Does a spiral pulley offer mechanical advantage if wrapped once?

[mathews4ever]

I'm sorry if this is the wrong place to post this but I can't find the answer anywhere.

Does a spiral pulley offer any mechanical adavntage if it is wrapped once around like in the drawing?

 

[tiny-tim]

Welcome to PF!

Hi mathews4ever! Welcome to PF!

Frictionless? Nope … moving one metre on one side makes the other side move by one metre also, and since the work done is always the same, the tensions must also be the same.

(but with static friction between the rope and the pulley … ? )

 

[Dr.D]

You did not draw what looks like a spiral pulley. Where is the axis of rotation for your pulley?

 

[ank_gl]

spiral pulley will have a larger angle of lap, hence higher value of ratio of tensions, higher power transfer capabilities, or in other words, for same power transfer, tension in both sides will be lesser, so belt material can be saved.
But spiral pulley will be costly in manufacturing (but maybe rolling can be used, dunno), axial thrust comes into the picture, so bearings becomes costlier(increased frictional loss also) & ..:zzz:

wait for an expert(who is in the business) to comment

 

[Phrak]

Is the diameter of the spiral pulley at the uptake as large as the diameter at other end?

(That rather puts a twist in things, doesn't it. I've never heard of such a thing, but why not.)

 

[Dr.D]

We seem to have some terminology difficulties here.

Any spiral pulley will necessarily have the rope or cable wind axially around it, a helix of some sort, since the rope cannot pass through itself to leave in the same plane in which it entered the pulley.

Then there is the matter of just what we mean by a "spiral"? Is it a simple helix, like a screw thread, or does it actually have a changing radius, such as an arcchimedes spiral? I have seen both, but I first thought of the second type when I read the question. From what ank_gl says, it sounds like the question must be more intendedf for the first type, the simple screw thread on a straight sided cyiinder.

For either of these types, there is a limit to the number of rotations that the pulley can make before the rope runs out of the groove.

 

[Phrak]

...does it actually have a changing radius, such as an arcchimedes spiral?...

That would be interesting. What sort of spiral would maintain constant mechanical advantage, as the number of turns varied depending on where on the spiral the rope hung.

 

[ank_gl]

aahhh... now i see the OP meant MECHANICAL advantage rather than advantage(which i assumed).
Second type of pulley that Doc C wrote about, can't be a pulley(proper), the surface velocity is varying whereas the rope velocity is constant & has to operate without skidding(for proper operations).
In the first type also, I (as of yet) don't see any mechanical advantage, but surely, power transfer capabilities(theoretically) do increase. As of design, it also adds extra inertia to the system.

 

[Dr.D]

Pulleys of the varying radius type (something like the archimedes spiral, but not exactly that) have been used in high precision clocks. They are part of a spring drive mechanism, and the spiral is used to compensate for the reduction in torque as the spring unwinds. The result is to keep a constant tension on the output cord, the other end being fixed on the pulley.

 

[Bob S]

Capstan winches used on sailing boats are close to what you are describing. Sailors wrap two or three turns around the capstan to get enough friction to keep the rope from slipping.