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A "Pulley" and a "Wheel and axle" seem much similar to each other. What is their actual difference and what are their precise definitions?

My understanding of the two terms is much relied on the context of Simple machines. The wikipedia articles of the two terms provide a definition which makes them seem very similar. But since simple machines are considered (by ancient greeks) as six distinct different basic machines then they must have an important difference.

I'm not sure, but maybe modern treament of mechanical machines in terms of "Linkage synthesis" could give a better explanation. If it's possible, please explain the differences and the definitions both in the context of "Simple machines" and "Linkage synthesis" methods.

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    $\begingroup$ the wiki articles seem clear to me. Could you be more specific about what you dont understand. $\endgroup$ – agentp Nov 30 '16 at 12:39
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The construction of a "pulley" and a "wheel and axle" can be similar or even same. But in the simple machines classification their purposes differ:

  • Pulley is used to change the direction of a rope or a chain. The actual rotation of the pulley wheel is a side effect.
  • Wheel and axle are used to amplify rotational force. The force can be provided through a rope wrapped around the wheel, but the change of direction is a side effect.

For example, a chain sprocket is an example of wheel and axle, while a chain idler would be an example of a pulley.

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  • $\begingroup$ Thank you for your answer. I also heard the pulley wheel is not rigidly attached to the axle while in a "Wheel and axle" setting the wheel is rigidly attached to the axle. Do you agree with this too? By the way if the rotation of the pulley wheel is a side effect, doesn't that mean the friction between pulley wheel and the rope should be as much as possible to achieve better efficiency? It's contrary to the sentence stated by most problems: "...by ignoring the effects of friction..." $\endgroup$ – Hamed Begloo Dec 1 '16 at 17:49
  • $\begingroup$ @HamedBegloo It doesn't matter whether the axle spins with the pulley or not, as long as the spinning of the axle is not used for anything. Typically the friction of the pulley wheel wouldn't matter much I think. Though from a very slippery material you could make a pulley that doesn't spin, but that the rope just slips over. $\endgroup$ – jpa Dec 2 '16 at 6:05
  • $\begingroup$ The importance of attachment of the wheel and the axle came to my mind when I was googling the subject in the question and reached "this page". By the way if the pulley haven't friction how it's possible to transfer the force. I think of it like when a car want to roll on a street there must be a friction between tires and the ground for car to move otherwise the car is chocking in its place(like when it's on an icy ground). $\endgroup$ – Hamed Begloo Dec 2 '16 at 21:14
  • $\begingroup$ the car tire example is clearly a wheel-axle situation and does indeed need friction. For a simple pulley it wouldn't matter if the wheel itself turns or the rope slides over it without friction. Does that help? $\endgroup$ – agentp Dec 4 '16 at 15:38
  • $\begingroup$ @agentp Somehow. But I think I need a bit more explanation. For sake of simplicity let us put it this way: Assume a plain shaft with no pulleys or wheels on it and just a rope hanging on it. There is a mass on one end of the rope and we are pulling the other end. Now by assuming there is no friction between shaft and the rope, how the force is actually being transferred between our hand and the mass? I mean don't we need there to be a sequential exertion of contact forces to transfer the force exerted by our hand to the mass? $\endgroup$ – Hamed Begloo Dec 4 '16 at 20:42

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