This was a project I completed for ME 314 at Northwestern University. It is a dynamics course focused on variational methods combined with geometry to provide relatively straight forward approaches to constrained rigid body mechanics. This includes impact mechanics and therefore lends itself to analyzing things like human locomotion. My project doesn’t go that far - it only uses a 1R robot - but the general strategy could be extended to a 7R robot which is reminiscent of a humanoid stucture in profile. More specifically, this project aims to simulate the dynamics of a basketball free throw in regards to the hand, ball, and hoop. The hand is the 1R robot I was referencing earlier and you can think of the rotational joint as the wrist.
All basketball players initially start there shot with the ball tightly coupled with their hand movement. They then release that relatively fixed constraint and allow the ball to roll up their hand and off their fingetips as they rotate the hand to push the ball up and forward. Once the ball leaves the fingertips, the ball only interacts with the hoop and floor through impacts and friction. A coefficient of restitution in used to handle the energy loss during bounces, but I have not yet added friction.