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Transcript
Xtreme Robot Olympiad
Adventure Racing
Peter Laz
Associate Professor
Department of Engineering
University 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
Front Wheel Drive
Rear Steer
= Steering
= Driven
Rear Wheel Drive
Front Steer
Front Wheel Drive
Front Steer
Two wheel configurations may be unstable
3-Wheel Configurations
Front Wheel Drive
Rear Steer
= Steering
= Driven
Rear Wheel Drive
Front Steer
Front Wheel Drive
Front Steer
4-Wheel Configurations
Front Wheel Drive
Rear Steer
Rear Wheel Drive
Front Steer
Front Wheel Drive
Front Steer
All Wheel Drive
Need for differentials and/or
steering linkages
= Steering
= Driven
Tank drive has difficulties
going straight as motors are
not identical.
Engineering Fundamentals
Force
• Units of force
• Newtons (N = kg*m/s2)
• Pounds (lb = lb*ft/s2)
SI system
US system
• Force = mass * acceleration
• Weight = mass*g
• Mass (kg), g = 9.81 m/s2
• Mass (slugs), g = 32.2 ft/s2
SI system
US system
Torque
A torque or moment is equal to a force x
distance at which it acts
  
T  r F

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:
î  ĵ  k̂
î   ĵ  k̂
î  î  0
ĵ  î  k̂
ĵ   î  k̂
ĵ  ĵ  0
Exercise
Find the magnitude and direction of the torque for
each of the conditions
a.
c.

r  2 î

F  6 ĵ

r  2 î

F  2 î  6 ĵ
b.

r  2 î

F  6 ĵ
Sir Isaac Newton
(1642-1727)
Three Laws of Mechanics
1. 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)

F  0
 Fx  0
 Fy  0
 Mo  0
Levers
• Consist of 3 parts
• Effort
• Resistance
• Fulcrum (pivot point)
Effort Force
W
Levers
• First class lever – fulcrum between the weight
and the effort
Effort Force
W
• What happens to the effort
• if the fulcrum moves to the left?
• if the fulcrum moves to the right?
Levers
• Second class lever
W
Effort Force
• Third class lever
W
Effort Force
Static Equilibrium
• Moments caused by effort and resistance
are equal
 Mfulcrum  0




 Mfulcrum  reffort  Feffort  rresist  Fresist




reffortFeffort  rresistFresist
Mechanical Advantage
• Measure of the ability of a machine to
amplify force
Resistance (Force)
M.A. =
Effort (Force)
Effort Arm
M.A. =
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 (w)
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
N1 r1

N2
r2
N = Number of teeth, r = radius
Gear Ratio - Velocity
• Velocity of pitch point C on both bodies
must be equal
w2
w1
Vc  r1  w1  r2  w 2
w2
w1

r1
r2

C
N1
N2
w= angular velocity
Driver or
Pinion
Driven
Gear Ratio - Torque
• Force of gear 1 on gear 2 is equal and
opposite to force of gear 2 on gear 1
F
w2
w1
T1
r1

r1
r2


w1 T1
T2
r2
N1
N2
C

w = angular velocity
T1
T2
Driver or
Pinion
Driven
T2
w2
Gear Problems
• Master Equation
w2
w1

r1
r2

N1
N2

T1
T2
• Small gear to large gear
• Slower angular velocity, increased torque
• Large gear to small gear
• Faster angular velocity, reduced torque
Exercise
w2
What are the gear ratios?
Let:
rgreen = 6 inches
rblue = 10 inches
rred = 15 inches
wgreen = 10 rad/sec
What is wred?
Is Tred < or > Tgreen?
w1
w1
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/vexrobotics-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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