Kinematic Diagram:
Manual position, velocity, and acceleration analysis: (Based on equations provided in Design of Machinery)
The resulting equations for position, angular velocity, and angular acceleration were put into a MATLAB script along with all the relevant constants. From here, I was able to create an animation of the mechanism, as well as the various plots shown below.
In the animation below, the cyan and magenta circles represent the path of the input links as they turn on their respective gears. The yellow circle represents the rotating platter. The path of the pen is plotted in green, showing the position of point P on the mechanism as the pen completes one period, or 3 full revolutions of the input link.
Below are some plots of the linear position, velocity, and acceleration of the pen as it moves. Note that these plots do not take into account the rotation of the paper on the platter; the plots reflect the movement of the pen only.
Figure 11. Linear Position, Velocity, and Acceleration of Pen.
The plots below show the same data, but plotted with respect to the angle of the input link, theta2.
Figure 12. Linear Position, Velocity, and Acceleration of Pen with respect to theta_2.
Next are some plots of the angular motion of link 3, to which the pen is fixed in the model. This motion is plotted with respect to the angle of the input link, theta_2.
Figure 12. Angular velocity and acceleration of link 3.