DYNAMIC ANALYSIS OF ROBOTIC MANIPULATORS WITH FLEXIBLE LINKS (OPEN-CHAIN, SEQUENTIAL, EQUIVALENT)
Abstract
The objective of this dissertation is to develop a dynamic model for flexible manipulator systems and a solution method to solve the equations of motion efficiently. The model describes the global motion of the flexible manipulators as a large motion and a small motion. The large motion is represented by the Equivalent Rigid Link System (ERLS) which is kinematically equivalent to the real rigid link system. The small motion represents deformations of the system relative to the ERLS. The 4 x 4 transformation matrix has been used to describe kinematics for the large motion, and the finite element method has been used to discretize deformations. The equations of motion are separated into a large motion part and a small motion part. The large motion part is a set of nonlinear equations in terms of joint variables and deformations while the small motion part is a set of linear equations with respect to deformations. The formulation of the damping forces and end effector loading is also included in this model. A sequential integration method is applied to integrate the equations of motion numerically to obtain significant improvement in computation efficiency. The sequential integration method integrates the nonlinear large (slow) motion equation explicitly and integrates the linear small (fast) motion equation implicitly. The explicit method is convenient for the nonlinear slow motion equation since the stability of the integration is not a problem while the implicit method guarantees stability for the integration of the linear fast motion equation. The sequential integration method is particularly efficient for solving the equations of motion of the manipulator system which possesses a wide range of frequencies of which only the lower frequencies are excited. Robotic dynamics of the flexible manipulator is useful in the design and the control areas. In this research, procedures are proposed to solve the robotic dynamics including both direct dynamics and inverse dynamics. A planar manipulator is used as an example to demonstrate the simulation results.
Degree
Ph.D.
Subject Area
Mechanical engineering
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