The kinematic challenge of this project was modeling the motion of the slider. The upper arm is idealized as the “ground”. The slider will move in two ways simultaneously. It will move counterclockwise along the helix (a helix which is defined about the vector R2), and it will rotate clockwise about R2. The slider is constrained onto the y-z plane by these two counteracting motions. A vector from the forearm to the slider, R3, will define the slider’s motion.
After setting up our vector loop, we had a three dimensional vector loop equation. We used MATLAB’s symbolic toolbox to get the th1 and c variables in terms of th2. The kinematics analysis was very valuable here, because we were able to explore the feasible range of dimensions for this mechanism. These results were then plugged back into our vector loop equation and used to perform velocity and acceleration analyses for our mechanism.
Figure 1. Mechanism Diagram Figure 2. MATLAB Animation of Mechanism Motion
Based on the measurements from a study on human hand motion [1], we converted the position, velocity, and acceleration data for the hand to angular positions, velocities, and accelerations of an elbow joint, theta 2. These values were then fed into our equations to determine the motion profiles of link R4's rotation (theta 1) and the slider's sliding (c).
Figure 3. Joint Motion Profiles Through a Normal, Human, Elbow-Bend
We also plotted the X,Y, and Z projections of the Coriolis acceleration for this range of motion:
Figure 4. Coriolis Acceleration Profiles Through a Normal, Human, Elbow-Bend