Kinematic Analysis of Cam and Wing

By inspection from the Krakuri book, we can see that the motion of the gear appears to follow a cubic relationship. Using this intuition, I used excel to run a cubic regression relating the thetas with the radius of the gear. Using the extracted equation, I was able to calculate the position of the penguin with respect to the input angle. Similarly, for the velocity of the penguin, the gear position equation was differentiated once to obtain the velocity equation.

The next section of analysis covers finding the wing tip velocity. Using the geometry of the wing tip area, we are able to find equations that relate theta4 with the input crank theta. This was useful because it allows us to find the wing tip velocities.