Dynamic Equations of a Manipulator With Rigid and Flexible Links: Derivation and Symbolic Computation

The objective of this paper is to present an efficient procedure for computer-generation of the dynamic equations for a planar robot manipulator with arbitrarily assigned rigid or flexible link using any desired flexible mode shape functions. The dynamic equations for the serial-link manipulator are derived using Lagrange´s formulation and elastic deflection with the assumed-mode method. Fewer approximations are made than in other approaches, resulting in greater accuracy. A method to determine the Centrifugal and Coriolis matrix is presented that yields an important structural property. The approach is systematic and allows a symbolic program to be written in Mathematica using a system of several groups and a constructed database. Four examples are illustrated to verify of the dynamic equations. The stability of the zero dynamics is compared for different mode shape functions.