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[Phys-L] Differential screw, was : Re: Chain Hoist Operation



pse. follow up with the differential screw, as found in optical stages
(e.g. interferometers)

bc

John S. Denker wrote:

On 06/20/2003 10:54 AM, Tony Wayne wrote:
Can anyone describe how a manual chain hoist works? I've looked
across the internet and have only found products and demonstrations
utilizing a chain hoist.

It's a differential pulley. Apparently invented by T.A. Weston
some time before 1875.
http://www.yale.com/historypop1875.htm

From a distance it looks like an ordinary block-and-tackle.

The trick is that on one block (let's call it the
upper block) rather than having two free-running
sheaves, the two sheaves are locked to each other,
typically made from a single piece of metal. Also,
one of these two sheaves is slightly smaller than
the other.

There are differential pulleys that use rope or
cable, but in the case of a chain, the sheaves
have pockets to grip the links of the chain,
ensuring zero slip.

In any case, the two sheaves on the upper block
have slightly different diameters.

The device is rigged with an endless chain, forming
two loops. One loop threads the lower block, while
the other loop is just free. In operation, one loop
gets bigger while the other gets smaller.

When you rotate the sheave of the upper block, it
changes the size of the loops in proportion to
the _difference_ in radii of the two sheaves on the
upper block. That's because it is taking up chain
with one sheave while it is letting out chain with
the other.

By making the radii nearly equal, you can get
arbitrarily large mechanical advantage (for
continuous rope or cable). For chains, the
minimum differential is one link, so the mechanical
advantage scales like the number of links that
fit around a sheave (plus a factor of two for the
conventional pulley effect).