Build Your Own Combat Robot

Torque
Force
Chapter 6: Power Transmission: Getting Power to Your Wheels 109
As a general rule, the greater the gear reduction, the more gears you will have to
use to achieve the gear reduction. In the real world, you may not find the exact
gear and sprocket diameters you want. This may be because the actual sizes do not
exist. For example, if you are using sprockets instead of gears, it is rare to be able
to find a sprocket that has a diameter 10 times greater than the driving sprocket.
You will usually have to choose components that are close to the values you want.
Thus, the speed reduction will be a little lower or higher than what you want.
The output torque is also a function of the gear ratios, but the torque and gear ratios
have an inverse relationship. When the speed is reduced, the torque on the output
shaft is increased. Conversely, when the speed is increased, the output torque is reduced.
Equation 7 shows the torque relationships from Figure 6-1. The direction in
which the torque is being applied is identical to the rotational directions.
T 1 and D 1 are the torque and the diameter of gear 1, and T 2 and D 2 are the torque
and diameter of gear 2. If D 2 is greater than D 1 , the output torque is increased.
From Figure 6-2, the output torque is shown in equation 8.
In the previous example, where we were looking for a 10-to-1 speed reduction,
this will increase the output torque by a factor of 10.
During the robot design process, the power transmission must be considered at
the same time while you’re selecting the motors. The number of gears, sprockets,
and pulleys and their sizes can have a significant impact on the overall structural
design of the robot. To simplify the overall power transmission design, you should
choose a motor that has the lowest RPM so that the number of components in the
power transmission (or speed reducer) can be minimized.
The robot’s pushing force is a function of the robot’s wheel diameters and the output
torque on the wheel, and the coefficient of friction between wheels and floor.
By definition, torque is equal to the force applied to some object multiplied by the
distance between where the force is applied and the center of rotation. In the case
of a gear, the torque is equal to the force being applied to the gear teeth multiplied
by the radius of the gear. Equation 9 shows this relationship, where T is the
torque, F is the applied force, and r is the distance from the center of rotation and
6.7
6.8