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.


1 Answer 1


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.

  • $\begingroup$ 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, 2019 at 21:50
  • 1
    $\begingroup$ Yes. That is true, B would not rotate. Sorry I am using my phone can't address you, James. $\endgroup$
    – kamran
    Mar 3, 2019 at 22:13

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.