Dynamics_Part59

Dynamics_Part59 - Problem Set 8 Problem 3 Problem For the...

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Unformatted text preview: Problem Set 8: Problem 3. Problem: For the switching device shown, the vertical control rod has a downward velocity v = -v j. If roller A is in continuous contact with the frictionless horizontal surface, determine the velocity of roller C as a function of v and . y ................ . . . . . . . . . . . . . ... . ................... . .................... . .. . . x Solution: We begin by noting that the velocity of roller A is vA = vB + B rA/B where we must determine angular velocity B . We know that vB = -v j as the control rod is constrained to move vertically. Also, we see from the geometry that rA/B = L sin i - L cos j So, the velocity of roller A is vA = -v j + B k (L sin i - L cos j) = -v j + B L(sin j + cos i) Regrouping terms, we conclude that vA = B L cos i + (B L sin - v) j But, roller A is constrained to move horizontally so that vAy = 0, which tells us that B L sin - v = 0 Turning now to roller C, we have and the geometry is such that Thus, we can say vC = -v j + vC = vB + B rC/B rC/B = -L sin i + L cos j v v k (-L sin i + L cos j) = -v j + L(- sin j - cos i) L sin L sin vC = -v cot i - 2v j = B = v L sin Regrouping terms, we conclude that ...
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