## PSN-L Email List Message

**
Subject: Re: The revised and corrected "zero force" hinge**

From: ChrisAtUpw@.......

Date: Sat, 20 May 2000 22:23:17 EDT

Dear Brett Nordgren,
The 'zero force' hinge analysis given in zerohng2.pdf as referred to the
rolling cylinders, may be easier to understand if you think of it in a
different manner. Consider two equal diameter pulleys with fixed parallel
axes of rotation having a crossed belt running around them, giving
contra-rotation. When you turn one pulley, the other moves through the same
angle, but in the opposite sense.
If you now fix one pulley and allow the axis of the other to rotate
around it, the moving pulley rotates twice while going once around the fixed
pulley. The position of the crossover of the belt moves in a circle half way
between the pulleys. This analysis can be extended to circles of different
diameter with different 'belt' lengths.
The slight 'catch' about this 'zero force' design is that unless the belt
is 'completely flexible', bending the belt over the pulleys involves a force
which tends to pull the pulleys together - the natural shape of the 'straight
bit' forming the hinge is actually 'S' shaped.
Regards,
Chris Chapman
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Larry Cochrane <cochrane@..............>