The mechanism analysis was split into two parts - the analysis of the bottom linkage; driven by the sliding joint, and the analysis of the top linkage, which includes the gripper.
The bottom portion of the mechanism can be modeled as a slider-crank which receives its power from the linear motion of the slider rather than the rotary motion of the crank. The angles and angular velocities of the joint can be derived as functions of slider position d and its derivative, the sliding velocity. Both of these are directly proportional to the motor output and the pitch of the screw.
The top portion of the mechanism can be modeled as a closed loop composed of one ground link (green), a grounded sliding joint, and two links. The angles and angular velocities of the joints can be derived as a function of the input angle, from the cyan link, which is solved for in the analysis of the bottom linkage.
TODO finish in gdocs
