I am writing a kinematics library in Go as part of my final year project. I am working with Product of Exponentials method and have successfully implemented the Forward Kinematics part of this. I need help with the Inverse Kinematics.
I understand the theoretical aspect of it. I would like a numerical example where actual numbers are used for the Paden-Kahan subproblems as the ones dealt in "A Mathematical Introduction to Robotic Manipulation - Murray,Li and Sastry" [freely-available online PDF].
I specifically need help with knowing what should p,q be when trying to solve the inverse kinematics. The book just says given, a point p,q around the axis of rotation of the joint. But how do you know these points in practice, like when the robot is actually moving, how do you keep track of these points? For these reasons I need a numerical example to understand it.