pp.164-167, one finds a skimpy explanation of how to design eccentric

cam clamps and spiral cam clamps. What follows is my synopsis, not what

Hoffman says.

In an eccentric cam, the cam is basically a disk and is rotated about an

interior point (called the pivot point) other than the center. The distance

between the center of the disk and the pivot point is called the eccentricity.

The throw seems to be the angle one wishes to rotate the disk, but the

characteristics of the end points of the rotation are not articulated.

A certain change of distance associated with that rotation is called the

rise but never defined. Naively, one might expect it to be the difference

in the distances of the pivot point to the points on the disk corresponding

to the end points of the rotation, but Fig.10-24 suggests that it might have

a different meaning. The formula E=R(1-cos throw) is given, where R is the

rise and E the eccentricity. The formula for the required radius of the

disk depends not only on the geometry but also on the coefficient Cf of

friction of the material, which is usually assumed to be 0.1. The formula

is: radius=E(cos throw + (sin throw)/Cf).

For spiral cams, I think they are talking about an arc of an Archimdean spiral,

viewed as a small deformation of an arc of a "base circle", and the center of

rotation is the center of the spiral, which coincides with the center of the

base circle. Here, the coefficient of friction doesn't enter explicitly into

the formula, which says that the rise equals 0.001 x radius of the base

circle x throw. But maybe the coefficient of friction is hidden in the 0.001

just as it could have been stashed in the number 0.1 in the earlier formula.

I'd like to know where these formulas are derived and explained in more

detail. I'd also like to know what the German word for cam is, on the off

chance that I can look this up in the Encyclopadie der Mathematischen

Wissenschaften, or else a pointer to where in that reference old stuff

like this might be discussed.

Ignorantly,

Allan Adler

snipped-for-privacy@zurich.ai.mit.edu

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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 ***

*** metropolitan area. ***

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