The penguin motion profile was plotted based on the displacements I measured in the previous section. I defined zero degrees to be approximately the point where the straight edge of the cam falls away from contact with the follower, and the follower returns to contact with the cam's base circle. No displacement was measured for the first 50 degrees and so I set the displacement, velocity, and acceleration of the penguin to zero for the first 50 degrees. Using Excel, I made a trend line for the rest of the displacement data points. The first and second derivative of this trend line define the velocity and acceleration of the penguin, respectively. The penguin's motion profile plots are given in Figures 13 - 15. The velocity plot is given in both in/s and in/rad, and the acceleration plot is given in both in/s^2 and in/rad^2. For the plots given in units with time, the time derivatives were taken on the trend line. For the plots given in units with radians, the trend line was multiplied by d/dtheta for velocity and multiplied by d^2/dtheta^2 for acceleration.
Figure 13. Ready To Fly Penguin Displacement And Trend Line.
Figure 14. Ready To Fly Penguin Velocity and Comparison to Point of Contact Plot.
Notice that the point of contact distance plot is also overlaid on the velocity (in/rad) plot.
The radius of the cam can also be defined by the following vector loop:
Recall Equations 1 and 2:
Equations 1 and 10 can be set equal to each other and separated into its real and imaginary components:
Real:
Imaginary:
