17-3 Kinematic Analysis
A Jansen linkage is an 8-bar mechanism which can be divided into 11 rigid links (plus ground) connected at pivot joints to produce a path for the “toe” that mimics a walking gait. The entire analysis we have used centers around “dyads”. A “dyad” is simply two links connected in series. Link A pinned to the ground or is a moving point and link B connects A to a known point. The entirety of the Jansen linkage can be broken into 6 total points that need to be found with 5 of those being a dyad and 1 being a simple trig problem. This method is also commonly referred to as the Law of Cosines.
So, given two known link lengths connected between two points, the solver treats the distance between those points as the third side of a triangle. By finding the magnitude and angle of the vector R (the displacement between your two known pivots), we use the Law of Cosines to calculate the interior angle α of the joint:
This method is preferable since we don't have to solve the entirety of the Jansen linkage in one giant system of equations or through complex large matrices. 17-3-1 includes the code used with additional comments on what each code part does.
Using this theory our team wrote a python program that is able to utilize this and quickly calculate all the values for position (figure 1), velocity, acceleration and force (figure 2) and visualize this.