Kinematic analysis performed in MATLAB displayed the link positions, a visualization of the mechanism, and the foot trajectory. The MATLAB scripts for this analysis can be found in the appendix. This analysis uses the kinematic diagram below for vector loop equations and angle measurements from the horizontal.
To solve the mechanisms position, the MATLAB script first solves the position of links J, B, C, and K for all values of Theta M using four-bar position analysis. It then uses geometry equations to solve the positions of the other links since they are fully dependent on the position of the four-bar mechanisms in this 1 DOF mechanism. The graph below plots the angles of each link against the input angle. The links from the two four-bar sub-mechanisms are solid lines. The foot links H and I are dash-dotted lines. The rest are all dashed lines.
While this plot contains a lot of information, one trend is readily present. This mechanism is able to convert a full rotation of the input link into a motion where no links individually have to rotate that much. No link rotates more than 150 degrees from its original position. One major cause of this is the very short length of link M which makes both the four-bar sub-mechanisms meet the Grashof condition. The links 3 and 4 of the four-bar sub-mechanisms only slightly rotating is what allows the rest of the mechanism to have movement that matches the flexing of a leg more than circular motion. Using these angles as a function of the input angle, I created a simulated animation of the Jansen mechanism for one full rotation of link M.
The Grashof characteristic of the mechanism is very clear in the animation. Most links do not rotate far from their original orientation to the horizontal. This Grashof motion is converted into a walking-like motion with the geometry of the couplers and the quadrilateral. Since the couplers are triangles, their shape has 0 DOF; they cannot change shape. So couplerÂ
I also used this MATLAB script to plot the path of the foot joint which will be addressed in the next section.