Following, the previous question, I am trying to calculate how much one rocker would rotate when the other is being rotated. I attached my calculation here.

I am trying calculate the rotation of gear B that connects to right rocket. Given gear A rotates at 0.05 rad, what is the rotation of gear B in rad? Gear ratio A:D is 4:1, and D:B is 1:4.

At the end, I ended up with rotational gear A = gear B. This somewhat puzzles me. Is my calculation correct?

My calculation given rotation of gear A that connects to left rocker


Your calculation is correct in magnitude but incorrect in sign, because gear B rotates oppositely to A (when the axis of D is fixed and D is not locked).

If D is locked (ie, the gear is not free to rotate in its plane) then A and B are locked together and rotate identically.

If the body V to which the axis of D is fixed rotates during rotation of A, then the rotation rate of B will differ from that of A. Example: Let rotation directions for A, B, and V be stated relative to a view from the left, and for D relative to a view from above. With V fixed, suppose A rotates CW at 40 rpm. Then D rotates CCW at 10 rpm, driving B CCW at 40 rpm. If V now begins to rotate CW at 20 rpm, D's rotation rate drops to 5 rpm, so that B begins to rotate at -20 rpm relative to A, 0 rpm relative to V, and 20 rpm to the frame of reference.

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  • $\begingroup$ Thanks. I am trying to understand "...D's rotation rate drops to 5 rpm..." bit. $\endgroup$ – ikel May 18 '13 at 6:54
  • $\begingroup$ When A and V rotate the same direction, D's rotation rate is 1/4 the difference. When they rotate oppositely, 1/4 the sum. $\endgroup$ – James Waldby - jwpat7 May 18 '13 at 13:31
  • $\begingroup$ Got that! Thanks for your simple approach to my convoluted problem. $\endgroup$ – ikel May 18 '13 at 22:12

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