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The radius of the cam can also be defined by the following vector loop:
Where c is the distance from the cam's axis of rotation to the center of curvature and rho is the radius of curvature.
Recall Equations 1 and 2:
Equations 1 and 10 can be set equal to each other and separated into its real and imaginary components:
The velocity in in/rad is obtained by taking the derivative of Equation 12 with respect to angle theta. This derivative is given in Equation 13.
As you can see, the point of contact distance is equal to the velocity in units of in/rad. Figure 14 compares my measurements for point of contact distance to the first derivative (d/dtheta) of the displacement trend line. The point of contact distance plot does follow the velocity plot well, but it is not a perfect match. As I stated previously, the point of contact distance was difficult to measure and there is some uncertainty in how accurate my measurements were since they were taken with my caliper from outside the model base rather than inside and against the cam.
I also noticed that the displacement of the penguin could be described by trigonometry equations after reaching the maximum displacement value. From 296 degrees to 350 degrees, the maximum radius of the cam is in contact with the follower and forms the triangle:
Real:
Imaginary
where displacement, s, is calculated with the following equation:
From 350 degrees to 360 degrees, the maximum radius of the cam loses contact with the follower and forms the triangle:
