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

[betwys1 at SBCGLOBAL.NET (Brian Whatcott)]

I am unsure why bc's question popped up in my reader after so long,
but for my own amusement I offer this:
A rigging screw is one heterodox example of a differential screw.
Here the screws are usually of the same pitch, one left hand and the
  other right hand, so that turning the body of the screw causes both
screws to enter the body of the rigging screw, or exit - together.
The overall effect is to provide a length change of two screw
pitches per revolution.

A rigging screw designed with two screws of the same chirality,
but with different pitch, would be a more understandable example of
  differential action.
Here, one screw departs one pitch, while the other enters the body
  by one pitch. The overall length change is the difference of the two
pitches per revolution.

Brian W

At 08:22 PM 6/20/2003, you wrote:
> 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).


Brian Whatcott    Altus OK    Eureka!