4. A Recursive Driving Constraint Approach for Inverse Dynamics Modeling of Flexible Multibody Systems

In this chapter, a novel procedure for inverse dynamics modeling of flexible multibody systems using a driving constraints approach in the form of a forward dynamics analysis is presented. The flexible 3RPR parallel manipulator is chosen here as a flexible multibody system with closed kinematic chains to introduce this approach. The equations of motion are derived using the floating frame of reference formulation. Assuming a prescribed trajectory of the end-effector, the generalized coordinates of the rigid manipulator associated with the prismatic and revolute joints are obtained from an inverse kinematics analysis of the manipulator. This solution is further exploited in a forward dynamics analysis of the flexible manipulator to form the required driving constraints for obtaining the approximate values of the actuating forces and torques. Finally, the inverse dynamics analysis of the flexible manipulator is carried out by including some additional driving constraints associated with the generalized elastic coordinates to obtain the high-accuracy approximate values of the actuating forces and torques for tracking the prescribed trajectory by the end-effector. To numerically validate the approach, the obtained actuating forces and torques are applied to the simulated flexible manipulator to check the final trajectory of the end-effector. The results confirm the accuracy of the proposed approach.