Wheeled Biped Pt. 3 Forward Kinematics

I started modeling the robot in more detail in Matlab and now have a forward kinematics (I give the system a motor joint angle, and it computes the keypoints and draws the system). The math was pretty terrible to solve the 4-bar linkage which may prove a problem for the dynamics I’m trying to work out now. My current plan is to use Matlab’s symbolic differentiation to do the majority of the work from now on.

First I defined some angles and defined my keypoints with respect to those angles. In this case, Theta 1 is my controlled angle, and Theta 2 is fixed. I tried solving the 4-bar kinematics in my own ways by finding the definition of points using 2 paths but couldn’t solve them. My formulation for Theta 4 was unpleasant and was flipped in Matlab so I ditched it because I didn’t need it.

Then I tried law of cosines, and also got stuck. So I went to YouTube and found a video explaining 4-bar kinematics, rotated and flipped my linkage to put it in their perspective, and solved it. The problem I had was with defining theta 1 and theta 2 separately I believe. The final worked out angles are mostly shown at the bottom, although the real solution is in the Matlab code. By finding alpha and beta, I could find Angle A, which led me straight to Theta 3.

When ensuring I solved the system correctly, it was extremely beneficial to have my Solidworks sketch model open to confirm angles as I found them. I’ve been known in my friend group as the goon who uses Solidworks to help me figure out kinematics, effective gear ratios, etc.

Next steps are tentatively to use Lagrange Equations to find the equations of motion. Then I generate a list of thetas from torque at the actuator, I can visualize them using this code.