In this thesis, it is proposed to solve for the accelerations and internal forces of multiple connected rigid bodies using recursive formulations and screw theory.
Screw theory allows for compact notation of the equations of motion and kinematics.
The concept of a single articulated inertia modeling the behavior of an entire subchain is used to simplify the equations such that a recursive solution is possible for systems with no kinematic loops. In planar cases, the graphical interpretation of the equations introduces the connection between projective geometry and dynamics with screw theory. Projective geometry uses subspace decompositions and projections to extract useful information from problems. Similarly in dynamics, to find the reaction forces on all the joints, the splitting of all the internal forces into active and reactive subspaces is required. The splitting of body accelerations into active and reactive parts is also needed in order to understand how each solution affects the next recursion.