How do you calculate velocity ratio for a belt drive given driver and driven pulley diameters?

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Study for the PMMI Mechanical Drives Test with engaging multiple choice questions and detailed explanations. Enhance your knowledge on mechanical drives and get ready for your exam!

Multiple Choice

How do you calculate velocity ratio for a belt drive given driver and driven pulley diameters?

Explanation:
In a belt drive, the belt’s rim speed is the same on both pulleys, so the no-slip condition gives the relation D1 n1 = D2 n2, where D1 and n1 are the driver’s diameter and speed, and D2 and n2 are the driven’s diameter and speed. If the velocity ratio is defined as VR = D1/D2, then solving for the driven speed in terms of the driver speed gives n2 = n1 × (D2/D1). This matches the option that sets the velocity ratio as D1/D2 and expresses the driven speed as the driver speed scaled by the reciprocal of that ratio. The other forms either mix up the inverse relationship or introduce arithmetic that doesn’t align with the belt-slip constraint, so this pairing is the consistent choice.

In a belt drive, the belt’s rim speed is the same on both pulleys, so the no-slip condition gives the relation D1 n1 = D2 n2, where D1 and n1 are the driver’s diameter and speed, and D2 and n2 are the driven’s diameter and speed. If the velocity ratio is defined as VR = D1/D2, then solving for the driven speed in terms of the driver speed gives n2 = n1 × (D2/D1). This matches the option that sets the velocity ratio as D1/D2 and expresses the driven speed as the driver speed scaled by the reciprocal of that ratio. The other forms either mix up the inverse relationship or introduce arithmetic that doesn’t align with the belt-slip constraint, so this pairing is the consistent choice.

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