After setting up our vector loop, we had a three dimensional vector loop equation. We used MATLAB’s symbolic toolbox to solve for 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 also useful for analyzing the position, velocity, and acceleration profiles of our mechanism.
In order to perform a reasonable motion study of our mechanism, we needed data from a normal human elbow bend. We searched around the literature and found a study on human hand motion [1]. The study had recorded the position, velocity, and acceleration data for a normal human hand raise over a 0.6 second period. Based on the length of the arm in our model, we converted this data into angular positions, velocities, and accelerations of an elbow joint, theta 2. These values were then fed into our earlier derived expressions 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. Note that the X component of this acceleration is 0.
Figure 4. Coriolis Acceleration Profiles Through a Normal, Human, Elbow-Bend
Figure 1. Mechanism Diagram
Figure 2. MATLAB Animation of Mechanism Motion