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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This note was uploaded on 05/12/2010 for the course AME 301 taught by Professor Shiflett during the Spring '06 term at USC.
 Spring '06
 Shiflett

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