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The pulley system can be analyzed with a mathematical proportion. The initial fromula can be stated as:
MOTOR RPM * MOTOR PULLEY DIAMETER = LATHE RPM * LATHE PULLEY DIAMETER. If you know three of these components you can solve for the unknown fourth component. For example, if you know the motor rpm, the motor pulley diameter, desired lathe rpm and want to calculate the LATHE PULLEY DIAMETER, you can rearrange the formula to state ((MOTOR RPM * MOTOR PULLEY DIAMETER) / LATHE RPM) = LATHE PULLEY DIAMETER. The homework assignment for today will be to solve for the other three components.
I found SINCERE TOOLS initially by going to Ebay and looking under WATCHMAKER LATHES. If you scroll through this section until you find a picture of their lathe you will find it. Also, they are always listing their cross slides for sale for $245.00 and you can click them on from there as well. I think they also have a page on the general internet and will take a look.