4 - Cam Shape

The vector loops stated previously are restated here for convenience:

Setting Equation 1 and Equation 2 equal to each other results in the following two equations:

In cam design, the above two equations can be used by a machinist to create the cam for a flat-faced follower (Norton, 2012). I did not design the cam, but to verify that these equations do indeed work out, I decided to measure the displacement of the follower, s, and point of contact distance, x, for every ten degrees of rotating the camshaft. The base circle of the cam, Rb, was measured at about 0.555 in. My measurements for s and x are plotted in the following two figures.

                                                                   Figure 8. Ready To Fly Penguin Displacement.                                                                                                                     Figure 9. Ready To Fly Point of Contact Distance.

Using the values for s and x before the drop off in the cam radius and plugging them into Equation 3 and Equation 4 with their corresponding values for theta to obtain values for r and q, plotted in the following figures.

                                             Figure 10. Ready To Fly r Value.                                                                                                     Figure 11. Ready To Fly Point q Value.

Again, these values r and q describe the Cartesian coordinates of the contact point between the follower and cam with respect to the rotating axis coordinate system embedded in the cam (Norton, 2012). The radius of the cam at different angles can also be calculated from r and q by calculating the hypotenuse of triangle formed by r, q, and the radius of the cam Ra (sqrt(r^2+q^2)). These radius values can be plotted on a polar plot with their respective angle values, and the resulting plot should reflect the shape of the cam. In Figure 12, the radius of the cam calculated from r and q is plotted along with the radius values I measured directly from a cam I reprinted to the same size as the cam used in the model. The radius of the cam measured from r and q very nearly match the radius I measured directly on the cam. The slight differences in radius values seen in the plot can most likely be explained by the way I constructed the cam I used in the model and the point of contact distance. I traced the cam shape from the Karakuri book onto the cardboard so the cardboard cam is probably slightly over-sized due to the outside trace. It was also difficult to measure the point of contact despite my efforts to get the best view by cutting out windows in the model base. Because I did not want to cut into the model base anymore than I already had and risk model collapse, I measured the point of contact from a distance, outside the model base. Perspective may have affected where I perceived the point of contact to be relative to my caliper.

                          Figure 12. Ready To Fly Cam Shape.