Kinematics and Dynamics of Flexible Robotic Manipulators Using Dual Screws

Abstract

In this article, we present a new procedure for the derivation of the linearized kinematics and dynamics of a flexible industrial robotic manipulator. We introduce the Lie groups of dual rotation and dual homogeneous transformation matrices, which are the basis for the derivation of dual twists. In addition, dual screws and dual screw transformation matrices are introduced, which are used for the development of a general and systematic linearization procedure for both kinematics and dynamics. This leads to expressions that are linearized in all the states associated with the elastic motion. The dynamic modeling procedure is based on Kane's method, where the partial velocities and partial angular velocities are given as dual screws arranged as columns of dual projection matrices. The elasticity of the links is modeled by the assumed mode method. The presented procedure is implemented numerically for a 4-degrees of freedom manipulator and the simulation results are given.