Recursive Formulation for Dynamic Modeling and Simulation of Multilink Spatial Flexible Robotic Manipulators

Abstract

The dynamics for spatial manipulator arms consisting of n flexible links and n flexible joints is presented. All the transversal, longitudinal, and torsional deformation of flexible links are considered. Within the total longitudinal deformation, the nonlinear coupling term, also known as the longitudinal shortening caused by transversal deformation, also is considered here. Each flexible joint is modeled as a linearly elastic torsional spring, and the mass of joint is considered. Lagrange's equations are adopted to derive the governing equations of motion of the system. The algorithmic procedure is based on recursive formulation using 4 × 4 homogenous transformation matrices where all the kinematical expressions as well as the final equations of motion are suited for computation. A corresponding general-purpose C++ software package for dynamic simulation is developed. Several examples are simulated to illustrate the performance of the algorithm.