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Dynamics_Part62

Dynamics_Part62 - Problem Set 9 Problem 1 Problem A...

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Problem Set 9: Problem 1. Problem: A gear-reduction system consists of three gears A, B and C. Gear A rotates in the clockwise direction with constant angular velocity ω A . (a) Determine the angular velocities of Gears B and C, ω B and ω C , respectively. (b) Determine the accelerations of the points on Gears B and C that are in contact, a B and a C , respectively. Solution: (a) Denote the contact point between gears A and B by D. Then, the velocity at Point D is v D = v A + ω A × r D/A Gear A is not translating so that v A = 0 . Also, ω A = ω A k and r D/A = R i . Hence, v D = ( ω A k ) × ( R i ) = ω A R j So, to find the angular velocity of gear B, ω B , we note that v D = ω B × r D/B = ω A R j = ( ω B k ) × ( 2 R i ) = 2 ω B R j Therefore, the angular velocity of gear B is
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