changed compared to the current Turtle, therefore the softwarethat controls the motor speeds has to be changed too.The new frame is designed based on stiffness. The base plate no longer is the maincomponent of the frame. The basic shape of the new frame can be compared to the Eif-fel Tower. Four legs are connected to a central box. The legs house the motors and thewheels. Both the central box and the legs are made of aluminum sheets, which are foldedto form closed boxes. The material is optimally used to guide the external forces throughthe frame.The base plate and the kicking mechanism are attached to the box and the legs. An octag-onal cone connects the omnivision unit firmly to the rest of the frame.FEM analysis show that the frame can handle impact forces of two robots that collide attop speed, without plastic deformation. The octagonal cone is stiff enough to cope withimpacts of balls traveling up to 10 m/s.The finished Turtle covers a floor area of 500 mm x 500 mm, has a height of 783 mmand an estimated mass of 36.3 kg. These specifications are within the RoboCup rules andregulations.It is recommended to perform tests to determine the power usage of the new Turtle. Thereis an extra motor and due to the wheel configuration, all motors are used most of the time.This was not the case in the current Turtle. This may result in the use of other types ofbatteries that deliver more power. It is also proposed to adjust the design of the activeball handling mechanism and the mechanism that actuates the adjustable kicking lever to

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overcome the 2009 season’s problems and to make them fit inside the new design.

Samenvatting

RoboCup is een internationaal onderzoek en onderwijs initiatief. Het doel is omkunstmatige intelligentie en onderzoek naar robotica aantrekkelijker te maken. Dit wordtgedaan door het aanbieden van standaard problemen waarbij een groot scala van tech-nologieën kunnen worden beschouwd en toegepast. Voetbal is het aangeboden probleemen dit wordt in verschillende soorten competities gespeeld.Een van die competities is de middle size league. Teams bestaande uit vijf autonomerobots spelen tegen elkaar. Tech United is het RoboCup team van de Technische Uni-versiteit Eindhoven dat uitkomt in deze competitie. Het team is constant bezig met deontwikkeling van zowel de software als de hardware om hun doel te bereiken: wereldkampioen worden.De huidige robots, Turtles genaamd, hebben nog mechanische problemen. Als ze botsenmet een andere robot, verbuigt de bodemplaat nog wel eens. Dit zorgt ervoor dat dewielen niet allemaal meer in hetzelfde horizontale vlak staan en daardoor gaat de Turtlewiebelen als hij rijdt. De beelden van de omnivisie unit bovenop de Turtle worden gebruiktom de positie op het veld te bepalen. Door het wiebelen gaat dit niet meer nauwkeurig,wat problemen geeft tijdens het spel. Om deze problemen te verhelpen is er een nieuwmechanisch ontwerp van de Turtle gemaakt.De wiel configuratie bepaald de basis vorm van het frame van de Turtle. Er zijn verschil-lende wiel configuraties vergeleken op het gebied van topsnelheid, acceleratie, bocht snel-heid en wendbaarheid. Er is gekozen voor en configuratie waarbij vier omniwielen op dehoeken van een 500 mm x 500 mm vierkant zijn geplaatst. De assen van de wielen liggenover de diagonalen van het vierkant. De wiel configuratie is veranderd ten opzichte van dehuidige configuratie, daarom moet de software die de motoren aanstuurt ook aangepastworden. Ook is het aanbevolen om testen uit te voeren waarmee het energie verbruik vande nieuwe wiel configuratie bepaald wordt. Er is een extra motor bijgekomen en de con-figuratie zorgt ervoor dat vaak alle vier de motoren gebruikt worden om in een bepaalderichting te kunnen rijden. Het energie verbruik zal dus hoger zijn en daarom moeten ermisschien andere batterijen in de Turtle geplaatst worden.Het nieuwe ontwerp is gebaseerd op stijfheid. De bodemplaat is niet langer het dragendedeel van de constructie, maar is nu aan het frame opgehangen. Het frame heeft de vormvan de Eiffel Toren. Aan een centrale doos zijn vier poten bevestigd. De motoren zijnonderin de poten bevestigd. De centrale doos en de poten zijn gemaakt van aluminiumplaten, die tot gesloten dozen zijn gevouwen. Zo wordt het materiaal optimaal gebruiktom externe krachten door het frame te leiden. Het schiet mechanisme is ook aan hetframe opgehangen. Een achthoekige kegel verbindt de omnivisie unit stijf aan de rest vanhet frame.FEM analyses tonen aan dat het frame botsingen met andere robots op top snelheid aankan zonder plastisch te vervormen. Ook tonen zij aan dat de achthoekige kegel geen

vi

plastische deformatie vertoond als er een bal met 10 m/s tegenaan getrapt wordt.Het nieuwe ontwerp beslaat een grond oppervlak van 500mm x 500mm, heeft een hoogtevan 783 mm en heeft een geschatte massa van 36.3 kg. Dit blijft binnen de maximaleafmetingen en gewicht beschreven in de RoboCup reglementen.Er is voorgesteld om het actieve bal behandeling mechanisme en het mechanisme dat deverstelbare lepel van het schiet mechanisme instelt aan te passen om de problemen uithet seizoen 2009 in de toekomst te voorkomen. Ook moeten de huidige ontwerpen vandeze mechanismen aangepast worden om ze in het nieuwe frame te laten passen.

Contents

Abstract iii

Samenvatting v

1 Introduction 1

2 RoboCup and Tech United 32.1 What is RoboCup? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.2 Tech United . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.3 The Turtle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.3.1 How does it work . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.3.2 Base frame . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.4 The assignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

3 Wheel configuration 93.1 Different wheel configurations and their kinematics . . . . . . . . . . . . 9

3.1.1 Platform with three omniwheels . . . . . . . . . . . . . . . . . . . 103.1.2 Three wheeled platform with regular wheels . . . . . . . . . . . . 113.1.3 Platform with four omniwheels . . . . . . . . . . . . . . . . . . . . 12

3.2 Rotation of the wheels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133.3 Acceleration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3.3.1 Slippage of the wheels . . . . . . . . . . . . . . . . . . . . . . . . . 163.3.2 Normal force acting on the wheels . . . . . . . . . . . . . . . . . . 173.3.3 Simulation of the acceleration . . . . . . . . . . . . . . . . . . . . 18

3.4 Cornering speed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213.5 Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

4 The bottom half of the new design 254.1 Central box . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254.2 Legs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

4.2.1 Motor clamp . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294.2.2 The closed box . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

4.3 Base plate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354.3.1 Connection of the base plate to the main frame . . . . . . . . . . . 364.3.2 Ball end stop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

4.4 Kicking mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384.4.1 The kicking lever . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

viii Contents

4.4.2 Solenoid and rocker . . . . . . . . . . . . . . . . . . . . . . . . . . 404.4.3 Comparison current and new kicking mechanism . . . . . . . . . 434.4.4 Analysis of the rocker . . . . . . . . . . . . . . . . . . . . . . . . . 454.4.5 The kicking mechanism attached to the frame . . . . . . . . . . . 464.4.6 The capacitor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

4.5 Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

5 The upper half of the new design 515.1 Omnivision unit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 515.2 Outer shape of the upper half . . . . . . . . . . . . . . . . . . . . . . . . . 52

5.2.1 The basic shape . . . . . . . . . . . . . . . . . . . . . . . . . . . . 525.2.2 The design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

5.3 Components inside the cone . . . . . . . . . . . . . . . . . . . . . . . . . 555.3.1 The computer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 555.3.2 The circuit boards . . . . . . . . . . . . . . . . . . . . . . . . . . . 575.3.3 The front camera and support frame . . . . . . . . . . . . . . . . . 58

5.4 The total design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 605.4.1 The cone with components attached to the bottom half . . . . . . . 605.4.2 FEM analyses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

5.5 Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

6 Conclusion and Recommendation 696.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 696.2 Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

A Specifications 73A.1 Motor and gear head . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73A.2 Electromechanical solenoid . . . . . . . . . . . . . . . . . . . . . . . . . . 76

B Experiments 79B.1 Height of C.O.G. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79B.2 Sliding friction coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . 80B.3 Ball stiffness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

C SAM simulations 83

D FEM results 87D.1 Rocker . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87D.2 Frame . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

E Proposal for the position of hardware components 91

Chapter 1

Introduction

Tech United is the RoboCup team of the Eindhoven University of Technology, that com-petes in the middle size league. In this league, teams of five autonomous robots play thegame of soccer against each other. To fulfill their goal of becoming world champion, sofarthey were second twice in the world championship, Tech United is constantly developingtheir software and hardware. Their current robots, which are called Turtles, face deforma-tion problems, as a result of collisions. To overcome these problems, they laid down theassignment to come up with a new mechanical design for the Turtle. This is the subjectof this report.

Chapter 2 gives an introduction to the RoboCup Federation, Tech United and the currentdesign of the Turtle. The deformation problems are addressed and the assignment isdescribed in more detail.

The wheel configuration is the starting point of the design, because this determines thebasic shape of the Turtle’s frame. Chapter 3 discusses different wheel configurations.Simulations are performed to compare them to each other and help to decide which con-figuration will be used in the new design.

The new design can be split in to a bottom and upper half. The bottom half is discussedin Chapter 4. This half is designed to overcome the deformation problems of the currentTurtle. It also houses the kicking mechanism.

Chapter 5 discusses the upper half of the design. The main task of this half is to connectthe omnivision unit of the Turtle firmly to the bottom half of the design, such that theycannot move with respect to each other. This Chapter also discusses the FEM analysesthat have been performed to validate whether the deformation problems are solved.

The conclusion and recommendations are presented in Chapter 6.

Chapter 2

RoboCup and Tech United

In this Chapter a general introduction to RoboCup is given, as well as an introduction toTech United and their robots. This leads to the description of the assignment.

2.1 What is RoboCup?

RoboCup is an international research and education initiative. Its goal is to foster artificialintelligence and robotics research by providing a standard problem where a wide range oftechnologies can be examined and integrated [10]. For this purpose the game of soccer ischosen. The RoboCup Federation proposed the ultimate goal of the RoboCup initiative tobe stated as follows:

"By 2050, a team of fully autonomous humanoid robot soccer players shall win a soccergame, complying with the official FIFA rules, against the winner of the most resent WorldCup of Human soccer." [10]

To achieve this goal, a large variaty of leagues exist within the RoboCup Federation.There are the simulation leagues. Their focus is on the development of artificial intelli-gences and team strategy. In the 3D simulation league, the focus is also on the low levelcontrol of humanoid robotics and the creation of basic behaviors such as walking andkicking. Afterwards, these behaviors can be implemented in real humanoid robots [11].Humanoid robots compete in one of the leagues that involve hardware. There are the hu-manoid leagues, standard platform league, small size league and the middle size league.The first two leagues involve walking robots. Their focus is on the development of hu-manoid robots and the software that is required to play soccer in the way humans do. Theother two leagues involve robots with wheels. Their focus is on communication betweenrobots that autonomously have to play the game, integrating sensors like vision systemsin the robots to analyse the game, as well as trying to implement team tactics.

2.2 Tech United

Several Dutch teams compete in different leagues of the RoboCup Federation. Tech Unitedis the RoboCup team of the Eindhoven University of Technology that competes in the mid-

4 Chapter 2. RoboCup and Tech United

dle size league. The team was set up mid 2005, by the Eindhoven and Delft Universitiesof Technology. It was a carrier project for research streams on mechatronics, computervision, software architecture and engineering, and sensing and planning. It had the am-bitious goal of competing at the 2006 World Championships. This goal has been realized[1]. From 2007 the team completely consists of people of the TU/e.From that point on, development went fast. At the 2007 World Championships the teamreached fifth place. Major improvements were made both at the software and the hard-ware. In 2008 Tech United won the German Open (the unofficial European Champi-onships) and reached second place at the World Championships. In 2009 third place wasreached at the German Open and the second place at the World Championships [12].

2.3 The Turtle

The Tech United robot is called Turtle. This is an abbreviation for Tech United RobocupTeam: Limited Edition. The Turtle’s design is adapted over the years to improve its me-chanical performances. The 2009 Turtle is the fourth generation. With the help of Figure2.1 the design is discussed in Section 2.3.1.

2.3.1 How does it work

The Turtle is fitted with three omniwheels (4), each powered by a 150 W servo motor.Therefore, it can drive instantaneously in any direction without turning first. This is calledholonomic drive.Each Turtle has its own omnidirectional vision system. This consists of a full color camera,that looks in upward direction (2), and a spherical mirror (1) positioned above it. Themirror reflexes a 360 ◦ view around the Turtle into the camera. The images are processedby an onboard computer (3), on which all the software runs. If the ball is detected, thesoftware sends control signals to the servo motors such that it drives towards the ball.Each Turtle is equipped with an active ball handling mechanism (7) with which it cancontrol the movement of the ball. It is not allowed to clamp the ball [3], but it has to rollnaturally in the Turtle’s direction of motion. The rubber wheels of the mechanism are incontact with the ball and each wheel is driven by a servo motor. By actuating the wheels,the movement of the ball and its position relative to the Turtle is controlled, even whendriving backwards.It is not allowed to enclose the ball more the one third of its diameter [3]. Two smallomniwheels (5) are mounted on the base plate to prevent this (8). The omniwheels allowthe ball to roll freely, but ensure a fixed end position of the ball in front of the Turtle. Thisis of great importance when the Turtle wants to shoot at the goal. The shot is much morereproducible if the ball is positioned each time at exactly the same position in front of thekicking mechanism.

2.3. The Turtle 5

1. Spherical mirror 5. Ball endstop wheel 9. Outer vertical support2. Camera 6. Kicking lever 10. Inner vertical support3. Onboard computer 7. Active ball handling mechanism 11. Upper base frame4. Omniwheel 8. Base plate 12. Motor mount

Figure 2.1: Turtle component naming.

6 Chapter 2. RoboCup and Tech United

To shoot a ball, the electromechanical solenoid pushes against a kicking lever (6). Thislever is pin jointed at the top. At the lower side, a pin is connected on the lever. This makesthe contact between the lever and the ball. The pin penetrates the ball, causing it to deformand act like a spring. This increases the top speed of the ball. At the time the solenoidreaches the end of its stroke and is slowing down, the ball is elastically deformed aroundthe pin. The ball pushes itself away from the pin when it returns to its initial shape. Theupper pin joint can move vertically to adjust the angle of the shot. In the upper positionthe pin hits the ball somewhat halfway its height, resulting in a horizontal shot. In thelower position (like in the upper right Picture of Figure 2.1) the Turtle performs a lob shot.It can also perform any shot in between.

2.3.2 Base frame

In the lower Figure of Figure 2.1 the base frame of the current Turtle is depicted. It consistsof a five millimeter thick aluminum base plate on which the motor mounts (12) are bolted.The motors are radially clamped in the mounts. The edges of the base plate are raised toincrease its inplane stiffness. A rubber strip is glued to the edge. Together they act like abumper.An outer vertical support (9) is bolted to each motor mount. Together with the innervertical supports (10), they support the upper base frame (11). This is a complex aluminumpart, which has to be milled. The frame supports the vision system and the computer.Especially the outer vertical supports are the weak spot in the Turtle’s base frame. Toincrease their out of plane bending stiffness the edges have been flanged. At the otherhand, large pieces of material have been removed to make room for the motor and theplunjer of the solenoid. Also holes are drilled, to attach various components. Duringthe 2009 season the outer vertical supports deformed plastically several times. This wasmeanly caused by collisions with other robots. That also caused the base plate to deform.

When another robot collides with the top half of the wheel of the Turtle, a collision force

Fc

P

Figure 2.2: Cross section view of the rear wheel.

2.4. The assignment 7

will act on the wheel as depicted in Figure 4.1.

This force acts not only on the wheel, but also on the motor and its mount. Together,they can be regarded as lever that is firmly attached to the base plate and the outer verticalsupport. Due to the collision force, the lever wants to rotate around the point ’P’ in Figure4.1. This causes the base plate to bend. This force also tries to bend the outer verticalsupport out of its plane. Because the support is relatively thin compared to is lengthand width, it will bend quite easily. If this happens, the omniwheel’s axle is no longerhorizontal. Therefore, the wheel rocks as it rotates. This results in unwanted vibrations inthe Turtle, which decrease the quality of the images produced by the vision system. Theseimages are also used to determine the position of the Turtle on the field, by calculating thedistance to the lines of the field. With a rocking robot, it is not possible to do this accurateenough.

2.4 The assignment

Tech United wants to prevent this kind of damage and wants to improve the overall me-chanical properties of their robots. The assignment is to make a mechanical design fora new generation Turtle. The new design must be able to carry all the hardware that isin the current Turtle. It also has to fullfill the RoboCup Middle Size League Rules andRegulations [3] about size and mass. These are given in table 2.1.

Table 2.1: Size and mass restrictions.

Maximum length: 500 [mm]Maximum width: 500 [mm]Maximum height: 800 [mm]Maximum mass: 40 [kg]

The design should not bring any other robots or people in danger. The outside of the robotmust be as smooth as possible.The new Turtle has to withstand collisions in such a way that the wheel axles stay horizon-tal and the frame does not break.For fast acceleration and high cornering speeds, it is important that the center of gravity(C.O.G.) is as close to the field as possible. Because the C.O.G. is located at a certain dis-tance above the field, it will cause the Turtle to tilt during acceleration and cornering. Thisaffects the images produced by the vision system and causes wrongly estimated ball andown positions. It also has to be on the vertical symmetry axis of the Turtle. This results inthe smallest possible inertia, when it rotates around that vertical axis.

Chapter 3

Wheel configuration

The wheel configuration determines the Turtle’s base plate shape. Currently, three om-niwheels are mounted under 120 ◦ with respect to each other. This is not the only wheelconfiguration that can be used. In this Chapter, a comparison between different wheelconfigurations is made. First the configurations are explained and their inverse kinemat-ics are given. Next, they are compared based on top speed, acceleration and corneringspeed.

3.1 Different wheel configurations and their kinematics

Most RoboCup middle size league robots nowadays have three or four omniwheels. In thepast, there were also teams that used a three wheeled platform with two regular wheelsand a castor wheel or omniwheel for support at the back. These three main wheel config-urations are depicted in Figure 3.1.

Figure 3.1: The three main wheel configurations with from left to right: The platformwith three omniwheels, the three wheeled platform with two regular wheels and anomniwheel and the platform with four omniwheels.

10 Chapter 3. Wheel configuration

3.1.1 Platform with three omniwheels

The base plate of this type of platform is an equilateral triangle. The omniwheels are at-tached to its corners. This makes this platform holonomic, it can move in every directionwithout turning first. The inverse kinematics are required to analyse the kinematic behav-ior of the platform. They determine the angular velocity of the wheels related to the globalplatform velocity and heading. It can also be used the other way around. The angularvelocities of the wheels are the input, resulting in a velocity and heading of the platform.A kinematic diagram of the platform is required to derive the inverse kinematics. Figure3.2 shows the kinematic diagram of the platform with three omniwheels. The kinematicswere derived in [4].

.

x

.

y

.

1f

.

2f

.

3f

.

q

1v

2v

3v

lx

ly

R

q

Figure 3.2: Kinematic diagram of the platform with three omniwheels.

The starting point of this derivation is the inverse kinematic equation of a single wheel(Equation 3.1). This determines the translational velocity v of the wheel with respect to theglobal velocity [x, y.θ] of the platform. It is a combination of translation and rotation ofthe platform.

vi = − sin(θ + αi)x+ cos(θ + αi)y +Rθ (3.1)

Where θ is the angle between the global [x,y] and local [xl, yl] frame attached to the plat-form (see Figure 3.2), α is the angle of wheel i relative to the local frame. Since this framecoincides with the C.O.G. of the platform and wheel 1 is located on the local axis (x1),α1 = 0 ◦. This means that α2 = 120 ◦ and α3 = 240 ◦. Finally, R is the distance betweenthe platform’s C.O.G. and the center of a wheel.The translational velocity of the wheel can be rewritten as its angular velocity ωi usingEquation 3.2 resulting in Equation 3.3.

vi = rωi (3.2)

3.1. Different wheel configurations and their kinematics 11

Where r is the radius of the wheel.

rωi = − sin(θ + αi)x+ cos(θ + αi)y +Rθ (3.3)

This can be transformed in to a matrix representation (Equation 3.4):

~ωi = Jinv~u (3.4)

In this Equation, Jinv is the inverse Jacobian for the holonomic platform. It provides therelationship between the angular velocities of the wheels ~ωi and the global velocity vector~u. The total matrix representation is described by Equation 3.5:ω1

ω2

ω3

=1r

− sin(θ + α1) cos(θ + α1) R− sin(θ + α2) cos(θ + α2) R− sin(θ + α3) cos(θ + α3) R

xyθ

(3.5)

3.1.2 Three wheeled platform with regular wheels

This type of platform has two regular wheels, which can have a higher friction coefficientthan the omniwheels. Therefore, more traction and a theoretically higher acceleration ispossible. This makes it interesting to investigate this type of platform.The platform steers like a tank. It cannot move instantaneously in any direction. There-fore, it is called a non-holonomic platform. It turns by introducing a difference in theangular velocity of the front wheels. They are positioned in front of the C.O.G. Therefore,a third wheel is necessary to support the platform and to keep its back end of the ground.Generally, a castor wheel is used. It is also possible to replace it by an omniwheel. Thisdoes not affect the forward motion, but it can assist when making a turn. The θ rotationaxis around which there is the lowest inertia, is a line through the C.O.G.. Because thefront wheels are in front of that, they have to overcome a larger inertia when turning theplatform. The extra omniwheel assists to speed up the θ rotation.

A kinematic diagram of this platform is depicted in Figure 3.3.


.

x

.

y

.

1f

.

2f

.

3f

.

q

1v

2v

3v

lx

ly

2R

1R

Figure 3.3: Kinematic diagram of the three wheeled platform with two regular wheelsand an omniwheel.

The wheels of this platform are not positioned at an equal distance from the center ofrotation, which is positioned in the origin of the local frame. The distance between theomniwheel and the center of rotation R2 is larger than half the distance between the frontwheels R1. This results in a small change in the inverse kinematics with respect to that ofthe previous platform. The inverse kinematics are described by Equation 3.6.ω1

ω2

ω3

=1r

− sin(θ + α1) cos(θ + α1) R1

− sin(θ + α2) cos(θ + α2) R1

− sin(θ + α3) cos(θ + α3) R2

xyθ

(3.6)

In this situation, α1 again is at the local axis, therefore α1 = 0 ◦. This means that α2 =180 ◦ and α3 = 270 ◦.

3.1.3 Platform with four omniwheels

The last type of platform is the one with four omniwheels. The wheels are positioned atthe corners of a square (see Figure 3.1), their axes along the diagonals. In the two previousconcepts the base plate was triangular shaped. Both the square and the triangle have tofit in the 500 mm x 500 mm square described in Section 2.4. This means that the baseplate of the platform with four omniwheels can be larger than the base plates of the otherconcepts. It is also a holonomic platform. For this reason, it is interesting to investigatethis wheel configuration.

The kinematic diagram is depicted in Figure 3.4. All wheels are positioned at an equaldistance R from the center of the platform. This is also its center of rotation.

3.2. Rotation of the wheels 13

.

x

.

y

.

1f

.

2f

.

3f

.

q

1v

2v

3v

4v

.

4f

lx

ly

R

q

Figure 3.4: Kinematic diagram of the platform with four omniwheels.

The additional wheel introduces an extra Equation that describes the inverse kinematics ofone wheel (Equation 3.1) in the matrix representation of the platform’s inverse kinematics.This representation is given by Equation 3.7.

ω1

ω2

ω3

=1r

− sin(θ + α1) cos(θ + α1) R− sin(θ + α2) cos(θ + α2) R− sin(θ + α3) cos(θ + α3) R− sin(θ + α4) cos(θ + α4) R

xyθ

(3.7)

As in the previous inverse kinematic relations, α1 is at the local axis. As a result, α1 = 0 ◦.This implies that α2 = 90 ◦, α3 = 180 ◦ and α4 = 270 ◦.

3.2 Rotation of the wheels

With the inverse kinematics it is possible to compare the rotation of the wheels of thedifferent platforms when they perform a global translation. This will provide some insightin the behavior of the different concepts. To that purpose, the platforms have completeda simulated trajectory in y direction (specified in the kinematic diagrams) with a constantvelocity. The angular velocities of the wheels of the different platforms are plotted. Thetrajectory and the plots are depicted in Figure 3.5.


Figure 3.5: A straight line, constant speed trajectory and the resulting angular wheelvelocities of the different platforms.

The plots show that the angular velocity of the third wheel of both the three wheeledplatforms is zero. This was expected. These wheels are positioned perpendicular to thedirection of motion and thereby, do not contribute to the propulsion of the platform in thisparticular direction. The left and right wheels of the platform with four omniwheels haveequal but opposite angular velocities. This was also expected, because of the definition ofthe positive direction of the wheel’s translational velocity in Figure 3.4.The plots also show a difference in angular velocity of the wheels of the different platforms.The wheels of the three wheeled platform with two regular wheels rotate the fastest, fol-lowed by the wheels of the platform with three omniwheels. The wheels of the platformwith four omniwheels rotate the slowest. This is against the expectations. The regularwheels are positioned in line with the direction of motion and it was expected that thiswould be the most effective way of propelling a vehicle in the forward direction. However,it seems that wheels positioned under an angle relative to the direction of motion, aremore effective.This phenomenon was described by Ashmore and Barnes [5]. They describe that a plat-form with omniwheels positioned under an angle relative to the direction of motion reachesa higher top speed compared to a platform with wheels in line with the direction of mo-tion, assuming equal angular velocities of the wheels.

3.3. Acceleration 15

Like regular wheels, omniwheels transmit a torque in one direction. However, an omni-wheel can move freely in the direction perpendicular to the torque vector. It then rolls overthe small wheels on its perimeter. Regular wheels cannot do that because of the non-slipcondition.An omniwheel will perform a translation in both its actuated direction and in the direc-tion perpendicular to this, when it is positioned under an angle relative to the direction ofmotion. This can be seen in Figure 3.6.

transv

rotv

rollv θ

Figure 3.6: Translational velocity of an omniwheel under an angle θ relative to thedirection of motion.

The translational velocity vtrans is a combination of the translational velocity in the regularrotational direction vrot and the sideways rolling velocity vroll. As a result, vtrans is largerthan vrot and increases when θ increases according to Equation 3.8.

vtrans =vrotcos θ

(3.8)

Ashmore and Barnes [5] state that a platform with four omniwheels (like the one describedbefore) benefits the most from this increase in forward speed. In that case, θ varies be-tween 0 ◦ and 45 ◦. If the platform moves in line with two omniwheels and perpendicularto the other two, θ = 0 ◦ and it will reach the same velocity as the platform with two regularwheels. If it moves along the line of motion (both forwards and backwards) specified inFigure 3.5, or perpendicular to it, θ = 45 ◦. This is a direct result of the symmetrical baseplate.A same distribution of θ around the platform exists for the platform with three omni-wheels. However, in this situation θ varies between 0 ◦ and 30 ◦. If one wheel is in linewith the direction of motion, θ = 0 ◦ and if one wheel is perpendicular to the directionof motion, θ = 30 ◦. The wheel with the smallest angle θ determines the translationalvelocity of the platform. For this reason it is of no use to add a fifth wheel. Locally thisresults in a θ larger than 45 ◦, but at the same time there is also a θ that is smaller than45 ◦, which limit the velocity.

3.3 Acceleration

There is a downside to this obtained extra speed. The angle of the wheel with respect tothe direction of motion can be regarded as an extra reduction that is added to the drive


train of the wheel. It has a gear ratio equal to or larger than one depending of θ (Equation3.9).

vtransvroll

=1

cos(θ)(3.9)

The total reduction itot from the angular motor velocity ωm to vtrans changes when θchanges. The total reduction is given by Equation 3.10.

itot = vtransωm

= vtransvroll

· vrollωm

= vtransvroll

· vrollωw· ωwωm

= 1cos(θ) · r · igh

= ighrcos(θ)

(3.10)

Where igh is the gear ratio of the gear head and r is the radius of the wheel. ωw Is theangular velocitie of the wheel. The total reduction of the drive train increases when θ isincreased.Each motor has to accelerate a load m, which is a part of the Turtle’s total mass. It de-pends on the number of wheels that contribute to the propulsion. For example, if twowheels propel the Turtle, each motor has to accelerate a load equal to half the mass of theTurtle. The motor’s angular acceleration αm depends on the inertia of the rotor Jr and thereduced inertia of the load on the motor axle JL it has to accelerate according to Equation3.11.

αm =Tm

Jr + JL(3.11)

The angular acceleration also depends on the torque Tm produces by the motor. JL de-pends on the load m and the total reduction of the drive train. It is described by Equation3.12.

JL = mi2tot (3.12)

aw =αmitot

(3.13)

From Equations 3.11 and 3.12 it is concluded that an increase of itot results in an increaseof JL. Correspondingly, αm and the translational acceleration of the wheel aw in thedirection of motion decrease according to Equation 3.13. This means, though the platformswith omniwheels can reach higher end velocities, the platform with the regular wheelstheoretically can accelerate faster.

3.3.1 Slippage of the wheels

The angle of the wheel is not the only factor that influences the acceleration of the plat-forms. The motor torque applied to the wheels is limited by the amount of torque the


wheels can transfer to the field without slipping. The torque Tw applied produces a tan-gential force Ftw at the outer perimeter of the wheel at the point where it is in contact withthe field (Equation 3.14).

Ftw = Twr (3.14)

Tw =Tmigh

(3.15)

Ffr = FNµ (3.16)

If this force exceeds the friction force (Ffr in Equation 3.16) in the contact, the wheel willslip. The magnitude of the friction force depends on the normal force FN and the slidingfriction coefficient µkin between the wheel and the field.The small rollers of the omniwheels are made of rubber. To get an indication of slidingfriction coefficient between omniwheel and the field, which is made of carpet, a simple ex-periment was performed (see Appendix B.2). This resulted in a µkin of 0.8. It is assumedthat the regular wheels have a rubber outer surface which is rougher. The sliding frictioncoefficient of these wheels in contact with the field is estimated at 1.0 [8].

3.3.2 Normal force acting on the wheels

The normal force acting on a wheel depends on the number of wheels, the mass of theplatform and the height of the C.O.G. when maneuvering. The masses of the differentplatforms are estimated referring to the mass of the current Turtle, some of its compo-nents and the number of wheels.Currently, the mass of the Turtle is approximately 35 kg. The three wheeled platform withtwo regular wheels and the platform with three omniwheels have an equal number ofwheels as the current Turtle. Therefore, their mass is estimated at 35 kg. The platformwith four omniwheels has an extra wheel, drive train and amplifier. This results in anadditional mass of approximately 1.6 kg. During forward motion, the platform with thefour omniwheels uses twice the number of motors when driving in forward direction,compared to the other platforms. This results in an estimated double power use. To com-pensate for this, the number of batteries is doubled. This introduces an extra mass of3 kg. Finally, its base plate larger. All together this platform has an additional mass ofapproximately 5 kg, giving it a total estimated mass of 40 kg.

In steady state, the platform’s mass is equally distributed over the wheels. This is not thecase during acceleration. The height of the C.O.G. above the field causes the platform totilt. This is explained with the help of Figure 3.7 and Equation 3.17.

∆FN =h

lmg (3.17)

Equation 3.17 is the final result of an equilibrium of moments around one of the contactpoints with the field of the schematic platform in Figure 3.7. When the platform accel-erates in forward direction, a force acts in opposite direction on the C.O.G.. Because ofthe equilibrium of moments, FN,front reduces with ∆FN , while FN,rear increases with anequal amount. This difference is indicated in Figure 3.17 as 2∆FN . In this situation thefront wheels can transmit less force from the motor to the field. The torque of the motor is


FN,rear FN,front

ma

2 FΔ N

h

a

mg

l

Ffr,rearFfr,front

Figure 3.7: Height h of the C.O.G. of the platform above the field, the wheel base l ofthe platform and all forces that are applied to it during acceleration.

reduced to prevent slipping. This also affects the maximum acceleration possible, whichdecreases as well.The height h of the C.O.G. of the current Turtle is determined, to get a reasonable indica-tion which value should be used in the simulations. This was done with an experiment,which is described in Appendix B.1. The height is estimated at 150 mm above the field.The wheel base l of the platforms are given in table 3.1.

Table 3.1: Wheel base of the different platforms.

Platform Wheel base [mm]Platform with three omniwheels 360Three wheel platform with two regular wheels 400Platform with four omniwheels 400

The wheel base of the platform with three omniwheels is shorter because of the dimen-sions of the largest equilateral triangle that fits in the 500 mm x 500 mm plane. The frontwheels of the three wheeled platform with two regular wheels are positioned further to thefront than those of the platform with three omniwheels, because they are not attached toan equilateral triangle.

3.3.3 Simulation of the acceleration

The motor torque is the input of the acceleration simulations. Currently, the Turtle’s useMaxon RE40 150 W DC servo motors (see appendix A.1 for the specifications). These haveto be simulated as well, because their maximum torque depends on the current applied tothe motor and its angular velocity. The faster a motor rotates, the less torque it can deliver.


This relation is described by Equation 3.18 [6].

ω = n02π60−

∆n2π60

∆TmTm

1000(3.18)

Where ω is the current angular velocity of the motor, n0 is the no load speed of the motorin rpm and ∆n

∆Tmis the torque gradient in rpm/mNm. The motor torque Tm (in Equation

3.18 in mNm) was determined with Equations 3.14, 3.15 and 3.16 by equating Ftw to Ffr.If the input torque is known, the angular acceleration of the motor (Equation 3.11) and thetime it takes for the motor the reach the maximum angular velocity it can achieve with thecurrent torque (Equation 3.19) can be determined [6].

∆t = ωmJr + JLTm

(3.19)

From this point on, the acceleration decreases linearly until its reaches zero at the timethe motor reaches its nominal speed. This is regarded as the maximum angular velocitythe motors can achieve in the simulations. With the known reduction of the drive train,this can be converted to a theoretical top speed of the platforms. The deceleration is linear,because the motor torque decreases linearly (Equations 3.11 and 3.18).With Equation 3.19 it is calculated how much time it takes to reach the nominal speed.During each interval i of length ∆t the acceleration of the motor is constant. This ac-celeration is converted to the platform’s acceleration awi in that interval via Equation 3.13.Therefore it is possible to calculate the distance traveled by the platform during an interval(see Equation 3.20).

si = 0.5awi∆t2i + vi−1∆t1 + si−1

vi = awi∆ti + vi−1

(3.20)

si And vi are calculated in an interval and function as si−1 and vi−1 in the next interval.If i has reached the number of intervals, si gives the total traveled distance during ac-celeration. This method makes it possible to simulate a drag race between the differentplatforms. The result of this simulation is depicted in Figure 3.8.

The Figure shows that the three wheeled platform with two regular wheels accelerates thefastest, as was expected. It is the first one to reach its theoretical top speed of 3.0m/s. TheFigure also shows the higher top speeds of the other two platforms. The platform withfour omniwheels is the first to catch up with the three wheeled platform. This happensafter roughly 1.1 second. Both platforms have traveled 2.5 meter at that time. After roughly1.7 second and a distance of 4 meter, the platform with three omniwheels catches up withthe platform with the regular wheels. The platform with four omniwheels has a theoreticaltop speed of 4.3 m/s and the platform with three omniwheels has a theoretical top speedof 3.5 m/s.Finally, the platform with four omniwheels accelerates faster than the platform with threeomniwheels. This is caused by the number of driven wheels. The four motors of theplatform with four omniwheels each have to accelerate less load compared to the twomotors driving the platform with three omniwheels.The catch up distances must be compared to the dimensions of the field to get an ideawhether the acceleration differences are relevant. The official RoboCup middle size league


Figure 3.8: Distance traveled in time during forward acceleration by each of the plat-forms.

field measures 18 m x 12 m [3]. Robots mostly cover distances larger than 2.5 meters eachtime they head for a ball or try to score. Therefore, the platform with two regular wheelsdoes not have that much of an advantage compared to the platform with four omniwheels.The advantage is more relevant compared to the platform with three omniwheels.Usually, small distances are covered during defending. Robots move sideways over smalldistances to stay in line between the attacker and the own goal. As Figure 3.8 shows, thereis not much difference between the platforms’ performances when the traveled distanceis less than one meter. The platforms also need to be vary maneuverable during defensiveactions. The holonomic platforms satisfy this requirement, because they can instantlymove in an other direction without turning first.

In the previous simulation, all platforms used the same motor. Therefore, they could notuse the same amount of power during the forward acceleration. The platform with thefour omniwheels has double the power compared the other two platforms. In the nextsimulation, this is compensated for by selecting different motors. The platform with reg-ular wheels and the platform with three omniwheels have Maxon EC45 250 Watt motors[6] installed and the other platform is powered by Maxon EC40 120 Watt motors [6]. Thesimulation results are depicted in Figure 3.9.

Again, the platform with two regular wheels accelerates the fastest and the other two plat-forms still catch up with it. However, it takes more time and the they have traveled greaterdistances. Especially the platform with three omniwheels catches up with the other plat-form relatively late. It has to travel almost one third of the length of the field.

3.4. Cornering speed 21

Figure 3.9: Distance traveled in time during forward acceleration by each of the plat-forms. All platforms use almost the same amount of power.

3.4 Cornering speed

Finally, it is investigated how fast the platforms can follow a random curve with constantradius without lifting a wheel off the ground or slipping out of the corner. These phe-nomenons are caused by the centrifugal force, which is calculated with Equation 3.21.

Fcen =mv2

rcur(3.21)

Where v is the forward velocity of the platform and rcur is the radius of the curve that theplatform follows. The centrifugal force acts on the C.O.G. similar to the acceleration forcein Section 3.3.2. It decreases the normal force acting on the inner wheel(s), until it reacheszero and the wheel(s) lose(s) contact with the field. Figure 3.10 shows the line over whichthe platforms roll when they lift a wheel off the field.

Both three wheeled platforms have a roll line that is not perpendicular to the centrifugalforce. F ′cen (see Equation 3.22) is a component of Fcen and acts on the C.O.G. perpendic-ular to the roll line.

F ′cen = Fcen cos(β) (3.22)

In the simulation, the platforms follow a curve with a constant radius, while maintaininga constant velocity. Figure 3.11 shows at which velocity and curve radius the inner wheelslose contact with the field. The platform with the four omniwheels loses contact first,


cenF

'

cenF

cenF

cenF

'

cenF

bb

Figure 3.10: Centrifugal force acting on the platforms and the line over which they willroll when they lift the inner wheel(s) off the field.

followed by the platform with three omniwheels and the platform with regular wheelsrespectably. It has to be investigated whether the wheels can cope with the required lateralforce to lift a wheel off the field, or that it starts to slip sideways before the inner wheel islifted.The regular wheels slip sideways if the centrifugal force is larger than the friction forceproduced by the tires in lateral direction. This is calculated with Equation 3.16.The lateral force an omniwheel can support depends on the angle of the wheel relative tothe direction of motion. This is explained with the help of figure 3.12.

Figure 3.11: The radius of the corner and the velocity of the platform at which a wheelloses contact with the field. Left to right: platform with regular wheels, platform withthree omniwheels and platform with four omniwheels.

3.4. Cornering speed 23

θ

θ

Froll

Fslip

Fcen

Direction of motion

Figure 3.12: The relation between the lateral friction force produced by an omniwheeland the angle of this wheel with respect to the direction of motion.

Figure 3.13: The radius of the corner and the velocity of the platform at which theplatform starts to slip sideways. Left to right: platform with regular wheels, platformwith four omniwheels and platform with three omniwheels.


If Fcen and Fslip are parallel, Equation 3.16 determines the force required to slip the wheelsideways. If Fcen and Fslip are not parallel (as depicted in Figure 3.12), the maximumcentrifugal force the wheel can handle decrease with a factor sin(θ). From θ and thenormal load of all wheels, the total lateral force the wheels can produce is calculated.Due to the shift in load distribution, the inner wheels can handle less lateral force. Thisis compensated by the outer wheels which can handle more. The robot starts slippingsideways if the centrifugal force is larger than the total lateral force the wheels can handle.Figure 3.13 shows at which forward velocity and at which curvature the robots start to slipsideways.

Figure 3.12 and Figure 3.13 show that all the platforms start to slip before a wheel loses con-tact with the field. They also show that the platform with the regular wheels can performthe tightest corners with the highest velocities, followed by the platform with the four om-niwheels. There is not much difference between the platforms with omniwheels. Thoughthe lateral forces (see Figure 3.13) of these platforms differ quite a lot, the platforms startto slip at almost the same velocity and curvature. The extra mass of the platform with fouromniwheels causes extra centrifugal force. The extra wheel produces extra friction forceto allow faster and tighter curves. This result in a cornering behavior like the platformwith three omniwheels.

3.5 Concluding remarks

All the simulations give some insight in the behavior of the platforms in different situ-ations. However, it is not possible to point out the best wheel configuration. There aretoo many variables left. The platform’s performances are heavily depending on the soft-ware it runs on. Also, team tactics play an important role in the decision. In the TechUnited tactics, maneuverability is important. Tech United is implementing dynamic pass-ing. Therefore, the platform has to be able to make small position adjustments in alldirections to position itself well to receive the pass and control the ball. This requirementcannot be fulfilled by the platform with two regular wheels. This leaves the platformswith three and four omniwheels. Besides forward motion, sideways motion is used a lot.The platform with four omniwheels reaches higher end velocities in both directions andcan make faster and tighter turns. Therefore it is decided to design a platform with fouromniwheels.

Chapter 4

The bottom half of the new design

The goal of the new design is a stiffer main frame of the Turtle. Thereby reducing thedeformation problems of the current frame. In the new design, the base plate no longeris the main component of the frame. The new frame looks like the Eiffel Tower. It hasa central box with four legs attached to it. These house the motors and the base plate isconnected to them. The bottom half of the design is described is this Chapter. The kickingmechanism is described here as well.

4.1 Central box

The central box is the base part of the new frame. All other frame component are attachedto it. The legs are attached under an angle of 90 ◦ with respect to each other. Logic basicshapes of the central box therefore are a square or an octagon. Both configurations areshown in Figure 4.1.

Figure 4.1: Top view of the possible basic shapes of the central box with schematic legsand base plate attached to them. A square (left) and an octagon (right).

26 Chapter 4. The bottom half of the new design

Schematic legs are attached to both configurations. This provides an indication of theamount of space left between the legs. The larger this space, the more components can beplaced on the base plate between the legs. This decreases the height of the C.O.G.. Theoctagon configuration requires the least amount of space. It also has a relatively large openspace in the middle in which a component can be placed. For these reasons, an octagonalshape is used as the basic shape of the central box.

It is important to keep the axes of the wheels in the same horizontal plane, even after acollision. This requires a stiff central box and stiff legs. If a wheel currently is hit in acollision, the base plate and the outer vertical support have to absorb the impact force.Sometimes, these components deform plastically, because they cannot handle the impactforce, as was explained in Section 2.3.2. They do not distribute the impact force over thewhole frame. Increasing the stiffness of a single leg prevents the plastic deformation andit transmits the impact force to the central box. A stiff box transmits the force to the otherlegs. Therefore, the whole frame contributes to the absorbtion of an impact. The legs arediscussed in Section 4.2.

The central box needs to be both stiff and light. This is achieved with the closed box princi-ple. This is a box with all the material in the walls. A closed box of constant wall thicknessis the stiffest and lightest design with that quantity of material within that volume [7].

3

5

2

1

4

6

1. Inner tube 3. Bottom sheet 5. Slot and merlon2. Radial sheet 4. Merlon 6. Flanges to attach the leg

Figure 4.2: The inner tube, radial sheets and the bottom plate of the central box.

The box is built up from sheet metal components, which are welded and pop rivetedtogether. The components are loaded in their plane. This addressed the shear stiffness

4.1. Central box 27

Figure 4.3: Top view of the central box. The radial sheets point towards the center ofthe box.

and the in plane bending stiffness of the sheet, which are much larger than its out of planebending stiffness.

The basic shape of the central box is a 3D octagon with a hole in the center. The ribs ofthe octagon plane have a length of 70 mm and the 3D object is 100 mm high. Figure 4.2shows some of the its components.The center of the box is a tube (1) with an inner diameter of 100 mm. Radial sheets (2) areattached to the tube. The legs are attached to these sheets via flanges (6). Figure 4.3 is atop view of Figure 4.2. It shows the orientation of the radial sheets. They point towardsthe center of the tube. The sheets transfer the radial forces applied to the legs to the centerof the box. This prevents unwanted torsion of the box.Three edges of the radial sheets contains merlons (4). These are inserted into slots (5) andthe remaining space in the slot is filled with a weld. This connects the sheets.

The connection between the tube and the radial sheets fixes the radial and axial degree offreedom of the sheet. It can now be regarded as a cantilever. One end is fixed and the restof the sheet can still bend out of its plane. A bottom (3) and a top sheet (8) (see Figure 4.4)are added to prevent this. Also merlons are used to connect the radial sheets to the topand bottom sheet.

Finally, vertical sheets are added between the outside edges of the top and bottom sheet.This creates the closed box. Figure 4.4 shows such a sheet (7). The edges of the sheetare folded to form flanges. The top and bottom flanges are pop riveted (9) to the top andbottom sheet of the box. These two sheets are now firmly connected and cannot rotatewith respect to each other. The left and right flange have screw clearance holes. These arealigned with the holes in the flanges of the radial sheets. Four of these sheets are posi-


7

7

9

8

7. Vertical sheet 8. Top sheet 9. Pop rivet

Figure 4.4: The vertical sheet (left) and the total central box (right).

tioned under 90 ◦ with respect to each other. This leaves four open planes at the outsideof the box. These are covered by the legs, which are bolted to the box.

All components of the box are made of 6061-T6 aluminum. The sheets have a thicknessof one millimeter. The components can be cut out from a sheet of aluminum with a lasercutter, after which the flanges can be bent.

4.2 Legs

The legs need to be stiff and light as well. Therefore, they are closed boxes too. The widthof the legs is determined by the length of the ribs of the octagon plane. The height of theleg at the point where it is connected to the central box is determined by the height of thisbox.Figure 4.5 shows a cross section view of the box (1) with a schematic leg attached to it.The centerlines of the front (2) and rear (3) plate of the leg point towards the contact pointbetween the wheel (4) and the field. The omniwheel has two rows of rollers around itsperimeter, spaced at an equal distance from the vertical midplane of the wheel. The rowsof rollers alternatively make contact with the field. Therefore, the average contact point isat the vertical midplane.

4.2. Legs 29

1

2

3

4

1. Box 3. Rear plate2. Front plate 4. Omniwheel

Figure 4.5: Cross section view of the box and a schematic leg. The centerlines of thefront and rear plate point towards the contact point of the omniwheel with the field.

Because of the virtual intersection of the front and rear plate at the contact point, the forceintroduced to the system only introduces tensile and compressive forces in the plates. Ifthe virtual intersection point and the contact point do not coincide, also a bending momentis introduced in the plates.

4.2.1 Motor clamp

The motor is located in the leg. Figure 4.6 shows the components that are used to installit in the leg. A gear head (1) and an encoder (3) are connected to the motor (2). Thisassembly is inserted in the motor support (4). It must be possible to remove the motorassembly from the completed robot, if this should be necessary. Therefore, it is axiallyinserted in the motor support. The encoder is inserted first, therefore the outline of the


1

2

3

4

5

1. Gear head 3. Encoder 5. Motor clamp2. Motor 4. Motor support

Figure 4.6: The motor and the components to install it in the leg.

encoder can be seen in the motor support. The support is a milled 6061 aluminum part.

Finally, the motor clamp (5) is positioned over the motor assembly. Two M5 bolts tightenthe clamp to the motor support. The motor assembly is clamped radially (see Figure 4.7).It also can be seen that the assembly is clamped at the gear head. There are several reasonsfor this.The gear head has four threaded holes in the front flange. These are designed to connectthe motor assembly to its surroundings. If these are used, the axial movement is blockedand the motor assembly cannot be removed axially. If it is radially clamped, it can beaxially .The assembly is clamped around the gear head, because its axle can cope with a largerradial force than the axle of the motor. The assembly is mainly loaded in radial direction.The gear head can support 150 N radially and the motor 28 N . (See Appendix A.1).Figure 4.7 shows that the gear head is not clamped over its total length. The part that is notclamped is surrounded by the wheel hub. The axial and rotational degree of freedom ofthe motor assembly is fixed by friction between the assembly, the support and the clamp.This Figure also shows that the support is wider than the clamp region. It is mountedto a larger area of the base plate, compared to the current Turtle (see Section 2.3). Thesupport can be regarded as a local reinforcement of the base plate, because it locally addsmaterial to it. This increases the base plates’s bending stiffness. Because the new support

4.2. Legs 31

Figure 4.7: A top view and a cross section view of the motor assembly clamped in thesupport.

increases the thickness of the plate over a larger area, it will bend less, compared to thecurrent design.


4.2.2 The closed box

The motor support has to be attached firmly to the central box via the closed box principle.The support can be used as one of the planes of the closed box. Two concepts for makingthe other planes are discussed in this Section. The first concept is depicted in Figure 4.8.

The leg is built up from a milled frame (2) which forms the front and rear plate of theclosed box. The frame is reinforced with two internal plates. They connect the front andrear plate and prevent twisting of the box. Side plates (1) are added to close the box. Theyare glued to the frame. The motor support, front, rear and internal plates are milled from asingle piece of material. This reduces the number of connections between different parts.There is also a downside to this. A large block of material is required to make a leg. A lotof material is lost during the milling process, which makes this an expensive concept.

In the second concept the frame of the leg is made out of sheet metal, equal to the centralbox. It is depicted in Figure 4.9. The motor support is the only part that has to be milled.Therefore, the material losses are reduced. A front (2) and a rear (3) plate are connectedto the motor support. There is also an internal plate (5) between them. Together with therear end plate (4) it prevents twisting of the leg. Side plates (1) are added to close the boxand to connect the motor support firmly to the rest of the leg.The different components are easy to manufacture, because they are all flat pieces of sheetmetal. However, it requires a lot of connections to put all the components together. If thisis not done properly, it will influence the stiffness of the leg negatively.

1

2

1

2

1. Side plate 2. Milled frame

Figure 4.8: 3D view (left) and a cross section view (right) of the leg with a milledframe.

4.2. Legs 33

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1. Side plate 3. Rear plate 5. Internal plate2. Front plate 4. Rear end plate

Figure 4.9: 3D view (left) and cross section view (right) of the leg that is built up fromsheet metal components.

To reduces the number of connections, folded sheet metal components can be used. Thefront and the side plates can be folded from a single piece of sheet metal, which createsan U profile. This can be seen in Figure 4.10. The U profile (1) has flanges at the upperand lower edge of the front plate. The lower flange connects the front plate to the motorsupport. The upper flange (2) is used for the connection of the upper half of the frame(see Chapter 5). The rear end plate (3) is inserted between the side plates of the U profile.This plate forms the vertical back plate and the horizontal top plate of the leg. Flangeswith holes (4) are added to the vertical plate. These align with the large holes in the sideplates. Rivnuts are inserted in these holes and connect the rear end plate to the side plates.The rivnuts provide the threaded holes required to bolt the leg to the central box. They arecountersank in the side plates to create a flat outer surface.The flange at the end of the horizonal top plate (6) is also used for the connection of theupper half of the frame. In the cross section view of Figure 4.10 it can be seen that aplate can be inserted between the U profile’s upper flange (2) and the top plate flange.The holes in both flanges align. Rivnuts are inserted in the holes of the top plate flange.They provide the necessary threaded holes to bolt the inserted plate to the leg. This platepresses on top of the leg. To prevent the top plate from bending, two horizontal flanges(5) are added. These are pop riveted (10) to the side plates. The top of the leg is closed bythe connection plate (7). This is pop riveted to the front plate of the U profile and to thetop plate. A rear plate (8) closes the box. The connection to the U profile is similar to theconnections used in the central box.


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1. U profile of front and side plates 5. Horizontal flange 8. Rear plate2. U profile’s upper flange 6. Top plate flange 9. Internal plate3. Rear end plate 7. Connection plate 10. Pop rivets4. Vertical flange

Figure 4.10: Exploded view (left) and cross section view (right) of the leg design.

4.3. Base plate 35

An internal plate (9) is added to provide extra torsional stiffness to the box. Finally, themotor support is glued between the side plates of the U profile.The sheet metal components of the leg are made of two millimeter 6061-T6 aluminumsheets. They can be cut with a laser cutter.

4.3 Base plate

The basic shape of the base plate is a 500 mm x 500 mm square. The outer edge of thesquare is formed by a 7 mm wide and 25 mm high raised edge (1) to which a 10 mm widerubber bumper (2) is glued (see Figure 4.11). This edge also provides stiffness to the plate(5).Four pockets (4) are removed from the square. The wheels are inserted in them. To protectthe wheel, a wheel protection (3) is added. It is a bar with a rubber strip glued to it and itis bolted to the raised edges. These edges are also located at the perimeter of the pockets,but an opening is left. The motor support is positioned here and fills the gap. The outerraised edges and those around the pockets are also connected to each other via an extradiagonal edge (7) to increase the bending stiffness of the base plate at the outside. Theedges also support the outer raised edges when they are hit sideways during a collision.The plate has a thickness of two millimeter.At the top of Figure 4.11, material is removed (6) from the square so that the ball can beenclosed. It is allowed to enclose one third of the diameter of the ball [3]. The space is alsorequired for the kicking mechanism.

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1

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2

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1. Raised edge 4. Wheel position 6. Ball location2. Rubber bumper 5. 2 mm plate 7. Diagonal strengthening edges3. Wheel protection

Figure 4.11: Basic outline of the base plate.


4.3.1 Connection of the base plate to the main frame

The base plate is connected to the frame via the legs. At the location where the motorsupports are in contact with the base plate, some material is added (1) (see Figure 4.12)and two screw clearance holes are made in it (2). M4 bolts are inserted from below. Theadded material makes it possible to sink the bolt heads in the base plate, creating a flatbottom side.

The base plate is also connected to the central box via two vertical plates (4). These platesare part of the kicking mechanism, which is discussed in Section 4.4. They are positionedon the raised strips of material in the center of the base plate (3). The extra material makesit possible to make threaded holes.

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2

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1. Extra material under motor support 4. Vertical plate2. Screw clearance hole 5. Lower flanges3. Raised strips under the vertical plates 6. Upper flanges

Figure 4.12: The mounting points of the base plate that are used to connect it to therest of the frame.

4.3. Base plate 37

The vertical plates have lower (5) and upper (6) flanges. Through the holes in the lowerflanges M4 bolts are inserted with which the plates are bolted to the base plate. The upperflanges are used to bolt the plates to the central box. The vertical plates are 3 mm thickaluminum sheets. The base plate is now supported both at its edges and in the center.This allows a thin base plate, that does not sag.

4.3.2 Ball end stop

In Figure 4.12 it can be seen that the strips of raised material (3) do not stop at the end ofthe vertical plates. Also the areas next to the ball opening are raised. There is no diagonalstrengthening edge ( (7) in Figure 4.11) in these corners, because components that have tobe installed here do not allow them. To stiffen the base plate here as well, it is thickened.

The ball end stops are two of the components located here. These prevent the Turtle fromenclosing the ball too much. A ball end stop consists of a small omniwheel which ispositioned in a holder. This holder contains the ball bearings, in which the axle of theomniwheel rotates. The design has not changed compared to the currently used ball endstop. Figure 4.13 shows them attached to the base plate. The holders are bolted to the baseplate with four M3 bolts which are inserted from the bottom side of the base plate. Theholes are counterbored to prevent the bolt heads from sticking out.

Figure 4.13: The ball end stops attached to the base plate. The ball is positionedagainst the ball end stops.


4.4 Kicking mechanism

The kicking mechanism is depicted in Figure 4.14. All components are attached to thevertical plates. They are discussed in the following sections.

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1. Electromechanical solenoid 4. Kicking lever 7. Rubber blocks2. Upper link 5. Rocker 8. Axle supports3. Upper link rotation axle 6. Plunger

Figure 4.14: 3D overview of the kicking mechanism (top) and a side view of the com-ponents between the vertical plates (bottom).

4.4. Kicking mechanism 39

4.4.1 The kicking lever

The kicking lever (4) (see Figure 4.14) is the part that kicks the ball. Like the currentdesign, it has a pin at the lower end which makes the contact with the ball. The pin isscrewed in the lever. At the upper side it is attached to a pivot point, which is part of theupper link (2). The upper link can rotate around the upper link rotation axle (3). Whenit rotates, the pivot point of the lever performs a rotation around this axle as well. Thischanges the point where the pin hits the ball. By varying the angle of the upper link,the Turtle can make a flat or a lob shot, or any shot in between. The upper and lowerposition of the pin in its initial position are shown in Figure 4.15. The current actuationof the upper link has to be adjusted to overcome the 2009 season’s problems. This is notdone yet. Figure 4.15 also shows that the pin is not in contact with the ball in its initialposition. Therefore, the lever can pick up speed before it hits the ball. This is a moreeffective manner of kicking the ball compared to a pin that is already in contact with theball. In that case, the lever pushes against the ball and cannot accelerate as fast as in thenon-contact situation.

The upper link rotation axle is supported by rubber blocks (7), which are mounted in theaxle supports (8). These are milled aluminum parts that are bolted to the ends of thevertical plates. The rubber blocks damp the reaction forces of the axle on the axle supportswhen the ball is kicked. They also minimize damage when the lever is hit sideways.

2

3

Figure 4.15: An overview of the initial positions of the lever for a lob (dashed) and flatshot (left) and a front and back view of the lever (right).


During a shot, the lever sticks outside the perimeter of the Turtle for a short period oftime. If another robot hits it sideways at that moment, the lever and everything attachedto it will twist. The rubber blocks deform due to the reaction forces of the axle and preventthe vertical plates from twisting. The lever is also shown in the right Figure of Figure4.15. It has a tapered shape. This increases its axial torsional stiffness. If the pin hits theball not exactly in its midplane, the left or right side of the pin makes contact first. Thisintroduces a sideways force on the pin, which results in a torque applied to the lever. Thiscould twist the lever, reducing the quality of the shot. Energy of the solenoid is lost duringthe deformation and this reduces the final velocity of the ball.The lever is partially hollow, creating a slot in the back of it. The connection between thesolenoid and the lever cannot be fixed, because the lever has to translate to adjust the angleof the shot. But it also must prevent the lever from swinging further when the solenoidreaches the end of its stroke. This connection is explained in Section 4.4.2.

4.4.2 Solenoid and rocker

The kicking mechanism is powered by an electromechanical solenoid (1) (see Figure 4.14).This solenoid is attached as low as possible to the frame, because it is a relative heavy part.It has a mass of six kilograms. It consists of a coil and a plunger (6). The plunger isbuilt up from a soft-magnetic and non-magnetic part [2]. When a current flows throughthe coil, the soft-magnetic part is pulled into the coil. This works in only one direction,therefore the plunger has to be returned to its initial position by an external force. Forthat reason, the mechanism is positioned under an angle of 5 ◦ with respect to the field(see lower Figure of Figure 4.14). Gravity pulls the plunger back to its initial position. Thesolenoid is powered by a capacitor. This is positioned in the hole in the central box on topof the vertical plates (see Section 4.4.6).Currently, the solenoid is positioned higher inside the Turtle. This allows a direct connec-tion between the plunger and the lever. In the new design this is not possible anymore.If the lever is in the position to perform a flat shot, the plunger is at equal height as thelower side of the lever (see Figure 4.15). The plunger travels in a straight line and the leverrotates. At a certain point the plunger is beneath the lever. If there was a direct connectionbetween the two, the mechanism would block during a flat shot. This problem cannot besolved by increasing the length of the lever. In case of a lob shot, the lever then would hitthe field in its initial position.A direct connection in the new design would be located at a larger distance from the rota-tion point, compared to the current design. This reduces the velocity and the stroke of thepin. The goal is to match or improve the properties of the current kicking mechanism.Therefore, the pin must at least reach the same velocity as it currently does.

A rocker (5) (see Figure 4.14) connects the solenoid and the lever. It is depicted in moredetail in Figure 4.16.In the frontal view, the rocker as an A shape. The two legs of the A are connected to thebase plate via pivot points. Half way up it is connected to the plunger and at the top it slidesthrough the slot of the lever. Therefore, two roller are added (see right Figure of Figure4.16). These roll through the slot, reducing friction in the contact. They also prevent thelever from swinging further at the end of the stroke of the plunger. The A shape results ina torsional and sideways stiff rocker.


Figure 4.16: The rocker that connects the plunger to the lever. Without (left) andwith (right) the rollers that roll through the slot of the lever.

From the side the rocker has a boomerang like shape. This is required by the location ofthe pivot points on the base plate and the connection point of the plunger to the rocker.The pivot points are in front of the lever and the plunger is connected behind the lever.Due to the boomerang and A shape, the lever can still reach all required positions.

Figure 4.17 shows the pivot points on the base plate. They rotate around an axle that isconnected between the vertical plate and the raised edge of the base plate. An M6 bolt witha small steel tube around it forms the axle. Threaded holes are needed in the raised edges.These cannot be made if the edge is attached to the base plate, because their locationcannot be reached with a drill. Therefore, a base plate connector (1) is made. The threadedholes are made in it and it is bolted to the base plate. The connecter is not as high as theedge of the base plate, otherwise the rocker would hit this edge. If the rocker is adjusted toclear the higher edge, the vertical parts that connect the pivot points to the tapered legs ofthe A shape would become larger. This decreases the lateral stiffness. The back end of theconnector is wider and contains threaded holes at the side planes. This is an extra support

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1. Base plate connector 3. Steel tube2. M6 bolt 4. Sliding ring bearing

Figure 4.17: The pivot points of the rocker.


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1. Connecting rod 3. Soft-magnetic part 5. Connecting rod axle2. Non-magnetic part 4. Rubber block

Figure 4.18: The plunger with the connecting rod.

for the vertical plates. They are bolted to the wider part of the connector too. This givesthe tip of the plate (where the pivot point is attached) some extra out of plane bendingstiffness. At both sides of the steel tube sliding ring bearings are added to prevent contactbetween the rocker and the connector or the vertical plates.

Due to the rotation of the rocker during a shot, the connection point between the rockerand the plunger also rotates around the pivot points of the rocker. The plunger on theother hand, only performs a translation. A connection between the two parts that cancope with this difference in motion has to be designed. Figure 4.18 shows the selectedsolution to this problem.

A slot is milled in the non-magnetic part (2) of the plunger. Herein, a connecting rod (1)is inserted which pivots around the connecting rod axle (5). A sliding bearing is used toreduce the friction between the two parts. The other end of the connecting rod is attachedto the rocker. An axle with a sliding bearing is also used here. Two pockets are milled inthe outer surface of the non-magnetic part to keep the locking rings of the axle inside thecontour of the non-magnetic part, such that it still fits inside the coil. A rubber block (4) atthe end of the soft-magnetic part (3) dissipates the energy in the plunger to slow it downat the end of the stroke and provides an end stop. In the right Figure in Figure 4.20 it canbe seen that if the stroke of the plunger is too large, the rocker will reach the end of theslot in the lever. If this happens, the mechanism can jam.Some material is removed from the flange of the non-magnetic part. This is needed toprevent a collision between the plunger and the rocker.


All axles in the kicking mechanism are made of steel.

4.4.3 Comparison current and new kicking mechanism

The goal is to keep the performances of the new kicking mechanism at least equal tothe current one. Both mechanisms use the same solenoid, therefore the performancesdepend on the mechanisms. Also the length of the lever is the same. The current kickingmechanism is depicted in Figure 4.19 and the new kicking mechanism is depicted inFigure 4.20.Two properties of the mechanisms are compared: the angle over which the lever rotatesand the angular velocity during rotation. The first property tells something about thetheoretical distance over which the ball is actuated by the solenoid. The second propertytells something about the velocity with which the ball is kicked away.

Both mechanisms are modeled in a program called SAM and the motion is simulated.The models can be found in Appendix C. Currently, the plunger has a stroke of 73 mm. Inthe new design this is reduced to 65 mm, because the rocker otherwise reaches the end ofthe slot in the lever, as was explained in Section 4.4.2. The angles of rotation are given inTable 4.1. It can be seen that in case of a lob shot the angle is more or less the same, butin case of a flat shot there is a difference. The new mechanism forces the lever to make alarger rotation.

The velocity of the plunger is the input of the angular velocity simulations. This was

Figure 4.19: The current kicking mechanism, with a direct connection between theplunger and the lever.


Figure 4.20: The initial position of the lever for a flat and lob shot (left). The finalposition of the lever after a flat and a lob shot (right).

Table 4.1: The angle in degrees over which the lever of the current and new mechanismrotates during both a flat and a lob shot.

Flat shot lob shotCurrent design 23.8 ◦ 35.7 ◦

New design 28 ◦ 35.4 ◦

determined in a simulation by K.J. Meessen, the designer of the solenoid. Graphs of thissimulation can be found in Appendix A.2. The angular velocities of the current and newkicking mechanism for both a flat and a lob shot are depicted in Figure 4.21.

There is a clear difference between the angular velocities of the current and new mecha-nism. In the current mechanism, the angular velocity increases until it reaches a maxi-mum value. This is caused by the direct connection between the solenoid and the lever.The solenoid has a similar velocity profile as the angular velocity of the current mecha-nism. The angular velocity of the lever in the new mechanism reaches its top and thendecreases again. This is caused by the rotation of the rocker. The contact point betweenthe rocker and the lever moves away from the rotation point of the lever during the strokeof the plunger. Therefore, the velocity of the plunger is applied at a larger distance fromthis rotation point. This reduces that angular velocity of the lever.Finally, Figure 4.21 shows a difference between the angular velocity of the flat and lob shot


Figure 4.21: Angular velocities of the lever of the current and new kicking mechanismfor both a flat and a lob shot.

in both mechanisms. This also is caused by the distance between the rotation point of thelever and the connection point of the plunger. During a lob shot this distance is smaller,resulting in a higher angular velocity.

From this simulation it can be concluded that the new kicking mechanism reaches thesame lever velocity as the current one. Because it accelerates faster, it will hit the ballwith an higher velocity. This makes the contact more like a collision instead of a push. Itis assumed that the new mechanism has at least the same performances as the currentmechanism.

4.4.4 Analysis of the rocker

The way the software decides to shot, sometimes causes the Turtle to shoot if there is noball but another robot in front of it. The impact causes large forces on the rocker. Thiscollision force Fc depends on the collision velocity vc, the mass m of the component thatcollides (in this case the lever) and the stiffness c of the contact of the components thatcollide. Their relation is described by Equation 4.1.

Fc = vc√m · c (4.1)


A FEM analysis is done to investigated the stresses in the rocker, which is intended to be a6061-T6 aluminum part. The stresses are determined at several positions over the strokeof the plunger. Due to the rotation of the rocker, the angle at which the force acts on therocker varies. Also the collision force varies as a result of the varying angular velocity of thelever (see Figure 4.21. These factors are part of the analysis. The analysis are describedin more detail in Appendix D.1. The maximum Von-Mises stress in the rocker duringthe stroke of the plunger is 207 MPa. Therefore, the rocker can be made of 6061-T6aluminum. It is a part that has to be milled.

4.4.5 The kicking mechanism attached to the frame

Figure 4.22 shows the base plate with kicking mechanism and the legs attached to thecentral box. The Figure shows that the outer ends of the vertical plates are not directlyconnected to the frame. The vertical plates are connected to the central box and the baseplate by flanges, as described before. Therefore, the parts of the plates that hold the upperlink rotation axle in position are not connected firmly to the frame. These plates canbend during an impact of a ball or another robot. To prevent this, a folded 3 mm sheetof aluminum connects the two outer ends of the plates to the front legs (see Figure 4.23).The added sheet is bolted to the front legs of the Turtle. This constrains both sideways andforward displacements of the upper link rotation axle.

Figure 4.24 shows how this is done. Steel threaded bushes (1) are welded in the ribs andside plates of the U profile of the leg. The folded sheet is connected with two M5 bolts toeach of the front legs. The centerline of the bush lies in the center plane of the side plate.This guides the forces applied to the folded sheet directly into the plates of the legs andinto the frame.

Figure 4.22: The main frame with the base plate and kicking mechanism attached toit.


Figure 4.23: The assembled lower half of the Turtle.

1 1

1. Threaded bush

Figure 4.24: The leg with threaded bushes. The figure at the right is a cross sectionview of the U profile where the bush is inserted.


It is also possible to attach the folded sheet to the upper plate of the central box. This is notchosen, because the upper part of the frame has to be removed first to reach the bolts thatconnect the sheet to the upper plate. If it is connected to the legs, it can easily be replacedin case of damage.

4.4.6 The capacitor

To power the electromechanical solenoid a 350 V , 4.7 mF capacitor is used. This acts likean energy buffer and it is powered from the central power supply. It has a diameter of 90mm, a height of 112 mm and mass of approximately 0.9 kg. It is positioned in the holein the central box as can be seen in Figure 4.25. At this position it is at the θ axis of theTurtle and minimizes the inertia around this axis, allowing faster angular acceleration ofthe Turtle.

The mass of the capacitor is supported by the two vertical plates of the kicking mecha-nism. In the upper Figure of Figure 4.14 it can be seen that material is removed fromthe upper edge of the large rectangular part of the vertical plates. The capacitor is locatedhere. It can still translate horizontally, therefore an upper capacitor support (2) is added.The support is depicted in Figure 4.26.It is a disk (3) with a tube (4) attached to it. The tube is positioned over the capacitor andthe disk is bolted to the top of the central box. This centers the capacitor in the hole of thecentral box and fixes it. A slot (5) is made in the tube for the power cables to pass through.The space between the wall of the central box and the capacitor is filled with a foam toisolate the capacitor from the impact shocks that go through the Turtle.

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1. Capacitor 2. Upper capacitor support

Figure 4.25: Cross section and detail view of the capacitor installed in the hole of thecentral box.

4.5. Concluding remarks 49

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3. Disk 5. Power cable slot4. Tube 6. Support edges for the computer casing

Figure 4.26: 3D view of the upper capacitor support.

Finally, two support edges (6) are added on top to support the computer casing (see Section5.3.1). The upper capacitor support is a plastic component. It shields the connection of thepower cables to the capacitor. The connection is made at the top of the capacitor and isnot isolated. The support prevents people from touching the connection by accident.


Unlike the current frame, the lower half of the new frame is mostly built up from alu-minum sheets. They form the closed boxes from which the main part of the frame isbuilt. This results in a frame that is stiffer than the current one.The base plate is still a milled component. However, its thickness is reduced, because it isno longer the main component of the frame. The upper base frame in the current Turtleis used to attach the upper half to the lower half of the Turtle. This is a milled part, aswas described in Section 2.3.1. This is replaced by the flanges on top of the legs. The newdesign’s upper part is discussed in Chapter 5.

The kicking mechanism is adjusted to position the solenoid as low as possible. This doesnot reduce its performances compared to the current mechanism, which already producesvery good shots.

The frame, that is the central box, the legs including motors and wheels, the base platewith the ball end stops and the vertical plates of the kicking mechanism have a mass of12.4 kg. The current lower part of the frame (depicted in the lower Figure of Figure 2.1)has a mass of 10,6 kg. The mass of a motor, encoder, gear head and omniwheel is 1.3kg. Therefore, most of the extra mass of the new frame is caused by the extra motor andwheel. The motor clamps are larger in the new design, adding extra mass too.

The bottom half of the Turtle is not completely finished yet. The current designs of theactive ball handling mechanism and an actuation mechanism to change between the typesof shots still have to be adjusted to fit in the new frame and to overcome the problem thatwere encountered in the 2009 season. The exact location of various hardware componentsis not determined yet. This depends on the battery that is going to be used. The team did


not decide this yet.

Chapter 5

The upper half of the new design

The main task of the upper half of the design is to fix the omnivision unit firmly to therest of the frame. The Turtle uses the lines on the field to determine its position. Softwareis used to extract the lines from the images produced by the omnivision unit. Thereforeits is important that the vision unit does not move with respect to the frame, otherwise anincorrect position of the Turtle is determined. The images of the omnivision unit are alsoused to determine the position of the ball, teammates, opponents and obstacles.

The upper half of the design also houses hardware components like the computer and afront camera. These components and how they are attached to the upper part of the frameis discussed in this Chapter, as well as a FEM analysis of the frame as a whole

5.1 Omnivision unit

The design of the omnivision unit has not changed much compared to the current unit.It is depicted in Figure 5.1. The base plate (1) of the unit is connected to the frame viafour mounting points (2), positioned at an angle of 90,◦ with respect to each other. Thebase plate is the only part that is changed. Its diameter has increased from 100 mm to 116mm to make the rest of the upper half wider, so all components fit inside. The number ofmounting points is changed from three to four.

The tube mounting ring (3) is bolted to the base plate. The transparant tube (5) is glued init. The tube is made of plexiglass and forms a stiff connection between de base plate andthe spherical mirror (7). The tube prevents movement of the mirror with respect to thecamera (4), which is also mounted on the base plate.

A pin (6) is screwed into the mirror. The pin creates a black spot in the center of theimage, which excludes the Turtle from the image. It indicates the center of the image,from which distances to the ball and lines are calculated. The mirror is bolted to the tubetop (8), which is glued to the tube. It is also a plexiglass part. An electronic compass islocated inside the tube top.

Finally, a top plate (9) is bolted on top of the tube top. It is a disk with a diameter of 200mm and is prescribed by the rules. A sticker with the number of the Turtle and the team

52 Chapter 5. The upper half of the new design

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1. Base plate 4. Camera 7. Spherical mirror2. Mounting points 5. Transparant tube 8. Tube top3. Tube mounting ring 6. Pin 9. Top plate

Figure 5.1: The vision unit and its components.

color is adhered on this plate.

5.2 Outer shape of the upper half

Figure 5.2 shows a top view of the main frame (discussed in Chapter 4) and the base plateof the omnivision unit (2). These two parts have to be connected. For this purpose, eachleg has two connection points (1). The basic shape of the body that connects the parts isdetermined by the shape of the main frame. A square or an octagon can be used. A squarewould stick out the central box too much, therefore an octagon is chosen.

5.2.1 The basic shape

The circle that fits inside the octagon at the main frame has a larger diameter comparedto the diameter of the omnivision unit’s base plate. Therefore, the body that connects thebase plate to the main frame is a cone with an octagonal outer shape. The rules prescribe amaximum height of the robot of 800mm. The distance between the topside of the centralbox and the bottom side of the base plate of the omnivision unit is 333 mm, resulting ina tapered angle of the cone of 8 ◦. There are several reasons to choose an octagonal coneinstead of a tube with an octagonal shape.

5.2. Outer shape of the upper half 53

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1. Main frame mounting points 2. Base plate omnivision unit

Figure 5.2: A top view of the bottom half of the design and the base plate of theomnivision unit.

A tube has the same diameter at both ends. Currently, this is not the case in the design,therefore one of them has to be adjusted. The diameter of the onmivision unit’s base platecould be enlarged to match with the diameter of the mounting point at the main frame. Alarge disk is then close to the mirror of the omnivision unit and therefore blocks a largepart of the field around the Turtle in the camera images. It cannot see obstacles or ballsthat are near to it anymore. This is a big disadvantage and therefore this option has notbeen chosen.Instead of enlarging the diameter of the base plate, the diameter of the mounting points atthe main frame can be reduced. This results in a narrow tube in which not all the requiredcomponents fit, therefore this concept has not been chosen.Because of its tapered shape, a cone can cope much better with horizonal forces, whichare introduced when a ball is kicked against it. In that situation, the tube concepts wouldbehave like a cantilever that is attached to the main frame. This can cause deformation.The cone can be regarded as a tapered cantilever, which deforms less with equally appliedforces.


5.2.2 The design

The octagonal cone is made out of two millimeter thick aluminum sheets. It is dividedinto a front side half (1) and a back side half (2) as can be seen in Figure 5.3. This simplifiesmanufacturing and improves accessibility of the components inside.

The octagonal shape of the cone can clearly be seen in the top view of Figure 5.3. It canalso be seen that the edges of the octagon at the base of the cone do not all have the samelength. The edges that are connected to the legs are shorter than the edges in between. Ifthe edges would have had an equal length, the base of the cone would have stuck outsidethe central box further, which reduces the space available for the hardware componentsbetween the legs. Now, the width of the plane that is connected to the leg is completelyclamped between the two flanges of the leg. Therefore, this plane cannot bend out of itsplane. If the edges would have had an equal length, the width of the plane would havebeen larger than the width of the flanges. This allows the part of the egde that is outsidethe flanges to bend out of its plane, which reduces the overall stiffness of the cone.At the top of the cone, the edges all have the same length, such that they are tangent to thebase plate of the omnivision unit.

The connection to the main frame and to the base plate of the omnivision unit fixes thehorizontal cross section of the cone twice. To increase the cone’s torsional stiffness, thehorizontal cross section needs to be fixed a third time. An octagonal frame is attached tothe inside of the cone. The location of this frame depends on the position of the hardwarecomponents inside the cone. This is discussed in Section 5.3.

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1. Front side half 2. Back side half

Figure 5.3: The cone attached to the main frame. Top view (left) and side view (right)

5.3. Components inside the cone 55

5.3 Components inside the cone

Components that are positioned inside the cone are: the computer, front camera and twocircuit boards for video processing and the electronic compass.

5.3.1 The computer

The computer is the largest hardware component that has to be fitted inside the cone. Itsdimensions are (W x H x D) 65 x 224 x 116 mm. It is an industrial computer which isproduced by Beckhoff. They advise to install the computer such that the 65 x 116 mmplanes are horizontal [13]. As a result, the C.O.G. of the computer is relatively high abovethe field. The influence of the location of this C.O.G. on the Turtle’s C.O.G. is investigated.Therefore, the mass of the Turtle without the computer mturtle, the mass of the computermcom, the height of the C.O.G. of the Turtle (without computer) above the field hturtle andthe height of the C.O.G. of the computer above the field hcom are required. With equation5.1 the height of the C.O.G. of the Turtle with computer is calculated.

hC.O.G. =hturtle ·mturtle + hcom ·mcom

mturtle +mcom(5.1)

The mass of the Turtle without the computer is estimated at 35 kg. The computer has amass of 1.75 kg [13]. The height of the C.O.G. of the Turtle above the field is estimated at150 mm, as was determined in Section 3.3.2. The bottom side of the computer is 275 mmabove the field in the new design. The height of the C.O.G. of the computer itself must beadded to this to determine the height of the computer’s C.O.G. above the field. The heightof the Turtle’s C.O.G. for the three possible computer orientations are given in Table 5.1.

Table 5.1: Height of the Turtle’s C.O.G. for different orientations of the computer.

Height of C.O.G. above the fieldComputer orientation of the Turtle with computerComputer lying on the 224 x 116 mm plane 158 mmComputer lying on the 224 x 65 mm plane 159 mmComputer lying on the 65 x 116 mm plane 161 mm

The Table shows that the height of the Turtle’s C.O.G. does not depend heavily on thecomputer orientation. The changes are in the order of ten millimeter. This is caused bythe relative small mass of the computer compared to that of the Turtle.

The computer is positioned in a protecting casing, which is placed on top of the uppercapacitor support. The top of the casing is connected to a support frame (see Figure 5.4),which is mounted to the two halves of the cone.

The casing is made from a single, one millimeter thick aluminum sheet. It is folded toform the casing. The bottom plate (1) is the base. Both the left (2) and right (3) side platehave a vertical flange (4). This increases their out of plane bending stiffness. They alsohave top flanges, which are used to attach to casing to the support frame (8). Three holesare made in each flange and bolts are inserted from below. The support frame contains


1

4

3

2

7

8

6

5

9

10

10

1. Bottom plate 5. Top flanges 8. Support frame2. Left side plate 6. Rear plate 9. Computer3. Right side plate 7. Connection flange 10. Foam rubber strips4. Vertical flanges

Figure 5.4: 3D view of the computer casing (left) and the computer casing with foamrubber strips and computer attached to the support frame (right).

the threaded holes for the M4 bolts.The rear plate (6) is folded from the right side plate. At the end of the rear plate, a connec-tion flange is folded with which it is connected to the left side plate. This is done with fivepop rivets. The rear plate does not have the same height as the side plates. This is causedby the shape of the cone. The part of the side plate’s edge that is not connected to the rearplate is chamfered. Otherwise, the casing would not have fitted inside the cone.Small holes are made in the side plates. These are used for the connection of two circuitboards to the outside of the casing. This is discussed in Section 5.3.2.

The casing is larger than the computer (9). This leaves space for shock absorbing materialaround the computer. Foam rubber strips (10) support the ribs of the computer, such that


it is not in contact with the casing. This also benefits cooling. The computer sucks in airat the bottom and blows it out at the top. For that reason, the rear plate is not connectedto the bottom plate. In the right Figure of Figure 5.4 it can be seen that there is an openspace between the bottom plate and the computer. Air is sucked in via this open space.Hot air that leaves the computer at the top, escapes through the openings in the supportframe.The plane of the computer that can be seen in Figure 5.4 contains the connectors. There-fore, this plane cannot be covered. The computer is not fixed, but it can still slide in andout the casing. Two Velcro strips spanned over the opening keep the computer inside thecasing. They are attached to the side plates of the casing, close to the bottom plate and thesupport frame.

5.3.2 The circuit boards

The video processing circuit board and the electronic compass circuit board are attachedto the computer casing. Both circuit boards are depicted in Figure 5.5.

The video processing board processes the images of the omnivision system, reducing theload on the computer. It is a new hardware component, which is developed in house and

1

5

2

3

4

4

1. Video processing board 3. Computer connectors 5. Compass circuit board2. Camera connectors 4. Threaded bushes

Figure 5.5: The circuit boards attached to the computer casing.


will be used in the 2011 season. It has to be positioned vertically for optimal cooling [9].The location where the video processing board (1) is connected to the computer casingis determined by the available space inside the cone. At the depicted position, there isenough space left to insert the plugs in the different connectors. The video processingboard is connected to the computer casing with four M3 threaded bushes (4). These areclamped between the casing and the board with bolts, as can be seen in Figure 5.5. Threeof the four connections are close to a folded edge. The plate of the computer casing hasa large out of plane bending stiffness here, therefore the video processing board is fixedwell.The compass circuit board (5) is used for the calibration of the compass. An externaltool is plugged on the circuit board when calibrating the compass. Therefore, it must bepositioned at the computer casing such that it can easily be reached, preferably withoutremoving a half of the cone. At the current position, it is close to an opening in the cone.This opening is discussed in Section 5.4. The compass circuit board is also connected tothe casing with M3 threaded bushes. Also here three of the four connections are close toa folded edge of the casing.

5.3.3 The front camera and support frame

Tech United has added an extra camera to the Turtles that looks in forward direction. It isused to counteract the shortcomings of the omnivision system, which cannot see the ballif it is at a height above 800 mm, neither can it determine the height of the ball when itis below 800 mm. The front camera provides a better and more accurate ball tracking. Itis a so called smart camera with onboard processing power. It processes the images andtransmits only the ball’s position and velocity to the computer. This reduces the load onthe computer. A disadvantage of this is the relative large size of the camera.The camera is depicted in Figure 5.6. Three M6 threaded holes (1) form the mountingpoints of the camera. The cable connectors (2) are positioned at the back end.

1

2

1. Mounting points 2. Cable connectors

Figure 5.6: The front camera

The front camera is attached to the same support frame as the computer casing, which isdepicted in more detail in Figure 5.7. It is a milled aluminum part with a height of 10mm.The support frame is the extra horizontal plane discussed in Section 5.2.2 that connects


Figure 5.7: The support frame

the two halves of the cone to stiffen it. Material is removed to reduce the mass and toallow cables of the omnivision unit to go from one side of the support to the other. Theslot where the camera is attached to the support frame, is as wide as the connection blockon the camera. This fixes the rotation of the camera. It rests at two narrow raised edgesand is bolted with two bolts to these edges. The translation of the camera is then fixed byfriction. One edge of the slot is removed. This makes it possible to slide the camera inthe slot, even when the support frame is already attached to the front half of the cone (see

Figure 5.8: The front camera attached to the support frame. Top view (left) and crosssection view (right)


Figure 5.8). One edge of the octagon is removed to make room for the inner half of thelens cover, which is discussed in Section 5.4.1.

5.4 The total design

5.4.1 The cone with components attached to the bottom half

Figure 5.9 shows the support frame connected to the front side half of the cone. Four M4bolts are used to connect the support frame to two planes of the half cone. Holes are madein the cone. These have various functions. Hot air from the computer leaves the Turtlevia the upper holes. The lens of the camera sticks out through the next hole. A protectivecover is positioned over the lens. The lens cover is depicted in Figure 5.10. It consists ofan inside half (1) and an outside half (2), between which the plate of the cone is clamped.The inside half is inside the cone and contains four threaded holes. M4 bolts are insertedin the outside half, through the plate of the cone and are screwed in the inside half. It isan aluminum component, which is made with a lathe and a milling machine.

The large hole in the middle allows to reach the back side of the computer. It can bepushed from here if it has to come out of the casing. It also reduces the mass of the coneand allows cold air to flow into it. At the bottom of the cone, some material is removedto make room for the upper link of the kicking mechanism. Otherwise this would hit thecone. The cone is bolted with four M5 bolts to the bottom half.

Figure 5.9: The support frame connected to the front side half of the cone.

5.4. The total design 61

21

1. Inside half 2. Outside half

Figure 5.10: Back side view and cross section view of the lens cover.

Figure 5.11 shows the back side half of the cone connected to the rest of the Turtle. Thesupport frame is also connected with four M4 bolts to this half.

Figure 5.11: The support frame connected to the back side half of the cone.


There are also holes in the back side half of the cone. The two holes positioned above eachother let hot air escape. The single hole in the middle provides access to the connectorsof the front camera. Its cables will come out here as well. The rectangular slot providesaccess to the connectors of the computer, such that connectors can be disconnected with-out taking the back side half of the cone of the Turtle. At the side of the cone, material isremoved from both halves. This is done at both sides of the cone. The openings provideaccess to the compass circuit board and video processing board.The front side half and the back side half meet at the top of the opening. To increase theoverall stiffness of the cone, the front and back side half need to be connected at the edgewhere they meet.

A strip of two millimeter thick aluminum is located inside the cone and is connected toboth halves of the cone. This is depicted in Figure 5.12. The strip contains rivnuts toprovide the necessary threaded holes for the M4 bolts that connect the halves to the strip.At the top of the cone, the two halves are not directly connected. Here, the planes aresupported by the base plate of the omnivision unit and the support frame, as can be seenin the cross section view of Figure 5.12. This prevent the planes from bending inward atthe top.

Figure 5.12: A two millimeter strip connects the two halves of the cone.


5.4.2 FEM analyses

The main frame of the Turtle is subjected to FEM analyses to get an indication of thestresses in the frame and the deformation of the frame during different kind of impacts.The model is converted into a finite element model by meshing of the components. Thecomponents are divided into small elements, which are connected at nodes. Figure 5.13shows the finite element model. The components in the finite element model are: Thebase plate, the legs without the motors and wheels, the central box, the part of the verti-cal plates that connect the base plate and the central box, the solenoid, both halves of theoctagonal cone, the support frame and the base plate of the onmivision unit. These com-ponents are meshed with a combination of 2D and 3D elements. The sheets of aluminumare meshed with 2D elements. The milled components and the solenoid are meshed with3D thetrahedral elements.

Figure 5.13: The finite element model.

Except from the solenoid, non of the hardware components are in the finite elementmodel. Their masses however, are of influence on the final result of the simulation.Therefore, their masses are added by changing the density of the materials used (6061aluminum, except for the solenoid) but maintaining their other material properties. Themass of the computer and its casing is added to the plates that make up the octagonalcone. The mass of the front camera is added to the support frame. The base plate of theomnivision unit has a mass equal to the total mass of this unit. The mass of the capacitoris added to the tube at the inside of the central box. This results in a mass of the finiteelement model of 20 kg.The rubber bumper at the perimeter of the base plate is not in the model. The solver


cannot cope with the large difference in elastic deformation of the rubber compared to thealuminum.

1

2

3

4

5

Figure 5.14: The five load cases to which the frame is subjected.

The frame is subjected to different load cases. These are depicted in Figure 5.14. Thefirst load case (1) simulates an impact of another robot at the rear edge of the base plate.The impact area is located between the strengthening diagonal edges. A collision of tworobots, both traveling at 4 m/s, is simulated. This is equal to a single robot that driveswith 8 m/s into a wall. The collision force Fc depends on the collision velocity vc, themass m of the robot and the stiffness c of the parts that collide. The relation is describedby Equation 4.1 in Section 4.4.4.

The stiffness of the rubber bumper is in the order of 10000 N/m. Because it is simulatedthat two robots collide, the bumpers form the contact. They can be regarded as two springsin series, therefore their replacement stiffness is in the order of 5000 N/m. With a massof 40 kg and a velocity of 8 m/s this results in a collision force of 3600 N . The stiffnessis not constant, because of the small volume of the rubber. During deformation it willincrease, but the velocity also decreases. It is assumed that this increases the collisionforce not that much. The force is simulated by gravity. The point where the robot collidesis fixed in six degrees of freedom in the simulation. A gravitational load in the directionof motion before the collision is applied to the frame. The gravitation constant is adjustedsuch that the force on the frame is equal to the collision force. With the mass of the framein the model being 20 kg, the gravitation constant needs to be 180 m/s2. Earth’s gravityis also applied to the frame. The simulation is a worst case scenario, because few robotscan reach velocities of 4 m/s.


Figure 5.15: The Von-Mises stress inMPa in the frame as a result of the first loadcase.

Figure 5.16: The Von-Mises stress in MPa in the frame as a result of the fourthloadcase.


Experience tells that most teams drive with velocities up to 2.5 m/s. The stresses that thefirst load case causes in the frame are depicted in Figure 5.15. The highest stresses occurat the top of the diagonal strengthening edges. The base plate wants to bend, because theTurtle still wants to move in forward direction. The diagonal edges limit the bending ofthe base plate. It does not deform plastically, if it is made of 6061-T6 aluminum. Thismaterial starts to yield at 241 MPa. This value is exceeded in the simulation, but that isonly in one badly shaped element. Therefore this can be regarded as a numerical error.The stresses in the surrounding elements are substantially lower.

The second (2) and third (3) load case also simulate an impact on the bumper, though atdifferent locations. The impact force is equal to that of the first load case. It is also appliedas a gravitational load. The results of these simulations can be found in Appendix D.2.They show similar results as the first load case, but the deformation is slightly larger. Thisis caused by the open space for the ball at the front side of the base plate. Again, someelements have stresses above the yield stress. This is also caused by numerical errors inthe simulations. Surrounding elements have substantial lower stresses.

The fourth load case (4) simulates a collision against the wheel. The impact force is trans-ferred from the wheel to the motor support, therefore this is loaded. This is an equalload case as was discussed in Section 2.3.2, which causes the current Turtle to deformplastically. Also here, the impact force is equal to the first load case. It is also applied as agravitational load in the direction of movement before the collision. The resulting stressesof this load case are depicted in Figure 5.16. It can be seen that there is no plastic defor-mation in the frame as a result of this load case. The stresses are guided to the centralbox, as was intended by the design.

The fifth load case (5) simulates a ball that is kicked against the octagonal cone. Equation4.1 is used to estimated the impact force. The ball reaches speeds of up to 10 m/s [2]. Themass and pressure of the ball is prescribed by the RoboCup rules and regulations [3]. Themass of the ball must be between 410 and 450 grams at the start of the game. The worsecase scenario is used in the calculation, which is a mass of 450 grams. The pressure ofthe ball must be between 0.6 and 1.1 atmosphere at sea level. Experience tells that mostgames are played with a ball which has a pressure of 0.6 atmosphere. An experiment isperformed to get an indication of the stiffness of a ball at different pressures. Masses areplaced on top of the ball and the deformation is measured. The experiment is described inmore detail in Appendix B.3. The stiffness at 0.6 atmosphere is in the order of 20 kN/m.This is used in the equation and results in an impact force of 950 N .

Experience tells that the Turtle’s wheels do not come off the field when a ball is kickedagainst the cone, neither does it roll away. This knowledge is used to constrain the framein the simulation. The contact areas between the motors and the motor supports are fixedin z direction and the edge of the base plate perpendicular to the direction of the ballimpact is fixed in the other five degrees of freedom. The results of this simulation are alsodepicted in Appendix D.2. It can be seen that there is no plastic deformation and thereforethe omnivision unit remains at its position.

5.5. Concluding remarks 67


With the upper half of the design attached to the bottom half, the design is finished. Themain goal of the upper half was to connect the omnivision unit firmly to the bottom halfof the design. The FEM analyses show that this goal is achieved. Also the front camera,the computer and two circuit boards are attached to the Turtle in the upper half.

The finished Turtle is depicted in Figure 5.17. It is within the required dimensions. Itcovers a floor area of 500 mm x 500 mm and has a height of 783 mm. This leaves somespace for a keeper device that probably will run over the top plate of the omnivision unit.The Turtle has a mass of 30.3 kg. This includes seven amplifiers that control the four mo-tors of the wheels, the two motors of the active ball handling mechanism and the motorfor raising and lowering the lever of the kicking mechanism. This also includes a 1.5 kgbattery that the team was investigating in the summer of 2009. It is not sure whether thisbattery will be used. Therefore, the battery mass is likely to increase. Also the Beckhoffethercat module is included. A proposition of the location of these components in theTurtle is given in Appendix E.Extra mass is added by components which are not in the design yet. The active ball handel-ing mechanism adds an estimated two kilogram. Circuit boards and power cables add anestimated 2.5 kg. The actuation mechanism that raises and lowers the kicking mechanismwill probably have a mass of 0.5 kg. The mass of the protective cover that is placed overthe bottom half of the Turtle is estimated at one kilogram. This results in a total estimatedmass of 36.3 kg, which is within the specified maximum mass of 40 kg.The current Turtle has a mass of 33 kg. This results in a difference of 3.3 kg, of which 1.6kg is covered by the extra motor, wheel and amplifier.

The C.O.G. of the Turtle lies at 150 mm above the field. This is equal to the C.O.G. ofthe current Turtle. The computer orientation is now in line with the manufacturer’s re-quirement, which positions it higher in the frame. The solenoid is positioned lower in theframe, counteracting the influence of the computer.The current battery mass is three kilogram, which is positioned at the base plate. In thenew design this is only 1.5 kg. As described before, this mass can increase, which willlower the C.O.G..The C.O.G. is positioned within two millimeters from the vertical symmetry axis of theTurtle. All heavy hardware components are positioned close to this axle. This is not thecase in the current Turtle. Therefore, the new Turtle has a smaller inertia around thevertical symmetry axle. This allows faster angular acceleration.


Figure 5.17: The finished Turtle.

Chapter 6

Conclusion and Recommendation

6.1 Conclusion

A new mechanical design of the Tech United Turtle is presented. With a covered floor areaof 500 mm x 500 mm, a height of 783 mm and an estimated mass of 36.3 kg, it is withinthe RoboCup rules and regulations.

Unlike the three wheeled current Turtle, the new one has four omniwheels and is poweredby four servo motors. These are positioned at the corners of a square, with their axes alongthe diagonals of this square. This wheel configuration provides a higher top speed andmaintains the maneuverability.

The new mechanical design is based on stiffness. The Turtle’s base plate no longer is themain component to provide the stiffness, therefore its thickness could be reduced. Thebasic shape of the new frame corresponds with the Eiffel Tower. The legs and the centralbox of the frame are formed by sheets of aluminum, which are folded to form closed boxes.This results in a frame in which the material is optimally used to cope with the externalforces. The base plate and the kicking mechanism are supported by the main frame.

The kicking mechanism is redesigned, because the electromechanical solenoid that pow-ers it, is positioned lower in the frame. The new mechanism accelerates the kicking leverfaster, resulting in a higher velocity of the lever at the moment it hits the ball. This in-creases the collision force and therefore the velocity of the ball.

An octagonal cone is used to fix the omnivision unit firmly to the rest of the frame. Thefront camera and the computer are located inside the cone. Compared to the currentTurtle, the heavy hardware components are positioned closer to the vertical symmetry axisof the Turtle. This reduces its inertia around this axis, increasing the angular accelerationFurther. This was already increased by the additional motor.The C.O.G. height is 150 mm from the field. This has not changed compared to thecurrent Turtle. It is relatively close to the field, therefore the Turtle does not tilt muchduring acceleration, keeping the omnivision unit steady.

FEM analyses of the frame show that it can cope with collisions with other robots at topspeed without plastic deformation of the frame. The octagonal cone does not deformplastically if a ball is kicked against it with a velocity of 10 m/s. This keeps the omnivision

70 Chapter 6. Conclusion and Recommendation

unit in position.

6.2 Recommendations

The current design of the active ball handling mechanism has to be adjusted to fit in-side the new Turtle and to overcome the problems that were encounter during the 2009RoboCup season. More damping should be added to the ball and socket joint which con-nects the mechanism to the base plate. It is recommended to insert a layer of rubber inthe socket which envelopes the ball. Currently, there is only additional damping when theball is pressed down in the socked. There is now damping if external forces try to pullthe ball out of the socket. It is proposed to design a mechanism that keeps the ball in afixed position in the socket under normal load. The mechanism allows vertical movementof the ball if large external forces, as a result of a collision, are applied. The mechanismdissipates energy, reducing the stresses in the ball handling mechanism.

The design of the mechanism that raises and lowers the kicking lever has to be redesignedto overcome the current problems with the rope. It also has to be adjusted to fit inside thenew Turtle.

The software that controls the motors of the wheels has to be adjusted. The new wheelconfiguration demands other input speeds of the wheels to move in a certain directioncompared to the current wheel configuration. The new configuration often uses four mo-tors, where the current configuration often uses two. It is recommended to do some teststo determine the power consumption and use that to decide which type of batteries aregoing to be used. If the dimensions of the batteries are known, all hardware componentscan be placed at a final position in the Turtle.

Bibliography

[1] J. G. Goorden, P.P. Jonker, TechUnited Team Description Paper 2006, in partial fulfill-ment of the 2006 RoboCup World Championships qualification process, 2006

[2] W.H.T.M. Aangenent, el al., TechUnited Team Description Paper 2009, RoboCup 2009

[3] MSL Technical Committee, Middle Size Robot League Rules and Regulations for 2009,Version 13.1, 2008

[4] R.P.A. van Haendel, Design of an omnidirectional universal mobile platfom, Interal re-port DCT 2005.117, Eindhoven University of Technology, 2005, pages 17-18

[5] M. Ashmore, N. Barnes, Omni-drive robot motion on curved paths: The fastest pathbetween two points is not a straight-line, Springer-Verlag Berlin Heidelberg, Germany,2002

[6] Maxon motor catalog, Program 08/09 pages 36-39, 84-85, 165, 167

[7] P.C.J.N. Rosielle, E.A.G. Reker, Constructie Principes 1, Lecture notes 4007, Technis-che Universiteit Eindhoven, 2004

[8] I. Hirai, T. Gunji Slipperiness and Coefficient of friction on the carpet, Otsuma Women’sUniversity, Sanban-cho, Chiyoda-ku, Tokyo, Japan, 2000

[9] G.A. Harkema, Private conversation, 2009

[10] The RoboCup Dutch Committe, http://www.robocup.nl, Netherlands

[11] RoboCup 2009, http://www.robocup2009.org/212-0-general, Austria

[12] Tech United, http://www.techunited.nl, Netherlands

[13] Beckhoff, Main catalog, http://www.beckhoff.de/download/document/catalog/main_catalog/ english/main_catalog_2009.pdf, 2009, Germany

Appendix A

Specifications

This appendix contains the specifications of the Maxon motor and the Maxon gear headthat are used [6]. Also, an overview of the specifications of the electromechanical solenoidis given.

A.1 Motor and gear head

74 Appendix A. Specifications

Operating Range Comments

Continuous operationIn observation of above listed thermal resistance(lines 17 and 18) the maximum permissible windingtemperature will be reached during continuousoperation at 25°C ambient.= Thermal limit.

Short term operationThe motor may be briefly overloaded (recurring).

Assigned power rating

n [rpm]

max

onD

Cm

otor

maxon Modular System Overview on page 16 - 21

Specifications

82 maxon DC motor May 2009 edition / subject to change

Stock programStandard programSpecial program (on request)

Order Number

RE 40 �40 mm, Graphite Brushes, 150 Watt

Thermal data17 Thermal resistance housing-ambient 4.65 K / W18 Thermal resistance winding-housing 1.93 K / W19 Thermal time constant winding 41.6 s20 Thermal time constant motor 1120 s21 Ambient temperature -30 ... +100°C22 Max. permissible winding temperature +155°C

Mechanical data (ball bearings)23 Max. permissible speed 12000 rpm24 Axial play 0.05 - 0.15 mm25 Radial play 0.025 mm26 Max. axial load (dynamic) 5.6 N27 Max. force for press fits (static) 110 N

(static, shaft supported) 1200 N28 Max. radial loading, 5 mm from flange 28 N

Other specifications29 Number of pole pairs 130 Number of commutator segments 1331 Weight of motor 480 g

Values listed in the table are nominal.Explanation of the figures on page 49.

OptionPreloaded ball bearings

Planetary Gearhead�42 mm3 - 15 NmPage 240

Encoder HED_ 5540500 CPT,3 channelsPage 268 / 270

148866 148867 148877 218008 218009 218010 218011 218012 218013 218014Motor Data

Values at nominal voltage1 Nominal voltage V 12.0 24.0 48.0 48.0 48.0 48.0 48.0 48.0 48.0 48.02 No load speed rpm 6920 7580 7580 6420 5560 3330 2690 2130 1710 14203 No load current mA 241 137 68.6 53.7 43.7 21.9 16.7 12.5 9.67 7.774 Nominal speed rpm 6370 6930 7000 5810 4920 2700 2050 1500 1080 7745 Nominal torque (max. continuous torque) mNm 94.9 170 184 183 177 187 187 189 189 1886 Nominal current (max. continuous current) A 6.00 5.77 3.12 2.62 2.20 1.38 1.12 0.898 0.721 0.5937 Stall torque mNm 1680 2280 2500 1990 1580 995 796 641 512 4158 Starting current A 102 75.7 41.4 28.0 19.2 7.26 4.68 3.00 1.92 1.299 Max. efficiency % 88 91 92 91 91 89 88 87 86 85

Characteristics10 Terminal resistance � 0.117 0.317 1.16 1.72 2.50 6.61 10.2 16.0 24.9 37.111 Terminal inductance mH 0.0245 0.0823 0.329 0.460 0.612 1.70 2.62 4.14 6.40 9.3112 Torque constant mNm / A 16.4 30.2 60.3 71.3 82.2 137 170 214 266 32113 Speed constant rpm / V 581 317 158 134 116 69.7 56.2 44.7 35.9 29.814 Speed / torque gradient rpm / mNm 4.15 3.33 3.04 3.23 3.53 3.36 3.39 3.35 3.37 3.4415 Mechanical time constant ms 6.03 4.81 4.39 4.36 4.35 4.31 4.31 4.31 4.31 4.3216 Rotor inertia gcm2 139 138 138 129 118 123 121 123 122 120

Industrial VersionEncoder HEDL 9140Page 273Brake AB 28Page 317

Brake AB 28�45 mm24 VDC, 0.4 NmPage 316

Encoder MR256 - 1024 CPT,3 channelsPage 265

M 1:2

Recommended Electronics:ADS 50/5 Page 282ADS 50/10 283ADS_E 50/5 283ADS_E 50/10 283EPOS2 24/5 303EPOS2 50/5 303EPOS 70/10 303EPOS P 24/5 306Notes 18

Planetary Gearhead�52 mm4 - 30 NmPage 243

Figure A.1: Specification sheet of the RE40 motor from the Maxon catalog.

A.1. Motor and gear head 75

240 maxon gear May 2009 edition / subject to change

overall length overall length

maxon Modular System

Stock programStandard programSpecial program (on request)

max

onge

ar

Planetary Gearhead GP 42 C �42 mm, 3 - 15 NmCeramic Version

Order Number

203113 203115 203119 203120 203124 203129 203128 203133 203137 203141

Gearhead Data1 Reduction 3.5 : 1 12 : 1 26 : 1 43 : 1 81 : 1 156 : 1 150 : 1 285 : 1 441 : 1 756 : 12 Reduction absolute 7/2 49/4 26 343/8 2197/27 156 2401/16

15379/54 441 7563 Mass inertia gcm2 14 15 9.1 15 9.4 9.1 15 15 14 144 Max. motor shaft diameter mm 10 10 8 10 8 8 10 10 10 10

Order Number 203114 203116 203121 203125 203130 203134 203138 2031421 Reduction 4.3 : 1 15 : 1 53 : 1 91 : 1 186 : 1 319 : 1 488 : 1 936 : 12 Reduction absolute 13/3 91/6 637/12 91 4459/24

637/2 4394/9 9363 Mass inertia gcm2 9.1 15 15 15 15 15 9.4 9.14 Max. motor shaft diameter mm 8 10 10 10 10 10 8 8

Order Number 203117 203122 203126 203131 203135 2031391 Reduction 19 : 1 66 : 1 113 : 1 230 : 1 353 :1 546 : 12 Reduction absolute 169/9 1183/18

338/3 8281/3628561/81 546

3 Mass inertia gcm2 9.4 15 9.4 15 9.4 144 Max. motor shaft diameter mm 8 10 8 10 8 10

Order Number 203118 203123 203127 203132 203136 2031401 Reduction 21 : 1 74 : 1 126 : 1 257 : 1 394 : 1 676 : 12 Reduction absolute 21 147/2 126 1029/4 1183/3 6763 Mass inertia gcm2 14 15 14 15 15 9.14 Max. motor shaft diameter mm 10 10 10 10 10 85 Number of stages 1 2 2 3 3 3 4 4 4 46 Max. continuous torque Nm 3.0 7.5 7.5 15.0 15.0 15.0 15.0 15.0 15.0 15.07 Intermittently permissible torque at gear output Nm 4.5 11.3 11.3 22.5 22.5 22.5 22.5 22.5 22.5 22.58 Max. efficiency % 90 81 81 72 72 72 64 64 64 649 Weight g 260 360 360 460 460 460 560 560 560 560

10 Average backlash no load ° 0.3 0.4 0.4 0.5 0.5 0.5 0.5 0.5 0.5 0.511 Gearhead length L1* mm 40.9 55.4 55.4 69.9 69.9 69.9 84.4 84.4 84.4 84.4

*for EC 45 flat L1 is - 3.5 mm

+ Motor Page + Sensor Page + Brake Page = Motor length + gearhead length + (sensor / brake) + assembly parts

RE 35, 90 W 81 111.9 126.4 126.4 140.9 140.9 140.9 155.4 155.4 155.4 155.4RE 35, 90 W 81 MR 265 123.3 137.8 137.8 152.3 152.3 152.3 166.8 166.8 166.8 166.8RE 35, 90 W 81 HED_ 5540 268/270 132.9 147.4 147.4 161.9 161.9 161.9 176.4 176.4 176.4 176.4RE 35, 90 W 81 DCT 22 277 130.0 144.5 144.5 159.0 159.0 159.0 173.5 173.5 173.5 173.5RE 35, 90 W 81 AB 28 316 148.0 162.5 162.5 177.0 177.0 177.0 191.5 191.5 191.5 191.5RE 40, 150 W 82 112.0 126.5 126.5 141.0 141.0 141.0 155.5 155.5 155.5 155.5RE 40, 150 W 82 MR 265 123.4 137.9 137.9 152.4 152.4 152.4 166.9 166.9 166.9 166.9RE 40, 150 W 82 HED_ 5540 268/270 132.7 147.2 147.2 161.7 161.7 161.7 176.2 176.2 176.2 176.2RE 40, 150 W 82 HEDL 9140 273 166.1 180.6 180.6 195.1 195.1 195.1 209.6 209.6 209.6 209.6RE 40, 150 W 82 AB 28 316 148.1 162.6 162.6 177.1 177.1 177.1 191.6 191.6 191.6 191.6RE 40, 150 W 82 AB 28 317 156.1 170.6 170.6 185.1 185.1 185.1 199.6 199.6 199.6 199.6RE 40, 150 W 82 HED_ 5540 268/270 AB 28 316 165.2 179.7 179.7 194.2 194.2 194.2 208.7 208.7 208.7 208.7RE 40, 150 W 82 HEDL 9140 273 AB 28 317 176.6 191.1 191.1 205.6 205.6 205.6 220.1 220.1 220.1 220.1EC 40, 120 W 157 111.0 125.5 125.5 140.0 140.0 140.0 154.5 154.5 154.5 154.5EC 40, 120 W 157 HED_ 5540 269/270 129.4 143.9 143.9 158.4 158.4 158.4 172.9 172.9 172.9 172.9EC 40, 120 W 157 Res 26 278 137.6 152.1 152.1 166.6 166.6 166.6 181.1 181.1 181.1 181.1EC 40, 120 W 157 AB 28 316 141.8 156.3 156.3 170.8 170.8 170.8 185.3 185.3 185.3 185.3EC 45, 150 W 158 152.2 166.7 166.7 181.2 181.2 181.2 195.7 195.7 195.7 195.7EC 45, 150 W 158 HEDL 9140 273 167.8 182.3 182.3 196.8 196.8 196.8 211.3 211.3 211.3 211.3EC 45, 150 W 158 Res 26 278 152.2 166.7 166.7 181.2 181.2 181.2 195.7 195.7 195.7 195.7EC 45, 150 W 158 AB 28 317 159.6 174.1 174.1 188.6 188.6 188.6 203.1 203.1 203.1 203.1EC 45, 150 W 158 HEDL 9140 273 AB 28 317 176.6 191.1 191.1 205.6 205.6 205.6 220.1 220.1 220.1 220.1EC 45 flat, 30 W 195 53.9 68.4 68.4 82.9 82.9 82.9 97.4 97.4 97.4 97.4EC 45 flat, 50 W 196 58.8 73.3 73.3 87.8 87.8 87.8 102.3 102.3 102.3 102.3EC 45 fl, IE, IP 00 197 72.8 87.3 87.3 101.8 101.8 101.8 116.3 116.3 116.3 116.3EC 45 fl, IE, IP 40 197 75.0 89.5 89.5 104.0 104.0 104.0 118.5 118.5 118.5 118.5EC 45 fl, IE, IP 00 198 77.8 92.3 92.3 106.8 106.8 106.8 121.3 121.3 121.3 121.3EC 45 fl, IE, IP 40 198 80.0 94.5 94.5 109.0 109.0 109.0 123.5 123.5 123.5 123.5

Technical DataPlanetary Gearhead straight teethOutput shaft stainless steelBearing at output preloaded ball bearingsRadial play, 12 mm from flange max. 0.06 mmAxial play at axial load < 5 N 0 mm

> 5 N max. 0.3 mmMax. permissible axial load 150 NMax. permissible force for press fits 300 NSense of rotation, drive to output =Recommended input speed < 8000 rpmRecommended temperature range -20 ... +100°C

Extended area as option -35 ... +100°CNumber of stages 1 2 3 4Max. radial load,12 mm from flange 120 N 150 N 150 N 150 N

M 1:2

Figure A.2: Specification sheet of the GH42 motor from the Maxon catalog.

76 Appendix A. Specifications

A.2 Electromechanical solenoid

The following graphs show the axial displacement of the plunger in time (Figure A.3), theaxial force produced by the plunger as a function of the displacement (Figure A.4) and theaxial velocity of the plunger as a function of the displacement (Figure A.5). The graphs areobtained by simulations. These were performed by the designer of the electromechanicalsolenoid, K.J. Meessen.

Axial displacement of plunger

0

10

20

30

40

50

60

70

80

90

100

0,000 0,002 0,004 0,006 0,008 0,010 0,012 0,014 0,016 0,018 0,020

Time [s]

Dis

pla

cem

en

t[m

m]

Figure A.3: Axial displacement of the plunger in time.

A.2. Electromechanical solenoid 77

Axial Force produced by the solenoid

-400

-200

0

200

400

600

800

0 0 2 5 12 21 33 47 63 80 95

Axial displacement [mm]

Axia

lF

orc

e[N

]

Figure A.4: Axial force produced by the plunger as a function of the axial displacement.

Axial velocity of the plunger

0

1

2

3

4

5

6

7

8

9

10

0 0 2 5 12 21 33 47 63 80 95

Axial displacement [mm]

Velo

cit

y[m

/s]

Figure A.5: Axial velocity of the plunger as a function of the axial displacement.

Appendix B

Experiments

The experiments that are performed are discussed in this Appendix. The first experimentwas to determine the height of the C.O.G. of the current Turtle. The second experimentwas performed to get an indication of the sliding friction coefficient between the om-niwheel and the field. The last experiment was performed to get an indication of thestiffness of a soccer ball.

B.1 Height of C.O.G.

The height of the C.O.G. of the current Turtle is required as an indication for the simu-lated platforms. An experiment was done, to determine the height of the C.O.G. This isexplained in this appendix.

h

l

1a

1x

Figure B.1: The angle α1 between the ground and the Turtle when it tumbles.

The Turtle tumbles if the C.O.G. is outside the base plate. In Figure B.1 this happens whenthe C.O.G. is left of the vertical dotted line. In Figure B.2 this happens when it is right ofthe dotted line. In the experiment α1 and α2 were measured. The height of the C.O.G. his derived using the following set of equations.

h = x1 tan(90− α1) (B.1)

80 Appendix B. Experiments

hl

2a

1xl -

Figure B.2: The angle α2 between the ground and the Turtle when it tumbles.

h = l tan(90− α2)− x1 tan(90− α2) (B.2)

Equating Equation B.1 and B.2 and reordering it to an expression for x1, results in Equa-tion B.3 and B.4.

x1(tan(90− α1) + tan(90− α2)) = l tan(90− α2) (B.3)

x1 =l tan(90− α1)

tan(90− α1) + tan(90− α2)(B.4)

Substitution of Equation B.4 in Equation B.1 results in an expression for the height of theC.O.G..

h =l tan(90− α1)

tan(90− α1) + tan(90− α2)tan(90− α1) (B.5)

with:α1 = 62 ◦

α2 = 60 ◦

l = 0.48 m

This results in an h of 0.13 m This is the height above the bottom side of the base plate.There is a clearance of 15 mm between the field and the base plate. Therefore the heightof the C.O.G. above the field is approximately 0.15 m.

B.2 Sliding friction coefficient

In the setup of this experiment, an omniwheel was clamped on a table, such that it couldnot roll anymore. A piece of the carpet of the field was glued to a metal strip with a massof 0.88 kg. This was placed on top of the wheel and a mass of two kilogram was placed ontop of this. The force it takes to drag the strip with the mass over the wheel was measured

B.3. Ball stiffness 81

Ffr

mg

Figure B.3: Schematic representation of the setup that was used in the experiment todetermine the dynamic friction coefficient betweeen an omniwheel and the field.

(see Figure B.3) at 23 N . The measured force represents the friction force between theomniwheel and the field. From this, the sliding friction coefficient can be determined byEquation B.6.

µkin =FpullFz

(B.6)

This results in a sliding friction coefficient between the omniwheel and the field of 0.8.

B.3 Ball stiffness

The stiffness of the ball is measured by placing different masses on top of the ball andmeasuring the height of the combination, as is depicted in Figure B.5. Before the experi-ment, the height of the ball and the masses was measured, to determine there undeformedheight. The experiment is performed at different pressures, varying between 0.5 and 1.0atmosphere and with masses of 11.8 kg and 18 kg. The results are depicted in Figure B.4.

82 Appendix B. Experiments

Stiffness of the ball at different pressures

0.0

5.0

10.0

15.0

20.0

25.0

30.0

1 0.9 0.8 0.7 0.6 0.5

Pressure [bar]

Sti

ffn

es

s[k

N/m

]

with 11,8 kg

With 18 kg

Figure B.4: Ball stiffness for different pressures and applied masses.

mg

Figure B.5: Schematic representation of the setup that was used in the experiment todetermine the stiffness of the ball.

Appendix C

SAM simulations

The models that were used to perform the SAM simulation of Chapter 4 are given in thisAppendix.

The models are simple kinematic diagrams of the kicking mechanisms. The coordinatesof the rotating and connection points are obtained from the part files of the design pro-grams. In Figure C.1 the initial positions for a flat and a lob shot of the current kickingmechanism are depicted. The plunger is the line which is indicated with 2©. In the de-sign the plunger is positioned under an angle of 10 ◦ with respect to the field. The wholemechanism is rotated 10 ◦ in the diagram, such that the plunger is horizontal. The SAMprogram only can handle horizontal and vertical linear motion inputs.

Figure C.2 shows the initial positions of the new kicking mechanism for both a flat and alob shot. The plunger is attached at point ’4’ and moves horizontal. This causes the rockerto rotate around point ’5’.

84 Appendix C. SAM simulations

Figure C.1: The SAM models of the current kicking mechanism for a flat (left) and alob (right) shot.

85

Figure C.2: The SAM models of the new kicking mechanism for a flat (left) and a lob(right) shot.

Appendix D

FEM results

D.1 Rocker

The collision force on the rocker is determined by Equation 4.1. The collision velocityvaries over the stroke of the plunger. The angular velocity of the lever for various situationswas depicted in Figure 4.21. The angular velocity of a lob shot is the highest, therefore thisvelocity is used in the simulation. With a length between the rotation point of the leverand the tip of the pin of 0.228 m, the velocity of the pin can be determined. The lever hasa mass of 0.25 kg. The stiffness of the lever is calculated as the stiffness of a cantileverof length l, which is the distance between the tip and the connection point of the rocker.This varies between 135 mm at the begin of the stroke and 73 mm at the end of the stroke.The cantilever becomes shorter during the stroke, because the connection point of therocker moves closer to the end of the lever. This increases its stiffness. The stiffness ofa cantilever is described by Equation D.1, where E is the Young’s modulus of aluminumand I is the first moment of area and is 1466 mm4.

c =3EIl3

(D.1)

The stiffness of the cantilever varies between 130 kN/m and 800 kN/m over the stroke ofthe plunger. The kicking lever will also bend between its rotation axle and the connectionpoint of the rocker. This will reduces the stiffness. If it kicks against another robot, it ismostly the protective plastic cover that is hit. The stiffness of this cover is in series withthe stiffness of the lever. This also reduces the replacement stiffness of the collision.

A stiffness of 100 kN/m is used in the simulations. Table D.1 shows the collision forceat several points along the stroke of the plunger. Also the maximum Von-Mises stress inthe rocker at that point of the stroke is given. In the simulation, the rocker is pin jointedat its rotation points at the base plate. At the point where it is connected to the plunger,the movement of the rocker in the direction along the axial axis of the plunger is fixed.The angle between the rocker and the plunger changes during the stroke, because of therotation of the rocker. The rocker is loaded at the point where it is connected to the lever.Also the angle under which the load is applied changes. The simulations show that thestresses in the rocker are the highest when the plunger has traveled 15 mm of its stroke.The rocker does not deform plastically if it is made of 6061-T6 aluminum. The stresses

88 Appendix D. FEM results

Table D.1: The force on the rocker and the resulting stresses in case of a collisionduring the stroke of the plunger.

Stroke [mm] Force [N ] Maximum Von-Mises stress [MPa]5 1370 13010 1900 18415 2350 20720 2450 17325 2425 16430 2275 10835 2125 10140 1800 8545 1625 7650 1375 6655 1100 3660 850 2665 575 19

in the rocker as a result of this plunger position are depicted in Figure D.1. The higheststresses occur at the point where the small top part of the rocker becomes wider.

D.2 Frame

This appendix shows the stresses in the Turtle’s frame as a result of the second, third andfifth load case discussed in Section 5.4.2.

D.2. Frame 89

Figure D.1: The Von-Mises stress in MPa in the rocker when the plunger has covered15 mm of its stroke.

Figure D.2: The Von-Mises stress in MPa in the frame as a result of the secondloadcase.

90 Appendix D. FEM results

Figure D.3: The Von-Mises stress inMPa in the frame as a result of the third loadcase.

Figure D.4: The Von-Mises stress inMPa in the frame as a result of the fifth loadcase.

Appendix E

Proposal for the position ofhardware components

In this appendix a proposal is made for the placement of the amplifiers, the ethercat mod-ule and the battery. This proposal depends on the battery that is going to be used. Theproposed positions are depicted in Figure E.1. There are seven amplifiers (1) placed onthe frame. Four of them are bolted to the vertical plates. Rivnuts provide the necessarythreaded holes. Two of these amplifiers can be seen in the lower Figure. The other two arebehind the battery (3) in the upper Figure. The rest of the amplifiers are mounted on thebase plate. The amplifiers are bolted to the base plate. To provide the necessary threadedholes, the base plate is thickened to five millimeter beneath the amplifier. The holes aredrilled in this thickening. The extra material also benefits the cooling of the amplifiers.The ethercat module and the battery are positioned at opposite sites of the frame. Theyhave more or less the same mass, therefore they balance each other.

92 Appendix E. Proposal for the position of hardware components

1

2

1

3

1. Amplifier 2. Ethercat module 3. Battery

Figure E.1: Proposal for the position of the amplifiers, ethercat module and the batteryon the Turtle.

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