Analysis of the Cams

Above is an image of one of the cams used in the model. They are attached to the horizontal axle where the yellow portion is. The center of the yellow square thus serves as a center of rotation for the cams. Notably, the shape of the cams (snail/drop cams) mean that the cams can only be turned in one direction, in this case, clockwise. If turned counterclockwise, the flat portion will get caught against the side of the follower rod base, impeding motion. The shape of the cam was taken to be two semicircles of differing radii, with the center of rotation being the midpoint of the smaller semicircles flat edge. The radius of the small semicircle was measured to be about 1.6 cm, while the radius of the large semicircle is about 3.9 cm. The instantaneous radius of the cam is defined as the vertical distance upwards from the center of rotation, as the cam is designed to pushed straight up on the penguin body. This means that the radius is constant while any point on the edge of the smaller semicircle points up, and increases from the point where the two semicircles meet points upwards to the position shown in the image above. The half where the radius increases is similar to half an eccentric cam, which is a circular cam with an offset center of rotation. From the Design of Machinery textbook by Robert L. Norton, eccentric cams follow simple harmonic motion, and thus the radius during this portion follows a cosine curve going from the minimum radius of 1.6 cm, to the maximum radius of 3.9 cm. After the cam hits the position shown in the image above, the sharp corner remains the highest point for a while. During this time, the vertical distance is the maximum radius of 3.9 multiplied by the cosine of the angle measured from the vertical axis to the sharp corner. A video of the cams in motion is shown below. The last part shows how it gets stuck if turned the wrong way.