I'm pretty much convinced now that the upright rail, although moveable,
can only move away from the motor, not towards it, from the upright position.
The argument is as follows:
(1) Let the rivet for the upright rail be A, the rivet for the release lever
be B, let the rivet joining the release link pivot to the release link be
C and let the rivet joining the release crank to the release link be D.
Assume the motor is on the left, so that A is the left of B. Then if one
tries to push the upright rail towards the motor, the motion of the
upright rail and the release lever will both have to be counterclockwise.
(2) Let E be a point on the base to the right of B. Then the angle CAE is
less than 90 degrees and angle DBE is more than 90 degrees. That means
that when the rails are rotated to the left, C moves up and D moves down,
and therefore, since D is lower than C to begin with, the vertical
distance between C and D increases.
(3) On the other hand, the right side of the release link pivot blocks the
left side of the release crank, which makes it impossible for the
horizontal distance between C and D to decrease. However, the actual
distance between C and D is always the same, since C and D are rivets
located on the release link, which is one piece of metal.
(4) The square of the distance from C to D equals the sum of the squares of
the horizontal and vertical distances between C and D (Pythagorean
theorem). If the motion towards the motor were possible, the horizontal
distance would not decrease and the vertical distance would definitely
increase, so the distance between C and D would have to increase, which
it can't.

Therefore, motion towards the motor is impossible.

I think that aspect of the design of the frame assembly is pretty clever
and is not explicitly mentioned by Gingery. There is nothing actually
blocking the path of the upright rail from moving toward the motor, but
it still can't move that way. And that feature would have to be preserved
by anyone proposing to modify the design for use with another motor. The
moral is that one has to make sure that the release link pivot and the
release crank have a significant overlap of their vertical edges.

There must be a lot of tricks like that which apparently everyone takes for
granted, but this is the first time I've seen anything like that. There is
an expensive (one could buy a Clisby instead) four volume work called
"Ingenious mechanisms" which might be the place to look for things like
this and might not. Does anyone know of a book that definitely has this
trick in it (besides the Gingery lathe book)?

Ignorantly,
Allan Adler


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* Disclaimer: I am a guest and *not* a member of the MIT Artificial *
* Intelligence Lab. My actions and comments do not reflect *
* in any way on MIT. Moreover, I am nowhere near the Boston *
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