How Does a Chain Hoist Work Mathematically?

[g.bashyam]

Can anyone explain the mechanics of a chain hoist and its mechanical advantage, in mathematical terms,?
thank you
Bashyam

 

[Quinzio]

It's a force multiplier.
You look the number of turns of the chain and this number multiplies the original force.

 

[DickL]

There are several different types of chain hoists. The most common type seen today has an input chain loop that drives the output (lifting) chain via a step down gear unit inside the hoist's housing. I think the gear unit is a planetary one.

 

[JohnMorriss]

The simpest form of chain hoist consists of a pair of discs of different diameters, locked together with their centres aligned. The two gears on the pedal crank of a ten-speed bike are what you should picture. The gear "teeth" are designed to mate without any chance of slipping with the chain being used.

The chain comes from somewhere, pases over one of the gears from (say) left to right, drops down and around an idler wheel. From there it goes up and over the SECOND gear, again from left to right, and then goes off somewhere. The cheapest way is to connect the two "somewhere" ends of the chain together.

Suppose the larger gear as T teeth, and the smaller has t teeth. If you pull in enough chain to rotate the paired gears 1 revolution clockwise, then you have removed T links of chain from the hanging loop, and added t links feeding off the smaller gear into the loop. So the loop gets shorter by ( T - t ) links, and since the loop goes down to the idler and then back up, the idler rises by ( T - t ) / 2 links.

So you exert a force through a distance of T links, and get an output through ( T - t ) / 2 links.

If the two gears have 24 and 20 teeth, for example, you pull in 24 links of chain to raise the load 2 links. 1 / 12 the distance means 12 times the force