Build Your Own Combat Robot

FIGURE 6-1
Simple speed
reduction schematic
Chapter 6: Power Transmission: Getting Power to Your Wheels 107
Equation 3 shows how the speed of the output gear relates to the speed of the
input gear.
In Equation 3, D 1 and N 1 are the diameter and rotational speed of the driving
gear, and D 2 and N 2 are the diameter and rotational speed of the driven (output) gear.
When D 1 is greater than D 2, the output gear will spin faster than the driving gear;
when D 1 is less than D 2 , the output gear will spin slower (gear reduction) than the
driving gear. When driving two shafts together, such as a front and rear axle being
driven with only one motor, the gear/sprocket diameters between the two axles
must be the same or the wheels will spin at different speeds.
If you have a 3000 RPM motor and you want a wheel speed of 300 RPM, you
will have to reduce the speed of the motor by a factor of 10. By looking at equation
3, you can see that the output gear, D 2, will have to be 10 times bigger than
the input gear, D 1 . This is a pretty big gear reduction with only two gears. If you
were using a 1.5-inch-diameter gear on the motor shaft, you would have to use a
15-inch-diameter gear on the wheel. If the wheel is only 10 inches in diameter, the
gear’s diameter will cause the gear to strike the ground, since it is larger than the
wheel. When this type of situation occurs, three or more gears/pulleys/sprockets
must be used together.
Figure 6-2 shows a more complex speed reduction.
Though the configuration shown in Figure 6-2 seems complicated, it can be
simplified by looking at it as two separate two-gear systems. In this example, the
speed of gear number 2 is the same as what is shown in Equation 3. The speed of
gear number 4, N 4, is first shown in Equation 4 that follows. It has the same exact
form as what is seen in Equation 3. Since gears numbers 2 and 3 are physically attached
to the same shaft, they will both spin at the same speed, which is shown in
Equation 5. Because of this, you can substitute Equation 3 into Equation 4 to de
termine the final speed of the output shaft. Equation 6 shows the speed reduction for
6.3