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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?
This workforce solution was funded by a grant awarded under the Workforce Innovation in Regional Development (WIRED) as implemented by the U.S. Department of Labor’s Employment and Training Administration working in partnership with the Colorado Department of Labor and Employment, the Metro Denver Economic Development Corporation, and the City and County of Denver's Office of Economic Development. The solution was created by the grantee and does not necessarily reflect the official position of the U.S. Department of Labor. The Department of Labor makes no guarantees, warranties, or assurances of any kind, express or implied, with respect to such information, including any information on linked sites and including, but not limited to, accuracy of the information or its completeness, timeliness, usefulness, adequacy, continued availability, or ownership. This solution is copyrighted by the institution that created it. Internal use by an organization and/or personal use by an individual for non-commercial purposes is permissible. All other uses require the prior authorization of the copyright owner.