Modeling and simulation of planar flexible link manipulators with rigid tip connections to revolute joints

Abstract

This paper presents the basis of a mathematical model for simulation of planar flexible-link manipulators, taking into consideration the effect of higher stiffness zones at the link tips. The proposed formulation is a variation of the finite segment multi-body dynamics approach. The formulation employs a consistent mass matrix in order to provide better approximation than the traditional lumped masses often encountered in the finite segment approach. The formulation is implemented into a computational code and tested through three examples; cantilever beam, rotating beam and three-link manipulator. In these examples, the length of the rigid tips at both sides of each link ranges from 0% to 6.25% of the whole link length. The zones of higher stiffness at the link tips are treated as short rigid zones. The effect of the rigid zones is averaged along with some portions of the flexible links, thereby allowing further simplification of the dynamic equations of motion. The simulation results demonstrate the effectiveness of the proposed modeling technique and show the importance of not ignoring the effect of the rigid tips.