Xtreme Robot OlympiadAdventure Racing

Peter Laz Associate Professor

Department of EngineeringUniversity of Denver

Current Standings

Team Points

Green, Aqua 50

Gold, Blue 47

Gray, Yellow, Orange, Teacher

44

Red, Purple 41

Robot Adventure Racing

• Develop your own original design • Choose a new body structure• Change the gears and wheels

• Additional materials will be available for “purchase”• Each team has a “virtual budget” of $25

• All team members will drive• Score is the average time for your team members

• Additional time bonus for a hanging robot• Teams will have 1 minute to get their robot to hang

from the pull-up bar

Outline

• Design tradeoffs

• Vehicle configurations

• Forces and Torques

• Gears • Speed and torque

• Wheels

Vehicle Configurations

• Subsystems• Structure• Steering• Drive train

• Considerations• Stability• Maneuverability• Power transmission – torque versus speed• Implementation

• Responsiveness (steering/oversteering)• Programming• Weight distribution• Cost

Vehicle Configurations

Many Questions:

• How many wheels? 2, 3, 4

• Two wheel or four wheel drive?

• Front wheel drive or rear wheel drive?

• How many motors?

• How will you turn?

Vehicle Configurations

• All wheel drive and all wheel steering may be too complicated.

www.howstuffworks.com

2-Wheel Configurations

= Driven

= Steering

Front Wheel DriveFront Steer

Front Wheel DriveRear Steer

Rear Wheel DriveFront Steer

Two wheel configurations may be unstable

3-Wheel Configurations

= Driven

= Steering

Front Wheel DriveFront Steer

Front Wheel DriveRear Steer

Rear Wheel DriveFront Steer

4-Wheel Configurations

= Driven

= Steering

All Wheel Drive

Front Wheel DriveFront Steer

Rear Wheel DriveFront Steer

Need for differentials and/or steering linkages

Tank drive has difficulties going straight as motors are not identical.

Front Wheel DriveRear Steer

Engineering Fundamentals

Force

• Units of force• Newtons (N = kg*m/s2) SI system• Pounds (lb = lb*ft/s2) US system

• Force = mass * acceleration

• Weight = mass*g• Mass (kg), g = 9.81 m/s2 SI system• Mass (slugs), g = 32.2 ft/s2 US system

Torque

A torque or moment is equal to a force x distance at which it acts

FrT

F

r

= perpendicular distance

Torque

The direction a torque acts is determined by the right hand rule.• Point your hand in the direction of r• Then bend your fingers in the direction of F• Your thumb points to the direction of the torque

For your unit vectors: but note:

kji kji

kij kij

0ii

0jj

Exercise

Find the magnitude and direction of the torque for each of the conditions

j6F

i2r

a.

j6F

i2r

b.

j6i2F

i2r

c.

Sir Isaac Newton(1642-1727)

Three Laws of Mechanics1. A body continues in its state of rest or motion until a force

is applied

2. The change of motion is proportional to the force applied

3. For every action there is an equal and opposite reaction

Static Equilibrium

• Newton’s First Law

• The sum of the forces and moments acting on a body are zero (0)

0M

0F

0F

o

y

x

0F

Levers

• Consist of 3 parts• Effort• Resistance• Fulcrum (pivot point)

W

Effort Force

Levers

• First class lever – fulcrum between the weight and the effort

• What happens to the effort• if the fulcrum moves to the left?• if the fulcrum moves to the right?

W

Effort Force

Levers

• Second class lever

• Third class lever

W

Effort Force

W

Effort Force

Static Equilibrium

• Moments caused by effort and resistance are equal

resistresistefforteffortfulcrum

fulcrum

FrFrM

0M

resistresistefforteffort FrFr

Mechanical Advantage

• Measure of the ability of a machine to amplify force

M.A. =Resistance (Force)

Effort (Force)

M.A. =Effort Arm

Resistance Arm

Gears

• Some examples include• Can opener• Cork screw• Transmission on your car• Bicycle

• Gears are used to• Change the direction of motion• Increase or decrease speed• Increase or decrease torque

• Gears are commonly used in power transmission applications because of their high efficiency (~98%)

Gears Configurations• Spur gears

• Wheels with mating teeth

• Rack and pinion gears• Changes rotational motion

to linear motion

• Worm gears

• Bevel gears• Connects shafts lying at angles

Gear Ratio

• A gear will rotate with an angular velocity () with units of radians/second

• Gears have teeth that must mesh• Same pitch = same distance between teeth • There is a fixed ratio between the teeth and the gear

radius

22

1r

r

NN 1

N = Number of teeth, r = radius

Gear Ratio - Velocity

• Velocity of pitch point C on both bodies must be equal

Driven

Driver or Pinion

C2211

rrVc

1 2

221 N

N

r

r112

= angular velocity

Gear Ratio - Torque • Force of gear 1 on gear 2 is equal and

opposite to force of gear 2 on gear 1

Driven

Driver or Pinion

C2r

T

r

TF 2

1

1 1 2

2221 T

T

N

N

r

r1112

= angular velocity

T1

T2

Gear Problems

• Master Equation

• Small gear to large gear• Slower angular velocity, increased torque

• Large gear to small gear• Faster angular velocity, reduced torque

2221 T

T

N

N

r

r1112

ExerciseWhat are the gear ratios?

Let:rgreen = 6 inchesrblue = 10 inchesrred = 15 inches

green = 10 rad/sec

What is red?

Is Tred < or > Tgreen?

1

2

1

Exercise

• What is the gear ratio for the squarebot?

• Does it increase or decrease the speed of the motor?

• Does it increase or decrease the torque of the motor

Motor Specification

• Free speed• 100 rpm @ 7.5 volts

• Stall Torque• 6.5 in-lbs

Gear Design Decisions

• Which gears will you choose for your design?

• What is the best ratio?

• Be careful not to overload your motor.

http://www.vexlabs.com/vex-robotics-motor-kit.shtml

Wheel Size?

• Large wheels• Faster top speed, slower acceleration

• Small wheels• Slower top speed, faster acceleration

• Which wheel will do better for rough terrain?

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