Automated Derivation of Equations of Motion for Open Chain Mechanisms

This paper describes a specialized computer algebra system for automated derivation of models of dynamics for open chain mechanisms. The considered mechanisms consist of a moving base and an arbitrary number of links, connected serially by prismatic and rotary joints. The order of the joint types is arbitrary. Given types of the joints, the system obtains equations for linear and angular velocities of each body in the mechanism. Then, the system obtains the Lagrangian for the mechanism in the symbolic form. Then, using symbolic differentiation of the Lagrangian, the system obtains the equations of motion for the mechanism. Finally, the equations are translated into the Matlab/Octave language. The algebraic expressions are represented by data structures based on a novel theory of generalized multisets. The whole system is implemented as a logic program, using the SWI-Prolog language. Completeness and correctness of the program has been verified by solving for robotic manipulator dynamics.