3s.ramasamy and m.r.arshad

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ROBOTIC HAND SIMULATlON WITH KINEMATICS AND DYNAMIC ANALYSISS.Ramasamy and M.R.ArshadSchool of Electrical and Electronic EngineeringUniversity of Science, Malay sia (Perak Branch Cam pus),

Perak Darul Rid zuan, Malaysia.r i za l neng .usm. inyAbstract:Robotics is a technology tha t is utilised tremen douslyin industrial and com mercial app lications. Different types o frobots are designed to fulfill the human needs. The aim ofthe work presented in this pape r is to simulate a robotic handthat emulate the shape and performance of a human hand(i.e. palm and fingers section). The robotic hand comprisesof five fingers, which each of them has three degree offreedoms (DOF) and 2 DOF for the thumb. This robotichand simulation is divided into three main parts. The mainobjective is to design a three dimensional graphic of arobotic hand and its movement animation that imitates themovement of a human hand. This graphic design is thenused as a foundation to find the kinematics and dynamicproperties of the robotic hand. The end result is a robotichand simulation that comes with analyses of the kinematicsand dy namic properties.Keywords: robot simulation, kinematics, 3D graphics

1. INTRODUCTIONThe robotic hand is an imitation of a human handthat consists of a palm and five fingers, i.e. a thumb, anindex finger, a middle finger, a ring finger and a pinkyfinger. Its simulation is done by considering each fingertogether with the palm as a single end-effector. So, everyfinger has a five degree-of-freedoms. The robotic handsimulation is divided into three parts. Th e main ob jective ofdesigning a 3D graphics is done using a software called 3 0Studio MaxTM 3DS Max) . This graphics of a 3-dimensionalrobotic hand is then used in another software called Maya3DTM o be animated into movements. The graphicalanimation produced is related, in the sense of the fun ction, tothe kinematics and dynamic simulation of every finger using

MatlabTM. n applying the coordinates or angles to everyjoint in the hand, produced the motion of the robotic hand.This coordinates or angles are then used as the ready posecoordinate in the Matlab program to find the kinematics anddynam ic properties an d vice versa [ I ]11. THEORY AND DESIGN PROCEDURE

A. 3D Graphical DesignThe objective of 3D graphical design is to producea real representation of the robotic hand in the virtual realityworld [ 2 ] . t can be divided into two main section s, 3 0

0-7803-6355-8/00/ 10.0002000 IEEE

Studio Max and M a y a 3 0 . 3 0 studio M a r is a software or atool that can be used to design quali ty 2D and 3D objects.The comerstone of 3DS Max is an integrated modelingenvironment that performs 2D drawing, 3D modeling andanimation within the unified workspace. Modeling, editingand animation tools are always available in the commandpanels and toolbar.3DS Mar provides a sophisticated material editorin a floating window. It is used to create realistic materialsby defining hierarchies of surface characteristics. Thesurface characteristics can represent static materials or canbe animated for special effects. Lights with variousproperties can be created to illuminate the designed scene.The lights can cast shadow, project images and createvolumetric effects for atm ospheric lighting. Cameras that arealso created, have real-world controls for lens length, field ofview and motion control.A bone s system is used at the joints of the robotichand as it is a jointed h ierarchical linkage of bone objectsthat demonstrates kinematics. Each bone is a parametricwireframe object. In 3DS Max, the bones system forms thebasis for the New IK(1nverse Kinematics). Using thisfeature, bones with an IK controller can be created to applyIK solutions procedurally across all frames [3].Rendering of the robotic hand is done using therendering toolbox in the main window. The 3D S maxrenderer includes features such as ray tracing, analyticalantialiasing, motion blur, volumetric lighting andenvironm ental effects. The robotic hand designed using 3DSMax with the Bones applied is as shown in Fig. IMayu 3 0 is a time-based animation program. Itcan animate any parameters in the scene; in the case of arobotic hand, the parameter involved is called bend angle.One minute of animation might require between 720 and1800 separate images, depending on the quality of theanimation. Creating a lot of images may take time, so thekeyframing technique is used. Keyframes are created torecord the beginning and end of each animated sequence.The values of these keyframes are called keys. Maya 3 0calculates the interpolated values between each ke y toproduce the completed animation. It measures time andstores the animation values a t 1/4800 of a second. Animationis produced by turning on the animate button, setting acurrent time and changing some parameters in the createdscene. Chang es also can be do ne to the position, rotation, orscale of an object or cha nge alm ost any setting or parameter.When the animate button is turned on, the time slider in theanimation wind ow sets the time where k eys are created.

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Figure I The robotic hand design with BonesB: Kinematics of a Robotic Hand

Kinematics properties considered are Denavit-Hartenberg parameter (i.e. translation and rotation), Euferangles, direct kinematics, inverse kinematics, Jacobianmatrix and singularity function. These properties are usedto find the joint parameters (i.e. coordina tes and spe ed) inthe trajectory, hom ogenou s transformation of the robot andsingularity of every joint [4].Denavit-Hartenberg parameter is a systematicway of representing coordinates of a robotic arm using amatrix method. Each joint in a robot is considered to beone degree-of-freedom. For robot with n joints, countingfrom 1 to n, here are n l arms counted from 0 to n Link0 is the base of the robot and the i-th joint connects i-tharm to the i - I . The Denavit-Hartenberg Parameters ar e :link lengfh, ai - distance between zi.] axis and zi axis along xi axislink twist, i - angle between zc1 axis and ti axislink offset di - distance from origin for i-1-th arm to x i axisalong zi- axisj o i n t angle, 8 , -angle between xi.]axis and xi axis

Rotation and translation are two basicmovements of a robot. The movement of this robotic handonly involves rotation. Th ree types o f rotations a re :ro - rotation around z-axis with angle Qpitch - rotation around y-axis with angle eyaw - rotation around x-axis with angle Y

These three angles are also called Eufer angles and areused to find coordinate orientation of a robotic arm.According to Euler s Law, any rotation can be representedby the m atrix R which is :

To find the homogenou s transformation matrix that showsthe coordinate of i-th frame of a robotic arm according tothe coordinate system of the arm before, 'Ti, Equation 2)are used

(2)T. = T. - A lwhere,frame relative to the i-I-th frame- Ai represents the displacemen t of the i-th

Direct kinematics method are used is order tofind the displacement and orientation of an end-effectorrelative to the base fram e, as a function of jointdisplacement. By doing multiplication to the Equation ( 2 ) ,the equation for the displacement of every finger in therobotic hand is obtained :

Inverse kinematics is the inverse to the directkinematics solution. It is used to find the join t anglesneeded to achieve a particular end coordinate. For that

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purpose, the inverse of the homogenous transformationmatrix in Equation (3) need to be find using the equationbelow :g = k-' ( T I (4)

The velocity relationship between frames canbe changed into differential form. The differential changein the orientation of an end-effector as a function of all njoint coordinates can be written into a 6 x n matrix, calledJacobian Matrix. The Jacobian relationship in the form dfmatrix for a prismatic and revolute joint is given by (5),i.e.XI x x ... xr Y, Y, . . Y,z, z z, ... z1 , '2 '3 * S . n x

1, 2, '3y * * e nye,: e,: e,: ... en:

CFG gravity force

explains the Coriolis and c entripetal effectshows the viscosity and Coulomb force

Furthermore, the torque needed for a set ofjoint angle, velocity and acceleration can be found. It isimportant as it can be used to find the kinematicsproperties such as angle velocity, angle acceleration andlinear accelerat ion. This is done ushg Newton-EulerFormulation. The equation used is called Euler Equation :

z = I d x I d (7)where ,I inertia tensorangle velocity

I CL. angle momentum

111. RESULTSwhere,

q = 62qi = dix.

or a revolute ointfor a prismatic joint68,8 . =a; IX q;X

C. Dynamics of a Robotic HandDynamic property of a robot is mentioned as thechanging rate of arm configuration depending on thetorque at a joint produced by the actuator. Dynamics of arobot explains the equation for a movement, that is the wayof the movement when a force is applied. There are twomethods that can be used to find the movement equation;Newton-Euler and Lagrangian Formulation [5].

Inverse dynamics is used to determine thetorque to be applied on a robotic arm to produce thedesired movement. The input that is inserted is the desiredtrajectory in the time function o f q,(t) through qn(t), whilethe output is the joint tor que to be ap plied by the a ctuatorto follow the trajectory. Th e value o f this torque isdetermined using the equation below := M f 8 ) 8 C f 8 , e ) e + F f ( 8 ) + G ( 8 ) (6)

where, e,, ..... 0. is the joint angle vector of thefingers in the robotic hand6 joint angle velocity vector

A . 3D Graphical DesignSom e results of the 3 D graphical design(created using the graphics softwares) displaying a fewposition and movements for the robotic hand are shown inthe appendix.

B. Kinematics and Dynamic PropertiesKinematics and dynamic properties of therobotic hand are simulated using the robotic toolbox in

Matlub simulation software [6] With the input of start andend coordinates, and also joint coordinates in the desiredtrajectory, the other properties such as velocity,acceleration and torque are determined. One example ofsimulation for the index finger (including palm of the handand the elbow as the base) are as shown below :1. Start coordinate, qZ = 0 0 0 0 02 End coordinate,qr = 1.5708 0 0.7854 0.7854 0.7854 (in radian)

3. Joint coordinate,q = 0 0 00.3297 0 0.1648 0.1648 0.16481.2411 . 0 0.6206 0.6206 0.62061.5708 0.7854 0.7854 0.7854

8 jo int angle acceleration vectorM robot inertia tensor

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4. Homogenous transformation,T = -1.0000 0.0000 0 0.0374-0.0000 -0.0000 1 OOOO 4.00000.0000 1 OOOO 0.0000 -0.05250 0 0 1.00005 . Velocity,

q d = 0 0 0 0 01.3852 0 0.6926 0.6926 0.69261.3852 0 0.6926 0.6926 0.69260 0 0 0 06. Acceleration,

q d d = 0 0 0 02.4735 0 1.2368 1.2368 1.2368-2.4735 0 -1.2368 -1.2368 -1.23680.0000 0 0.0000 0.0000 0.00007. Torque for every joint,

= 1.0e+003-0.0000 0.0310 -0.0051 -0.0027 -0.00101.3312 0.0342 -0.0023 -0.0000 -0.0001-1.3302 0.0294 -0.0063 -0.0026 -0.00090.0000 0.0355 -0.0006 0.0015 0.0007

8. Torque caused by gravity,= -0.0000 31.0453 -5.1204 -2.7164 -0.9702-0.0000 3 1.4568 -4.7090 -2.2286 -0.8540-0.0000 34.3480 -1.8177 0.5242 0.2783-0.0000 35.5398 -0.6260 1.5434 0.6860

IV. DISCUSSION AN D CONCLUSIONThe graphical design of a robotic handsimulation using 3 0 Studio Max and Maya 30 can be usedto relate to the actual kinematics and dyn amic properties of

a robotic hand. Since the coordinates that are used indesigning certain graphics position and movements areportable, i.e can be extracted, it can be used in motionsimulation using Matlab simulation function, and viceversa. By exploiting this approach, we are able tofind the properties such as velocity, acceleration andtorque for a desired movement or coordinates of therobotic hand graphics. One problem still has to be tackledis when the robotic hand is not able to move according tothe desired trajectory. So, trajectory planning is alsoimportant in designing a robotic arm so it can proceed thetask given correctly. For this to happen, every parameterused should be accurate and according to the correctparameters. Many questions and obstacles were met whileaddressing this problem, mainly in how to optimallyinterface the graphics and mathematical softwares, and toconsider all relevant parameters in translating thetheoritical understanding to actual simulation. It is hopethat the results presented in this paper will be helpful inutilising the existing graphic softwares for conductingrobotic hand simultion, and understanding how to relate

the kinematic and dynamic analysis to the actualsimulation procedure.V. REFERENCES

[11 Biran, A., Breiner,M., Matlab For Engineers,Addison-Wesley Publishing Co., Harlow, 1996.[2] Ranky, P.G., Ho, C.Y., Ro bot Modelling, ControlAnd Applications with Software, IFS Publications, NewYork, 1985.[3] Kinetix, 3D Studio Max Users Guide, Autodesk,Inc., Berlin, 1997.[4] Asada,H. and Slotine,J.J.E., Robot Analysis andControl, Wiley Interscience Publication, New York,1986.[ 5 ] Murray, R.M., Zex iang Li, Sastry, S S RobotManipu lation, CRC Press, Florida, 1994.[6] Etter, D.M., Enginee ring Problem Solving withMAT LAB, Prentice-Hall,lnc., New Jersey, 1993.

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VI APPENDIX

Figure 3 Top view o f robotic hand rendered)

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Figure 6 Side view rendered)

Figure 7. Side view rendered)

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3s.ramasamy and m.r.arshad

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