- Motors supply the force and torque needed for robots to move through wheels, arms, etc. The speed of a robot is determined by the wheel diameter and motor RPM. - Factors like motor torque, robot weight, acceleration, and wheel diameter must be balanced to achieve proper velocity. The robot motor factor (RMF) can be used to quickly calculate torque requirements. - For robot arms, the torque required at each joint must be calculated based on the load weight and distance from the pivot point to select the appropriate motor. Gears can be used to exchange torque and velocity.

1. ROBOT DYNAMICS

2. MOTORS supply the FORCE that the
robot needs to move
Rotational Force is called TORQUE
The motor needs to supply force to
• wheels
• arms

3. The Rolling of WHEELS
without slipping or spinning
Everytime a wheel rotates an entire revolution, the robot travels a
distance equal to the circumference of the wheel.
Multiply that distance by the number of rotations per minute (rpm) and
you get the distance your robot travels in a minute (its speed)
)
)(
2
( rpm
r
v 

r
nce
Circumfere 
2


4. For example, if your motor has a rotation speed
(under load) of 100rpm (determined by looking up
the motor part number online) and you want your
robot to travel at 3 feet per second, calculate the
wheel diameter you would need:
inches
or
ft
d
rps
d
rpm
r
v
89
.
6
57
.
0
)
67
.
1
(
3
)
)(
2
(






5. Wheel diameter and the motor rpm are not the only
factors that determine robot velocity:
• motor torque
• robot weight
• robot acceleration
To achieve proper velocity/movement, you
must balance
• motor torque
• robot acceleration
• wheel diameter

6. Motor datasheet
• motor torque
• motor speed
Motor Torque and Force / Acceleration
High force is required to push other robots around,
or to go up hills, or have high acceleration.
r
F 


Acceleration
ma
F 
rps
or
rpm Robot mass

7. Robot Motor Factor, RMF
Something to make life simpler, Can do quick
calculation to optimize your robot or select the
appropriate motor for your needs
)
(
)
(
2



v
ma
rps
rps
r
ma
rps
r
F







RMF
(depends on motor specs)
Robot characteristics
or requirements
)
)(
2
( rpm
r
v 

Wheel speed

8. Robot Motor Factor, RMF
Example: You found the following 3 motors
Motor A: 2 ft lb, 1 rps
Motor B: 2.5 ft lb, 2 rps
Motor C: 2 ft lb, 4 rps
rps
RMF 

RMFA= 2 ft lb rps
RMFB= 5 ft lb rps
RMFC= 8 ft lb rps
Suppose you want a velocity of 3 ft/s, an acceleration
of 2 ft/s2, and you estimate your robot to weigh 5 lbs
rps
lb
ft
RMF
ma
RMF v
77
.
4
)
2
/(
3
2
5
)
( 2




 

Motor B & C will both work. Motor C is overkill, waste of $
Wheel diameter
to use?
in
ft
rps
v
d 73
.
5
48
.
0
)
2
(
3








9. Robot Efficiency
RMF is for 100% efficient systems. Gearing and friction
and many other factors cause inefficiency. General rules
for estimating inefficiency – If your robot
• has external gearing, reduce efficiency 15%
• uses treads, reduce efficiency 30%
• operates on high friction terrain, reduce efficiency 10%
%)
63
(
63
.
0
)
10
.
0
1
)(
30
.
0
1
( 



Efficiency
Example: Tank robot on rough terrain would have
what efficiency?

10. Robot Motor Factor, RMF
incorporating efficiency
Something to make life simpler, Can do quick
calculation to optimize your robot or select the
appropriate motor for your needs
)
)(
( 1
2 efficiency
v
ma
rps 
 

RMF
(depends on motor specs) Robot characteristics
or requirements
(efficiency is a decimal # ie 80% is 0.8)
Link to RMF Calculator

11. Robot Arm Torque
determine the torque required at any given lifting
joint (raising the arm vertically) in a robotic arm
L
mg
L
F






Weight
of load
Torque
needed to hold a mass a given
distance from a pivot
L is the PERPENDICULAR
length from pivot to force

12. Robot Arm Torque
To estimate the torque required at each joint, we must choose
the worst case scenario
As arm is rotated clockwise, L, the perpendicular distance
decreases from L3 to L1 (L1=0). Therefore the greatest torque is
at L3 (F does not change) and torque is zero at L1.
Motors are subjected to the highest torque when the arm is
stretched out horizontally
Greatest
torque

13. Robot Arm Torque
Load
)
2
/
(
)
2
/
(
)
(
1
1
W
mg
L
L
W
L
mg







WL=mg
W1
L
L/2
)
/
1
)(
)(
2
/
1
( efficiency
rps
W
mg
L
rps 



Arm weight
You must also add the torque imposed by the arm itself
RMF (motor specs) Robot arm torque

14. WL=mg
W3
L3
L3/2
W2
L2
L2/2
W1
L1
L1/2
Wm3
Wm2
Wm1
Robot Arm Torque
)
2
/
(
)
( 3
3
3
3 L
W
L
mg 




If your arm has multiple points, you must determine the torque
around each joint to select the appropriate motor
    )
(
)
(
)
(
)
( 2
2
2
3
2
2
3
2
3
2
2
3 L
m
L
W
L
W
L
W
L
L
mg 










     
  )
(
)
(
)
(
)
(
)
(
)
(
2
1
1
2
2
1
2
2
1
3
2
2
1
3
1
2
3
1
1
2
3
L
m
L
m
L
W
L
W
L
W
L
L
W
L
L
W
L
L
L
mg




















15. Robot Arm Torque
Link to Robot Arm Calculator
WL=mg
W3
L3
L3/2
W2
L2
L2/2
W1
L1
L1/2
Wm3
Wm2
Wm1

16. Gears
No good robot can be built without gears.
Gears work on the principle of mechanical advantage
With gears, you will exchange the high velocity of
motors with a better torque. This exchange happens
with a very simple equation that you can calculate:
new
new
old
old v
v 

 

Motor specs

17. Example:
Suppose your motor outputs, according to spec are
3 lb-in torque at 2000rps ,
but you only want 300rps.
3 lb-in * 2000rps = Torque_New * 300rps
new torque will be 20 lb-in.
Now suppose, with the same motor, you need 5 lb-in of
torque. But suppose you also need 1500rps minimum
velocity. How do you know if the motor is up to spec and
can do this? Easy . . .
3 lb-in * 2000rps = 5 lb-in * Velocitynew_
New Velocity = 1200rps
You now have just determined that at 1200 rps the selected
motor is not up to spec. Using the simple equation, you have
just saved yourself tons of money on a motor that would
have never worked. Designing your robot, and doing all the
3
new
new
old
old v
v 

 


18. Moves slower
More torque
Moves faster
Less torque
Gear Ratios
HOW do you mechanically swap torque and velocity
with gears?
The gearing ratio is the value at which you change your
velocity and torque. It has a very simple equation. The
gearing ratio is just a fraction which you multiple your
velocity and torque by. Suppose your gearing ratio is 3/1.
This would mean you would multiple your torque by 3
and your velocity by the inverse, or 1/3.

19. Gear Ratios
Example: Suppose you have a motor with output of
10 lb in and 100 rps (old=10 lb in, vold=100rps) and you
have a gear ratio of 2/3
Gearing ratio = 2/3
new=10 lb in x 2/3 = 6.7 lb in
vnew=100rps x 3/2 = 150 rps

22. Building your First Robot
(for beginners)
1. Design! Plan out everything on paper or computer
(what material you will use, where to put every screw,
how to attach sensors. Draw to dimension, mark holes
and understand how the parts connect)
1. Keep it simple, look at other robots for design
ideas. Don’t get imaginative or creative with your first
robot. Use fewer and simpler parts
2.