Computer Scanner
The mechanism in a desktop computer scanner converts the rotation of a motor’s shaft into the side-to-side motion of the scanning head (Figure 8.32). During a portion of a scan operation, the drive motor turns at 180 rpm. The gear attached to the motor’s shaft has 20 teeth, and the timing belt has 20 teeth/in. The two other gears are sized as
indicated. In the units of in./s, calculate the speed at which the scanning head moves.
Approach
To find the speed of the scanning head, we must first determine the speed of the transfer shaft by applying Equation (8.9).
VR=\frac{output speed}{input speed}=\frac{\omega _{g}}{\omega _{p}}=\frac{N_{p}}{N_{g}} (8.9)
Equation (8.2)
v=r\omega (8.2)
can then be used to relate the rotational speed of the transfer shaft to the belt’s speed.