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I'm trying to get an answer for something potentially quite simple, but I can't visualize it (nor do I have the parts yet to build it). It's for a little hobby project, but I'm slightly concerned I have made an assumption about what will happen, which may not be correct. I've drawn the problem below.

enter image description here

In essence you have two pulleys connected by a timing belt.

Pulley A = 80 Teeth
Pulley B = 120 Teeth

Pulley A is static, it does not rotate at all. Pulley B is free to spin around its own axis. It also then rotates around the axis of A, keeping the timing belt taught.

In one revolution of pulley B around the axis of A (dotted line), how many times would pulley B have rotated?

My assumption would be that it would be 2/3 rotations of pulley B for every time it does an entire revolution around pulley A.

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yes, you are right, but only partially.

In one clockwise revolution, the belt is wound around, pulled, by A at a rate of 80 teeth. So pully B will have turned

$80/120 =\frac{2}{3}\quad$ counterclockwise.

But we have to add to this one clockwise rotation that we initiated.

So the total B rotation is 1-2/3 = 1/3 clockwise.

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  • $\begingroup$ Thank you for this. Just a quick bonus question. Are you saying that if the pulleys are both 80 teeth then it would not rotate at all? (I.e 1-(80/80)) $\endgroup$
    – J.Zil
    Mar 3 '19 at 21:50
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    $\begingroup$ Yes. That is true, B would not rotate. Sorry I am using my phone can't address you, James. $\endgroup$
    – kamran
    Mar 3 '19 at 22:13

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