Involute gears: dependence of sliding velocity on contact position Consider a point of contact on the line of action at a distance from the pitch point. State how the sliding velocity varies with the distance from the pitch point.
Mechanical Engineering
Machine Design
Difficulty: Medium
Choose an option
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AIt is directly proportional to the distance from the pitch point
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BIt is inversely proportional to the distance from the pitch point
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CIt equals cosφ times the rolling velocity
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DIt does not depend on the contact location
Answer
Correct Answer: It is directly proportional to the distance from the pitch point
Explanation
ConceptFor involute gears, the rolling (no-slip) point is the pitch point. The sliding velocity at any other contact point on the line of action is proportional to its distance from the pitch point:
vslide = (ω1 − ω2) · r′with r′ measured along the line of action from the pitch point.
Implication• At the pitch point, distance = 0 → no sliding.• Away from the pitch point, sliding increases linearly.
Final AnswerDirectly proportional to the distance from the pitch point