Page 130 - Build Your Own Combat Robot

Chapter 6:
Power Transmission: Getting Power to Your Wheels
So how much can a robot push? The maximum pushing force will be equal to 111
the sum of all the frictional forces, F , for all of the wheels. When the reaction
f
forces of an immovable object, such as a wall or a bigger robot, exceeds the total
frictional forces, your robot will stop moving—and, in this case, your robot could
actually be pushed backward! By combining Equations 9 and 11, the torque re-
quired to produce the maximum pushing force will be as shown in Equation 12.
6.12

For a robot with all identical wheels and motors that can deliver all the torque it
could need, the total maximum pushing force, F , will become the product of the
max
weight of the robot and the coefficient of friction. Equation 13 shows this.
6.13

If the motor torque can produce a force greater than the frictional force, the
wheels will spin. If the maximum torque of the motors cannot produce forces
greater than the frictional forces, your robot’s motors will stall when you run up
against another robot or a wall. In Chapter 4, you learned that stalling a motor is
not a good idea, so it is a better idea to have the wheels spin rather than being
stalled. Equation 14 shows the stall torque relationship for each wheel. This infor-
mation can be used to help you determine the speed reduction in the power trans-
mission and help you pick the right-sized motors. Equation 13 is a rather
interesting equation. This maximum force is the maximum force your robot can
exert, or it is the force another robot needs to exert on your robot to push it
around. This force is a function of two things: weight of the robot and the coeffi-
cient of friction between the robot’s wheels and the ground. So, this tells you that
increasing your robot’s weight can give you a competitive advantage.

6.14
One of the difficult tasks in determining the pushing force is determining the
coefficient of friction. The coefficient of friction between rubber and dry metal
surfaces can range from 0.5 to 3.0. In your high school science classes, you probably
learned that the coefficient of friction cannot be greater than 1.0. This is true for
hard, solid objects; but with soft rubber materials, other physics are involved. It is
not uncommon to find soft, gummy rubber that has coefficients of friction greater
the 1.0, and some materials have a coefficient of friction as high as 3.0. For all
practical purposes, the coefficient of friction for common rubber tires and steel
surfaces is between 0.5 and 1.0.
The other factor that affects the coefficient of friction is how much dirt is on the
surface. A dirty surface will reduce the overall coefficient of friction. This is why
off-road tires have knobby treads to help improve the friction, or traction.
As a worse-case situation, assume that the coefficient of friction is equal to 1
and size all your components so you will not stall the motors in these conditions.
This will give most robots a small safety margin. If you want to be more conserva-
tive, use a coefficient of friction greater than 1.