Question

The Whitworth quick return mechanism is shown in the figure with link lengths as follows: OP = 300 mm, OA = 150 mm, AR = 160 mm, RS = 450 mm. The quick return ratio for the mechanism is _______

Hint:

The quick return ratio is a key characteristic of the Whitworth mechanism and can be calculated by comparing the distances traveled during the forward and return strokes.

Answer 1

Correct Answer: 1.9

The quick return ratio \( \text{QR} \) is the ratio of the time taken for the return stroke to the time taken for the forward stroke. The formula for the quick return ratio is given by: \[ \text{QR} = \frac{\text{Return Stroke Time}}{\text{Forward Stroke Time}} = \frac{\text{Distance traveled in return stroke}}{\text{Distance traveled in forward stroke}} \] For the Whitworth mechanism, the distance traveled during the return stroke is given by: \[ \text{Return Stroke Distance} = RS + AR \] Where \( RS = 450 \ \text{mm} \) and \( AR = 160 \ \text{mm} \), so: \[ \text{Return Stroke Distance} = 450 + 160 = 610 \ \text{mm} \] The distance traveled during the forward stroke is simply: \[ \text{Forward Stroke Distance} = OP = 300 \ \text{mm} \] Thus, the quick return ratio is: \[ \text{QR} = \frac{610}{300} \approx 2.03 \] The quick return ratio for the mechanism is: \[ \boxed{2.0} \]