calculating cam clamps

In Ch.10 of Edward G. HOFFMAN's book, Jig and Fixture Design, 3d ed.,
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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Reply to
Allan Adler
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don't speak German, but babelfish says 'cam' is 'Nocken'
if i'm not mistaken...
'throw' and 'rise' for cams is sometimes interchangeable. though i believe 'rise' is the proper name for cam displacement 'throw' is sometimes used to describe the overall motion of a system (& 'throw' intends a direction, whereas 'rise' might not. sort of the scalar/vector thing)
rise is the total change in distance at a contact point during one revolution... or the difference between the base circle and a circumscribed one. (for a cylindrical cam)
throw, for a cam used directly as a mechanical clamp, may be the rotation required, in degrees or inches (depending on design), to exert a predetermined pressure on the work. this may include a few more degrees (+ % rotation) to place the cam in a stable position for clamping (or it may be designed into the cam).. although maximum pressure would be exerted at the point of maximum rise, that point may not be stable (the cam could 'roll back').
those coefficients of frictions may be ratios, and not direct coefficients. depending on your design (or the one mentioned in the book), you may be dealing with both sliding and rolling contact. in which case two coefficients would need consideration and may be reduced into their ratios (0.1 or 0001, etc)
for further info on cam design i'd suggested either Mark's Standard Handbook for MechanicalEngineers or the Machinery's Handbook.
dont know if any of that helps, -tony
Reply to
tony
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I'm not sure what a spiral cam is, but most cams we come across are those in cars. The simplest way to think of an automotive cam is as two circles, one on top of the other, with the upper circle having a smaller radius of curvature than the other, and continuous lines are drawn to "connect" up the circle. This make up a continuous shape, but I would surprised if there were a simple analytical expression for the shape. The cam rotates around the centre of the lower circle (this is known as the base circle). As a cam rotates around it pushes on the valve, pushing it into the combustion chamber. The shape of the cam is determined by what type of valve lift profile is required for effective combustion. The valve lift curve often is an analytical function. A good description may be found in the following book: "Cam Design & Manufacturing Handbook" by R.L. Norton Hope this helps
Ian Taylor
Reply to
Ian Taylor

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