Money Changer Geartrain
A gear reduction mechanism is used in a machine that accepts bill currency, inspects it, and returns coins in change. The numbers of teeth on the pinion and gear in the first speed-reduction stage are shown in Figure 8.26.
The worm has a single tooth that meshes with the 16-tooth worm gear. Determine the velocity ratio between the output shaft’s speed and the speed of the direct-current motor.
Approach
To find the velocity ratio between the output shaft and the input speed, we recognize that the motor’s speed is reduced in two stages: first, in the gearset comprising the 10-tooth pinion and 23-tooth gear, and second, at the mesh between the worm and worm gear. We denote the angular velocity of the motor’s shaft as ω _{in} in. To determine the speed of the transfer shaft, we will apply Equation (8.9).
VR=\frac{output speed}{input speed}=\frac{\omega _{g}}{\omega _{p}}=\frac{N_{p}}{N_{g}} (8.9)
In the second speed-reduction stage, the worm gear will advance by one tooth for each rotation of the transfer shaft.
