motion-multiplying pulleys: linear to rotary encoder

How to get more precision from existing rotary encoder
whose shaft is turned by wire, ends attached to table:

Consider a force-multiplying pully system:

T -----------------------------\
O |
/ -----------------------------/
| TP
\ -----------------------------\
O|
ES ----------------------------/
- _
- _
<-------


T is table, that end of wire is fixed to.
O are pulleys, attached to a base (not the table), and do not move with the table.
TP is a pulley mounted on the table, and travels with the table
ES is an encoder shaft with the wire wrapped around it.
The lines are a single wire going around the pulleys and around the encoder shaft.

There is a mirror image to the left not shown for clarity. For
explanation, assume we are pulling the wire to the left. The
table moves to the right 1/4 as fast as the wire moves to the left.

Conversely, if the table is forced to the right (by a ballscrew or
whatever), the wire is pulled from the left at four times the rate of
the table.

I hope this shows how to amplify the precision of the encoder by four.
Other pulley arrangements can obviously be used for different ratios.

Note also that if ES is replaced by a servo or stepper motor shaft,
that the torque and precision is increased by four, and if an encoder
is attached to the motor you'd also gain the benefits above. The downside
is of course 1/4 the speed (but perhaps some of that is overcome by
the much reduced load).

Doug Fortune