Dynamics of a flexible five bar manipulator

Abstract

With the increasing requirements on speed and accuracy in current day manipulators, flexibility effects have become important. In this paper, the flexural dynamics of a parallel drive five bar manipulator are studied. The parallel drive five bar configuration is a very attractive design due to its considerably simplified rigid body dynamics. Specifically, the equations of motion for an inertia invariant five bar manipulator are given by a pair of linear time invariant (LTI) differential equations. This permits application of existing single axis servo control techniques to the control of such a manipulator. Besides, strategies such as direct drive actuation, etc., are also easily implemented. These lead to increased accuracy, better control performance and less uncertainty. It is shown in this paper that the simplicity afforded to the rigid body dynamics of the parallel drive five bar configuration also extends to its flexural dynamics. The elastic vibrations of the manipulator are also modeled by a set of linear time invariant differential equations. Also, when (invariant) modal coordinates are used to model the elastic vibrations, it is seen that the number of equations representing the flexural dynamics of the manipulator equals the number of modes under consideration. For the five bar example presented in this paper, only three modes were found to be significant. Thus, the overall dynamics of the manipulator (rigid body and flexural) is represented by a set of five decoupled linear time invariant differential equations. Such a model does not involve any more approximation than that of ignoring higher modes. Thus, this permits real time control of the manipulator based on an accurate linear time invariant model.