first class lever

To do in classTo do in class

• Mechanical design is an important component of this class – how it relates to your project

• What you want to learn?

• What you plan to do?

Kinematics

• The study of motion without regard without regard to the forces or mass of the things moving.

• Kinematic diagrams are scaled drawings symbolizing how mechanisms work.

• We studied robot kinematics in Fall but we did not take into account forces.

1. Gears2. Pulleys3. Chains4. Cams5. Bearings6. Wheel and Axle7. Inclined Plane8. Wedge9. Screw10. Lever11. Cranks and sliders12. Ratcheting mechanisms13. Clutches14. Brakes

Examples of machines

MachinesMachines and Tools1. Machines and tools are mechanical devices

that work by transmitting or converting energy.

2. Machines are made up of a variety of mechanisms.

3. What are some examplesexamples of machines?

Simple MachinesSimple Machines

LeverPulley Wheel and Axle

WedgeScrew

Inclined Plane

All of these are related to robotics. Think how?

Mechanisms1. Mechanisms help extend human capability by

creating some desired output or motion.

2. A mechanism takes an input motion or force and creates a desired output motion or force.

MECHANISMMotion or force

Motion or force

Types of Motion

• Common types of motion:– Linear– Reciprocal– Rotary– Oscillating

All these have applications in robotics

Energy: Ability to do work

Work= Force x Distance

Force: A Push or a Pull

Definitions:Definitions:

LinkagesLinkages

mot

or

Rotating ArmsRotating Arms

Torques are large

Use counterweights and gears to compensate

Attach the gear to the arm

Attach the motor to the robot driven gear

gear

bolted to arm

counter weight

Role of Linkages

• Linkages transmit the motion or force to the desired output location.

• Linkages:Linkages:1. change the direction of the force2. Change the length of motion of the force3. Split the motion and force over multiple paths

LeversLevers

LeverLever– Downward motion at one end results in upward motion at the other end.

– Depending on where the pivot point is located, a lever can lever can multiplymultiply either the force applied or the distance over which the force is applied

http://www.csmate.colostate.edu/cltw/cohortpages/viney/balance.html

Pivot point, fulcrum

Simple Lever MachineSimple Lever MachineExplanation

• This simple machine is based on the position of the effort force, resistance force, and fulcrum.

• First class lever– FulcrumFulcrum located between effort force and

resistance force– Usually used to multiply a force– ExampleExample: Seesaw

R

F E

This kind changes the direction of force.

length1 length2

Effort force

Resistance force

R * length1 = E * lenght2

Simple Experiment: Balancing Act• Using only a meter stick and a wooden block, balance two

masses in a seesaw kind of structure.

• How did you get them to balance?– Could you do it in one try?

• Compare your setup with other possible setups

Engagement

This is useful in

robot arm design

Do this by yourself, not in class

Lever Forces

Exploration

• Materials– Computer/calculator– Force Probe– 500g mass– String– Meter stick– Wooden Block

Simple Experiment: Balancing Act

High school robotics

Lever ForcesExploration

• Measure the Weight of the 500g mass (in Newtons).

• Balance the middle of the meter stick on the wooden block.

• Place the 500g mass at the 90 cm line.

• Attach the string to the meter stick at the 10 cm line.

• Attach the string to the force meter and pull down on the sensor until the meter stick is balanced.

• Record the force needed to balance the meter stick.

• Repeat the above steps with the 500g mass at the 70 cm line and the 60 cm line.

Simple Experiment: Balancing Act

Lever Forces

Exploration

• After recording your data in a table, perform the following calculations for the three trials:

– Divide the weight of the 500g mass by the force required to balance the meter stick.

– Divide the distance between the force meter and the wooden block by the distance between the 500g mass and the wooden block.

• How do these numbers compare?• What do these numbers indicate about the

lever system?

Simple Experiment: Balancing Act

Why use a Simple Machine?Why use a Simple Machine?Explanation

• Simple Machines make work easier by giving the user a mechanical advantage.

• How do we calculate the mechanical advantage for a lever system?

• Ideal Mechanical Advantage (IMA) = Leffort / Lresistance

• Why do we stipulate that the MA is ideal? Because we’ve assumed that the machine puts out exactly as much work as we put in. This implies 100% efficiency

• This situation is never possible…why?

Leffort is the distance between the effort force and the fulcrumLresistance is the distance between the resistance force and the fulcrum

100% efficiency is never possible because of FRICTION.

Mechanical Mechanical Advantage = MAAdvantage = MA

Lever ExampleExplanation

• A worker uses an iron bar to raise a manhole cover that weighs 90 Newtons. The effort arm of the bar is 60 cm long and the resistance arm is 10 cm long.

• Draw a picture of this scenario

• Calculate the IMA of the lever systemIMA = Le/Lr = 60 cm/ 10cm = 6

• What force would the worker need to apply to lift the manhole?

90 N?

• We need 90 N of force to lift the manhole cover, but we have a mechanical advantage of 6.

• Now we only need 15 N of force to lift the manhole.

Three Three Classes of Classes of

LeversLevers

“First Class Lever”• A first-class lever is a lever in

which the fulcrum is located between the input effort and the output load.

• In operation, a force is applied (by pulling or pushing) to a section of the bar, which causes the lever to swing about the fulcrum, overcoming the resistance force on the opposite side.

• The fulcrum may be at the center point of the lever as in a seesaw or at any point between the input and output.

• This supports the effort arm and the load.

Examples:•Seesaw•Scissors (double lever)

Classes of LeversClasses of Levers

Fulcrum is between EF (effort) and RF (load)Effort moves farther than Resistance. Multiplies EF and changes its direction

The mechanical advantage of a lever is the ratio of the length of the lever on the applied force side of the fulcrum to the length of the lever

on the resistance force side of the fulcrum.

First Class LeverFirst Class LeverfulcrumEffort

Resistance

Common examples of first-classfirst-class levers include – crowbars, crowbars, – scissors, scissors, – pliers, pliers, – tin snips tin snips – and seesawsand seesaws.

Examples of first class levers

RF (load) is between fulcrum and EF Effort moves farther than Resistance.

Multiplies EF, but does not change its direction The mechanical advantage of a lever is the ratio of the distance from the applied force to the fulcrum to the distance from the

resistance force to the fulcrum.

Second Class LeverSecond Class LeverEffortEffortResistance

Three Lever ClassesExplanation

• Second class lever– Resistance is located between the effort force and the fulcrum. – Always multiplies a force

– Example: Wheelbarrow

R

F

E

Always multiplies a force.

“Second Class Lever”

In a second class lever the input effort is located at the end of the bar and the fulcrum is located at the other end of the bar, opposite to the input, with the output load at a point between these two forces.

Examples:•Paddle•Wheelbarrow•Wrench

Examples of Second class levers

• Examples of second-class levers include:

• nut crackers, nut crackers, • wheel barrows, wheel barrows, • doors, doors, • and bottle and bottle

openersopeners.

Examples of second-class levers

EF is between fulcrum and RF (load) Does not multiply force

Resistance moves farther than Effort. Multiplies the distance the effort force travels

The mechanical advantage of a lever is the ratio of the distance from the applied force to the fulcrum to the distance of the

resistance force to the fulcrum

ThirdThird Class Lever

• For this class of levers, the input effort is higher than the output load, which is different from second-class levers and some first-class levers.

• However, the distance moved by the resistance (load) is greater than the distance moved by the effort.

• In third class levers, effort is applied between the output load on one end and the fulcrum on the opposite end.

““Third Class Third Class Lever”Lever” Examples:

•Hockey Stick

•Tweezers

•Fishing Rod

Classes of Levers

Three Lever ClassesExplanation

• Third class lever– Effort force located between the resistance and the fulcrum. – Effort arm is always shorter than resistance arm– MA is always less than one

– Example: Broom

R

F

E

There is an increase distance moved and speed at the other end.Other examples are baseball bat or hockey stick.

Examples of Third Examples of Third Class Levers

• Examples of third-class levers include:– tweezers, tweezers, – arm arm

hammers, hammers, – and shovels.and shovels.

Third class lever in human body.

Natural Levers Natural Levers in Human Bodyin Human Body

Natural LeversNatural LeversElaboration

• Identify an example of a 1st class lever in the human body

Remember to relax the body and feel the muscle groups working to move the bones

Example of first class lever in human body

Natural Levers• Identify an

example of a 2nd class lever in the human body

Elaboration

Remember to relax the body and feel the muscle groups working to move the bones

Second class lever in human body

Natural Levers• Identify an example of a 3rd class lever in the human body

Elaboration

Remember to relax the body and feel the muscle groups working to move the bones

Mechanical AdvantageMechanical Advantage• Mechanical Advantage Mechanical Advantage is the ratio between the

load and effort.

• Mechanical Advantage Mechanical Advantage deals only with forces.

• Mechanical Advantage > 1 > 1 means that the output force will be greater than the input force. – (But the input distance will need to be greater than the

output distance.)

•First and Second class levers have a positive mechanical advantage.

•Third class levers have a mechanical disadvantagedisadvantage, , meaning you use more force that the force of the load you lift.

Mechanical AdvantageMechanical Advantage

Velocity RatioVelocity Ratio• Velocity Ratio deals with the distance gained

or lost due to a mechanical advantage.

• Velocity Ration >1 means that the input distance (or effort) to move a load will be greater than the output distance of the load.

Mechanical Advantage: Example

Mechanical Advantage = effort arm resistance arm

Crazy Joe is moving bricks to build his cabin.

With the use of his simple machine, a lever, he moves them easily.

The “effort arm” of his wheel barrow is 4ft., while the resistance arm of his wheelbarrow is 1 ft.

4/1 is his mechanical advantage. MA= 4.

How the Lever How the Lever changes the Force?changes the Force?

“The length of the effort arm is the same number of times greater than the length of the resistance arm as the resistance to be overcome is greater than the effort you must apply.”

Plugging these into an equation gives you the change in force by using a lever.    whereL = length of effort arm,l = length of resistance arm,R = resistance weight or force, andE= effort force.

One convenience of machines is that you

can determine in advance the forces

required for their operation, as well as the forces they will

exert.

F o r c e C h a n F o r c e C h a n g eg e• Suppose you want to pry up the lid of a paint can with a 6-inch file scraper, and you

know that the average force holding the lid is 50 pounds. • If the distance from the edge of the paint can to the edge of the cover is 1 inch,

what force will you have to apply on the end of the file scraper?

L = 5 inchesl = 1 inchR = 50 pounds, andE is unknown. = 10 pounds

• You will need to apply a force of only 10 pounds.

Compound machine:Can Opener

Simple machines1. lever2. wheel and axel3. gear4. wedge

Where can I find levers?

There are as many as 4 simple machines in a stupid CAN OPENER!

Compound Machine:Stapler

Simple Machines:-Lever-Wedge

Where can I find levers?

Every complex mechanism can be decomposed to a network of simple machines

Compound Machine:Wheelbarrow

Simple Machines:-Lever-Inclined Plane-Wheel and Axel

Where can I find compound machines?

Wheelbarrow

Levers and Linkages: Conclusions

• Fulcrum• Load• Effort• Classes

– First– Second– Third

Concepts discussed

Understanding of levers and linkages is important for those who build robots, especially humanoids

Rotary Rotary MechanismsMechanisms

Rotary MechanismsRotary Mechanisms• Gears, Pulleys, Cams, Ratchets, Wheels, etc.

• These rotary mechanisms rotary mechanisms transfer of change input rotational motion and force to output motion and force.

• Output force can be either rotational or reciprocating.

Rotary mechanismrotational motion and force rotational or reciprocating motion

and force.

Belts/Pulleys & Chains/Sprockets

• Use belts and chains to convert motion and force.

• Uses same measures of Mechanical advantage and Velocity Ratio as gears.

Inclined Inclined PlanePlane

Inclined PlaneInclined Plane– Sloping surface used to lift heavy loads with less effort

http://www.sirinet.net/~jgjohnso/simple.html

Inclined Plane in antiquity

Inclined Plane - Egyptians• The Egyptians used simple machines to build the pyramids. • One method was to build a very long incline out of dirt that

rose upward to the top of the pyramid very gently. • The blocks of stone were placed on large logs (another type of

simple machine - the wheel and axle) and pushed slowly up the long, gentle inclined plane to the top of the pyramid.

Inclined Plane Principles• An inclined plane is a flat

surface that is higher on one end

• Inclined planes make the work of moving things easier

A sloping surface, such as a ramp. An inclined plane can be used to alter the effort and distance involved in doing work, such as lifting loads. The trade-off is that an object must be moved a longer distance than if it was lifted straight up, but less force is needed.You can use this machine to move an object to a lower or higher place.  Inclined planes make the work of moving things easier.  You would need less energy and force to move objects with an inclined plane. 

• A sloping surface, such as a ramp. • An inclined plane can be used to alter the effort

and distance involved in doing work, such as lifting loads.

• The trade-off is that an object must be moved a longer distance than if it was lifted straight up, but less force is needed.

• You can use this machine to move an object to a lower or higher place. 

• Inclined planes make the work of moving things easier. 

• You would need less energy and force to move objects with an inclined plane. 

Inclined Plane -Inclined Plane -Mechanical AdvantageMechanical Advantage

• The mechanical advantage of an inclined plane is equal to the length of the slope divided by the height of the inclined plane.

• While the inclined plane produces a mechanical advantage, it does so by increasing the distance through which the force must move.

Work input and outputWork input and output• Work input Work input is the amount of work done on

a machine. – Input force x input distance

• Work output is the amount of work done by a machine.– Output force x output distance

15 m

3 m

Wout = Win

Fout x Dout = Fin x Din

10N x 3m = 2N x 15m 10 N Fin

DinDout

ScrewScrew

ScrewScrew

The mechanical advantage of an screw mechanical advantage of an screw can be calculated by dividing the circumference by the pitch of the screw.

Pitch equals 1// number of turns per inch.

A screw is an inclined plane wound around a central cylinder

ScrewScrew– ConvertsConverts a rotary motion into a forward or

backward motion

http://www.sirinet.net/~jgjohnso/simple.html

WedgesWedges

WedgeWedge– Converts motion in

one direction into a splitting motion that acts at right angles to the blade

– A lifting machine may use a wedge to get under a load

http://www.mos.org/sln/Leonardo/InventorsToolbox.html

Wedges• Two inclined Two inclined

planes planes joined back to back.

• Wedges are used to splitsplit things.

Wedge – Mechanical AdvantageMechanical Advantage

• The mechanical advantage of a wedge can be found by dividing the length of either slope (S) by the thickness (T) of the big end.

S

• As an example, assume that the length of the slope is 10 inches and the thickness is 4 inches.

• The mechanical advantage is equal to 10/4 or 2 1/2.

• As with the inclined plane, the mechanical advantage gained by using a wedge requires a corresponding increase in distance.

TS/TS/T

For Example…• Assume that the length of the slope (S) of a wedge

is 12 inches and the thickness (T) is 3 inches. • MA = S/T• MA = 12 inches/3 inches• MA = 4

How Does a Wedge Change the Force?

• Wedges change the direction of an applied force.

• When force is applied downward on a wedge, it distributes the force outward in two directions, separating a material.

Example of mechanical advantageExample of mechanical advantage

• A box is lifted by two supporting ropes. What is the mechanical advantage?

• MA=number of supporting ropes

• MA=2

Compound Compound MachinesMachines

… more examples of …

Compound Machine #1• Bowflex: Pulley lifts the weight, the seat is an

inclined plane, and the lever is what you pull to adjust the seat

Compound Machine #2

• Crane: Crane: The lever is the horizontal beam that lifts the object, the pulley is used to make the rope tight so that it is easier for the crane to lift the object

Compound Machine #3• Ski LiftSki Lift: It is an

inclined plane to travel up a mountain.

• The pulleypulley is used to pull the ski lift to the top of the mountain

A Wedge in a A Wedge in a Compound Machine: Compound Machine:

StaplerStapler• Staples are wedges: they cut through paper because their ends are pointed in a wedge shape.

• There are two simple machines in a stapler:1.1. WedgeWedge2.2. LeverLever

Examples of compound machinesExamples of compound machines

A Wedge in a Compound Machine: Can Opener

• The cutting edge of a can opener cuts through metal because it is shaped like a wedge.

• Simple machines in a can opener:– Wedge– Lever– Gear– Wheel and axle

Examples of compound machinesExamples of compound machines

A Wedge in a Compound A Wedge in a Compound Machine: ScissorsMachine: Scissors

• The cutting edge of The cutting edge of scissors is a wedge.scissors is a wedge.

• Simple machines in Simple machines in a pair of scissors:a pair of scissors:– WedgeWedge– LeverLever

Examples of compound machinesExamples of compound machines

1. Gears2. Pulleys3. Chains4. Cams5. Bearings6. Wheel and Axle7. Inclined Plane8. Wedge9. Screw10. Lever11. Cranks and sliders12. Ratcheting mechanisms13. Clutches14. Brakes

Questions to Questions to students:students:

1. Explain the following concepts

2. Give examples of each

3. How each can be used in robotics?

1. Give definitions of energy, work and force2. Give examples of these types of motion in robotics:

– Linear– Reciprocal– Rotary

3. Oscillating4. What are linkages?5. What are the types of linkages?6. Give examples of different types of linkages?7. What is a lever?8. Explain the definitions and give examples of three

classes of levers.

1. Give definition of mechanical advantage2. Give examples of mechanical advantages in simple

machines such as various classes of levers.3. Give at least three examples of compound

machines.4. What are Parallel Linkages, Treadle Linkages amd

Toggle Linkages5. What is a rotary mechanism?6. Describe a humanoid arm as a compund machine.7. The same for a leg8. The same for a torso9. The same for a head and neck combination.

Questions.

1. How much effort will be needed to lift a 100 pound load if distance to effort is five feet and distance to resistance is one foot?

2. How much effort will be needed to lift a 48 pound load if distance to effort is two feet and distance to resistance is 8 feet?

Project RelatedProject Related1. Create a kinematic model of your robot2. Relate it to pulleys, gears, levers,

linkages, etc3. Perform simple calculations related to

torque, speed and power

Philosophy

• Be able to see and appreciate simple machines around you

• Be able to steal every idea for your robot.

• http://en.wikipedia.org/wiki/LeverI got the three types of levers, examples and their functions. (used)

• http://www.tpub.com/machines/1c.htmI got the formula for mechanical advantage and example. (used)

• http://www.edheads.org/activities/simple-machines/frame_loader.htm

I found a list of compound machines and how simple machines were used in them. (used)

• http://www.coe.uh.edu/archive/science/science_lessons/scienceles1/lever.htm

I found examples of levers and how they work.

BibliographyBibliography

Bibliography• http://dictionary.reference.com/browse/

wedge• http://www.uark.edu/depts/aeedhp/

agscience/simpmach.htm• http://www.sciencetech.technomuses.ca/

english/schoolzone/Info_Simple_Machines2.cfm

• http://www.edheads.org/activities/simple-machines/frame_loader.htm

• http://www.teachervision.fen.com/machines/printable/45019.html

Bibliography

• http://library.thinkquest.org/27948/pulley.html – This site explains the use of the pulley system. Also

provides an equation to figure out the force needed to lift an object with the pulley.

• *http://library.thinkquest.org/J002079F/pulley.htm – This site defines a pulley and explains how it makes lifting

easier. This site also shows simple examples of pulleys.

• http://www.science.jrank.org/pages/4060/Machines-Simple.htmlI used this site to find mechanical advantages, examples, and how a basic lever works.

Bibliography (Cont.)*http://en.wikipedia.org/wiki/Pulley

– This site gave the definition of a pulley, different types of pulley systems, and explains how these systems work.

• http://www.swe.org/iac/lp/pulley_03.html – This site gives a detailed explanation about pulleys. It shows how it

was invented, by whom it was invented, and provides pictures to show how a pulley works.

• *http://library.thinkquest.org/CR0210120/MA%20of%20PS.html – This site showed how to get the mechanical advantage for a pulley.

Sources

Shawni YeagleyNate Yavoich

Raquel y Victoria