The cam design for the Tarba Tron prototype was great for a proof of concept but didn't produce the intended Sine wave. I didn't have much luck looking for a Sine wave cam model online because that is not the mathematical model it usually needs to produce. Wikipedia had a good explanation and model of a traditional application.
A cam is a rotating or sliding piece in a mechanical linkage used especially in transforming rotary motion into linear motion or vice versa. It is often a part of a rotating wheel (e.g. an eccentric wheel) or shaft (e.g. a cylinder with an irregular shape) that strikes a lever at one or more points on its circular path. Source
I set upon creating a model myself. I currently plan on using a 8 ft piece of lumber as the follower. The pivot point will be located at 1/5th of the total length or 16 inches from of the "back" end. So a deflection of 1 unit will create of 4 units of movement on the front end. In other words if the variable a in the following diagram has a magnitude of 10 inches, bwill be 40 inches.
So the knowns are that I would like the back end of the follower to have a total deflection (a) of 10 inches in a sine wave pattern. I plotted the sine function from 0-360 degrees in 20 degree increments with multiplier of 5. Then, I chose a minimum cam radius of 3" and used the values derived in the previous step to calculate distance from center of cam to the point where the cam contacts the follower. This is what the two values look like at different angles.
Since the values were calculated in 20 degree increments, I now had 19 different points that define the cam shape. The information was in Polar coordinates and was converted to Cartesian so it could imported to inventor. This is the Inventor screenshot post-import.
I used the spline interpolation tool and added the shaft and alignment holes to finish the cam profile!
The final dimensions are just under the 18"x24" footprint of the 60W laser cutter at the Milwaukee Makerspace. Which is great since I highly prefer using the laser cutter over the CNC router.
The concave shape at the lowest point on the cam profile will likely not touch the follower (piece of lumber) unless a small idler/bearing is added whose radius is smaller than the groove. I may have to do some experimentation on the effects on the wave shape first. Though, a lower friction contact point may be a good idea anyway.
Next step is to cut this profile out of cardboard and get a feel for the shape and size in real life.