PULLEYBLOCK AND TACKLECompound Drive Pulley Trains

PulleysPulleys

Building Building Drive Drive Robot Robot TrainsTrains

Building Robot Drive Trains1. Building Robot Drive Trains is the first volume in the

new "Robot DNA" series by McGraw-Hill/TAB Electronics.

2. It is just what robotics hobbyists need to build an effective drive train using inexpensive, off-the-shelf parts.

3. Leaving heavy-duty “tech speak” behind, the authors focus on the actual concepts and applications necessary to build – and understand -- these critical force-conveying systems.

4. If you want a clear, straightforward guide to the nuts-and-bolts of drive trains, this is the way to go.

Building Robot Drive Trains• Chapters include:

• The Basics of Robot Locomotion * • Motor Types: An Overview * • Using DC Motors * • Using RC Servo Motors * • Using Stepper Motors * • Motor Mounting * • Basic Motor Control * • Advanced Motor Control * • Electronics Interfacing * • Wheels and Treads * • Locomotion for Multipods * • Glossary of Terms, Tables, Formulas * 75 illustrations

PulleysPulleys

• Pulley are wheels and axlesaxles with a groovegroove around the outside

• A pulley needs a rope, chainchain or beltbelt around the groove to make it do work

Lifting PulleysLifting Pulleys• Lifting Pulleys in transmission

systems–Single pulley–Moveable pulley–Block and Tackle

Pulley ExamplesPulley Examples• Reverses the

directiondirection of force• Two or more pulleys Two or more pulleys

connected together permit a heavy load to be lifted with less with less forceforce

http://www.sciencemuseum.org.uk/on-line/leonardo/InventorsToolbox.asp

Fixed Pulley:Fixed Pulley:•Wheel attached to surface

•Changes the direction of the applied force

•NO mechanical advantage – same amount of force is required

Fixed (single) pulleyFixed (single) pulley

Single Pulley

• The resistance arm and the effort arm are both the radius of the pulley.

• Since they are equal, there is no mechanical advantage.

100 ft

100 lbs 100 lbs

100 lbs

100 lbs

Single PulleySingle Pulley• Provides change of

motion, but no mechanical advantage

Movable PulleyMovable Pulley:

• Pulley moves along the rope

• Wheel supports the load

• Effort is in the same direction as movement

• Reduces the forces needed to move an object

Movable pulleyMovable pulley

MA in a Moveable pulley

• A moveable pulley is a second-class pulley.

• The effort arm is the diameter and the resistance arm is the radius.

• MA = dE ÷ dR

• MA = 2 ÷ 1 = 2Mechanical Advantage = 2Mechanical Advantage = 2

Another Moveable pulleyAnother Moveable pulley• Provides change of direction and a mechanical

advantage of 1:2 (at the expense of having to increase the amount of line to pull)

50 lbs 50 lbs50 lbs

50 lbs100 lbs100 lbs

These kinds of diagrams are easier to analyze

http://www.swe.org/iac/LP/pulley_03.html

In the second picture, the weight is

held by two ropes instead of one. That means the weight is

split equally between the two

ropes, so each one holds only half the

weight.

Combined (double) Combined (double) PulleyPulley:

•Has at least two wheels

•The more complex the pulley, the more the effort needed to move the object decreases

COMBINED PULLEYCOMBINED PULLEY

COMBINED PULLEY

• The effort needed to lift the load is less than half the weight of the load.

• The main disadvantage is it travels a very long distance.

Mechanical Advantage

• Mechanical Advantage is the same as the number of ropes number of ropes supporting the object

MA=2 MA=2 MA=4

How How about about these?these?

Calculate MA for these and similar

Illustration of Efforts and Loads on Illustration of Efforts and Loads on pulleyspulleys

Calculate MA

Pulley Pulley CalculationsCalculations

Pulleys as used in robots

• A pulley is basically a wheel with a groove in the circumference of the wheel, with a belt or cable being fed around the groove.

• Pulleys create a mechanical advantage by connecting a small input drive pulley to a larger follower with a belt.

Driver(Effort)

Follower(Resistance)

Mechanical Advantage of Mechanical Advantage of a Pulley Drive Traina Pulley Drive Train

MA = FOLLOWER ÷ DRIVER

• The Pulley Drive Train above produces an MA of 4. This means 10 lbs of input torque will create 40 lbs output, but the driver must rotate 4 times to rotate output 1 time. Speed is reduced by 4.

Driver1mm

Follower4mm

Mechanical AdvantageMA = FOLLOWER ÷ DRIVER

Driver3mm

Follower9mm

Driver2mm

Follower14mm

Increasing Speed

• Increase the speed of the output by using a larger driver gear and a smaller follower gear. Speed increases and power decreases.

Driver4mm

Follower1mm

Compound Drive Pulley Trains• A Compound Drive Pulley Train has pairs of pulleys

working in combination, with the follower of one pulley sharing the same axle as the driver of the next sequential pulley train.

Example 1: Compound Drive Pulley Trains

MA = (FOLLOWER 1 X FOLLOWER 2) ÷ (DRIVER 1 x DRIVER 2)

– Driver 1 = 2mm Follower 1 = 8mm– Driver 2 = 3mm Follower 2 = 9mm

Calculate MA (8*9)/(2*3) = 72/6 = 12)

MA = (FOLLOWER 1 X FOLLOWER 2) ÷ (DRIVER 1 x DRIVER 2)

– Driver 1 = 3mm Follower 1 = 9mm– Driver 2 = 2mm Follower 2 = 14mm

Example 2: Compound Drive Pulley Trains

Calculate MA

Problem 2

• Sketch the following two pulley trains:– A: Simple pulley train with belt wrapped

so both pulleys rotate in same direction.– B. Simple pulley train with belt wrapped

so both pulleys rotate in opposite direction.

Solution to Problem 2

• A: Simple pulley train with belt wrapped so both pulleys rotate in same direction.

Solution to Problem 2

• B. Simple pulley train with belt wrapped so both pulleys rotate in opposite direction.

Problem 3

• Calculate the mechanical advantage of the compound pulley drive train model.– Show your work.– Small Pulley Diameter = 25mm– Large Pulley Diameter = 100mm

Last slide on Tuesday Jan7

Block and Block and TackleTackle

Block and Tackle

• Multiple pulleys providing a greater mechanical advantage.

• MA is determined by the number of pulleys.

25 lbs 25 lbs

25 lbs

25 lbs100 lbs100 lbs

25 lbs

100/4 = 25

Block and Tackle

Gun Tackle Luff Tackle

Block and Tackle

Block and Tackle: Luff-upon-Luff Luff-upon-Luff TackeTacke

1200/100 = 12

Pulleys are used to gain mechanical advantage trading the amount of the amount of

rope you have to pull rope you have to pull to lift an object for how heavy the object

can be.

http://www.swe.org/iac/LP/pulley_03.html

The more lines of support (ropes) a pulley has, the more mechanical advantage it has!

Review of Pulleys1. Give real-world example of each of the following pulleys.

1. Force Multiplier2. Speed Multiplier3. Direction Changer

2. Give one example of a simple machine or transmission that changes output motion. Identify both input and output motions.

3. Give examples of using Pulleys in Robotics, especially humanoid robot design.

Pulley EngineeringElaboration

• Design, Create, and Verify a pulley system with a mechanical advantage of:

– 4– 5– 6

• Be sure to include drawings of your systems and how you verified the MA of the systems

• For block and tackle systems, what effect most greatly reduces the MA?

Evaluation

Pulley Puzzlers

• The girl in the illustration is trying to lift herself and the swing using the rope.

• What would you predict would happen if she pulled down on the rope?

• If she weighs 90 pounds and the swing weighs ten pounds, how much force does she need to apply?

Evaluation Pulley Puzzlers1. We should assume that it is an extensionless, massless rope, a

massless pulley that does not hinder its rotation, and a rigid support.

2. We should imagine a box around the girl and the swing with only the rope extending out from the box to isolate the forces acting on the objects inside the box from the external forces.

3. The rope supports the box once, goes through the pulley and supports the box again.

4. The tension of the rope going upwards is T on each side, so the total tension is 2T.

5. The combined force from the tension in the rope must be greater than the combined weight of the girl and the chair for the chair to be lifted.

6. For a 90 pound girl and 10 pound chair, she must use a force of 50 pounds of more to be able to lift herself off the ground.

Evaluation

Pulley Puzzlers• The man in the illustration

below is trying to lift himself and the block on which he is standing off the ground.

• Is this possible?

1. This movable pulley allows the man to pull upwards and the block on which he stands will rise with him on top.

2. He must apply a force equal to his weight and the weight of the block because there is only 1 supporting rope outside the system.

3. There is a mechanical advantage of 1. 4. Yes, it can be done.

Evaluation

Pulley Puzzlers• A long rope passes over a

single pulley and has bananas on one end and a monkey on the other.

• If the monkey and the bananas have the same mass, can the monkey ever reach the bananas if he climbs the rope?

• Assume that the rope is massless, there is no friction, and the rope is limitless.

Evaluation

Pulley PuzzlersPulley Puzzlers• The opposite external torques produced by the

bananas and the monkey will cancel each other out.

• Any upward movement of the monkey will be equaled by an upward movement of the bananas.

• If the monkey started below the bananas, the distance between the two will always stay the same.

• Because we assume that the rope is limitless and the bananas will never wedge into the pulley, the monkey will never be able to reach the bananas.

How to use pulleys in your robot?

• Look to the pulleys used in other robots.• Look to gears, chains and other similar

constructions in our robots.• How to use old Goodwill/Home Depot

components?

Pulleys in Pulleys in historyhistory

Engagement

Ancient PulleysEngagement

Archimedes, who was kinsman and a friend of King Hieron of Syracuse,wrote to him that with any given force it was possible to move any givenweight, and emboldened, as we were told, by the strength of hisdemonstration, he declared that, if there were another world, and hecould go to it, he could move this. Hieron was astonished, and begged him to put his proposition into execution, and show him some great weight moved by a slight force. Archimedes therefore fixed upon a three-master merchantman of the royal fleet, which had been dragged ashore by the great labors of many men, and after putting on board many passengers and the customary freight, he seated himself at a distance from her, and without any great effort, but quietly setting in motion with his hand a system of compound pulleys, drew her towards him smoothly and evenly, as though she were gliding through the water.

- Plutarch

Instructor: Read this in your best theatrical voice

What else did Archimedes study?

Archimedes Advantage• Have two volunteers attempt to hold two metal rods apart while the

instructor attempts to force them together with a “pulley system.”• Discuss the Mechanical Advantage offered by pulleys

Engagement

Teacher 2Teacher 1Instructor

Ask volunteers to keep the bars parallel and to hold the ends not the middle

Sources

R. Lindeke, Gerald Rothenhofer