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At my local gym there is this leg extension machine and I'm trying to figure out the mechanical advantage.leg extension machine The pulley attached to the disk (marked by red arrow) confuses me because the disk moves when the force is applied at the pad (marked by green arrow). The pulley moves along with the disk. The rest of the parts on this machine are just cords and fixed pulleys that change the direction of force.leg extension simplified

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The porbably easiest way to figure out the mechanical advantage would be to:

  • measure the length $r$ between the pad that you push against and the yellow axis of rotation
  • figure out the angle of one full movement - should be about 135°
  • from this derive the path $p$ the black pad travels ($p=2r\pi\frac{135°}{360°}$ or so)
  • measure the length the weights travel over one full rep. maybe you can bring a chalk and mark the low and the high point during a rep, no need for max load

Then the mechanical advantage is the ratio of these two.

My guess is that the marked pully just serves as an attachment point. If you are really really sure the mechanics are as simple as you describe, the advantage is length between axis of rotation to pad divided by length of axis of rotation to outter radius of the marked pulley (to where the rope or band is attached)

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  • $\begingroup$ I need some clarification about the 4th bullet point "measure the length the weights travel over one full rep.", this does not include the distance traveled by the weights all the way back right? Because one full rep actually means lifting and releasing the weights. $\endgroup$ Commented Jul 15, 2022 at 6:54
  • $\begingroup$ You are right, I meant one way travel. $\endgroup$
    – mart
    Commented Jul 15, 2022 at 7:22

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