Treadmill’s Belt Drive
A timing belt is used to transfer power in the exercise treadmill from the motor to the roller that supports the walking/running belt (Figure 8.33). The pitch diameters of the sheaves on the two shafts are 1.0 in. and 2.9 in., and the roller has a diameter of 1.75 in. For a running pace of 7 min/mi, at what speed should the motor be set? Express your answer in the units of rpm.
Approach
To find the appropriate speed of the motor, we first find the roller’s angular velocity and then relate this to the motor speed. The speed of the walking/running belt is related to the roller’s angular velocity by Equation (8.2).
v=r\omega (8.2)
Since the timing belt’s speed is the same whether it is in contact with the sheave on the roller or with the sheave on the motor, the angular velocities of those two shafts are related by Equation (8.23).
VR=\frac{output \ speed}{input \ speed}=\frac{\omega _{output}}{\omega _{input}}=\frac{d_{input}}{d_{output}} (8.23)