Modelling of single link flexible manipulator with flexible joint

Abstract

This paper presents a systematic approach to dynamic modelling of a single link flexible manipulator with flexible joint for the case in which the link is oriented vertically. Flexibility is attained by attaching the link to the motor shaft using a pair of springs. The systems has two degrees of freedom, corresponding to the rotation of the motor shaft with respect to a coordinate frame fixed to the base, and the rotation of the flexible joint to which the link is attached with respect to the motor. The output of the system is the tip angle, which is given the sum of the motor angle, ? and the joint deflection a with respect to the motor shaft. A dynamic model of the system is developed based on Lagrange’s equations of motion. The presence of the gravity is accounted in this model which introduces a non-linearity into the system in the form of a sinusoid, as a result of the potential energy due to gravity. The nonlinear model of the dynamics will be linearized by a reasonable assumption. The resulting generalized model is validated through computer simulations and the results will be validate with the existing results. The investigations on the dynamic model in terms of time and frequency responses also are carried out. Besides, a design technique for a vibration suppression of the system is also presented.