Heart cam size

[Achiles]

How to calculat a heart cam shape size?

[R.G.]

Nobody else seems to be helping, I'll try.

A circle is a cam with all radii being equal length. A cam is a circle with radii of unequal lengths.

A cam rotates and pushes some cam-follower in and out by the variation of it's radii as it turns. To calculate the shape of the cam, you make a list of what distances you want the cam follower to be from the center of revolution of the cam for each unit of turning.

In the case of a heart shaped cam for a wiring traverse, you pick some minimum radius for the innermost extent, and some maximum radius for the outermost extent. The difference between them is the traverse distance. Since a heart-cam is symmetrical, you only have to calculate one half, the other is the mirror image.

If, for instance, you want a 1/2" (0.50") traverse, you can calculate the length of the radius at each degree for 180 degrees. Notice that if you start with a circle of some radius and make that radius be the minimum, then you only have to add the calculated distance to the radius. Each degree gets another 1/180th of the 0.5" traverse added to it.

So at
0 degrees, d=0 ("d" stands for what you add for each incremental degree)
1 degree d= 0.5/180 = 0.0027777"
2 degrees d= 0.00555555"
3 degrees d = 0.00833333"
4 degrees d = 0.011111"

and so on, adding 0.0027777" each time.

I haven't said how big a basic circle to add these to. That's because in some ways it doesn't matter. If you start with a "circle" of radius 0", then you add 0 to each of the calculated lengths and you get a "heart" that varies from 0 radius up to 0.5".

Why isn't it done that way? Because it's hard for the cam follower to follow it. The bigger the radius of the center circle, the easier it is to follow the variations in distance from the center.

Looking back I realize this explanation is a modell of obscurity; it wasn't intended that way, it's just hard for me to explain without pictures or equations.

[David King]

Wouldn't a heart shaped cam pile more wire on one side of the bobbin than the other?
I used to have an old sewing machine (Singer) that came with all sorts of cams to move the needle from side to side to make different stitch patterns. I bet you could buy a box of those cams and play around with them -eventually filing them down to get just the right tone. Sewing machines are amazing in that they so closely resemble a coil winder that needs to be unscrambled like an anagram.

[David Schwab]

David, the idea is supposed to be that it piles more wire in the middle, but this compensates for a regular side to side traverse tending to pile more wire on the two ends of the coil.

[R.G.]

The point of a cam is that it converts rotary motion to linear motion.

If you had a circular "cam" with a pushrod crank on it, the pushrod end would move in something close to a sine wave velocity - speed fastest in the middle, with lots of dwell at the ends as it changed direction. That's what DS is referring to. The side to side motion of a traverse piles up more wire where it moves most slowly. So a pushrod style traverse would pile up wire at the ends of travel.

By changing to a cam, you get a chance to "program" the motion by making the lateral distance pushed by the cam surface be non-sinusoidal. A cam that linearizes the traverse motion to a constant movement per unit of rotation with two reverses has an inward point and an outward point, because you want the reversal at the end of the traverse to be instantaneous to keep from having a pileup at the ends.

[Joe Gwinn]

How to calculate a heart cam shape size?With great care?

A heart-shaped cam is intended to impart linear back-and-forth motion to the cam follower, with abrupt changes of direction at the ends. So, there are two segments. One segment is the linear increase of radius with angle, going from minimum radius at 0 degrees to maximum radius at 180 degrees. The other segment is the mirror image of the first segment, going from max at 180 degrees back to minimum radius at 360 (=0) degrees.

[Arthur B.]

How to calculat a heart cam shape size?

You mean caridiod? Just use the polar quation in this Wikipedia article (http://en.wikipedia.org/wiki/Cardioid). For more info go here (http://mathworld.wolfram.com/Cardioid.html).

[Joe Gwinn]

You mean caridiod? Just use the polar quation in this Wikipedia article (http://en.wikipedia.org/wiki/Cardioid). For more info go here (http://mathworld.wolfram.com/Cardioid.html).The desired cam shape is not necessarily a cardioid

[Achiles]

how should be a football ball shape cam,making it "fat" or "slim"?