Abstract
In this paper, we revised and applied the parallel solution scheme of inverse dynamics to flexible link systems where elastic deformation and vibration normally occur in constituting link members. The calculation process of the scheme is based upon the Finite Element Method (FEM), which evaluates the analyzed model in absolute Cartesian coordinates with the equation of motion expressed in dimension of force. The calculated nodal forces are converted into joint torques using a matrix form equation divided into terms of force, transformation between coordinates, and length. Therefore, information from the entire system can be handled in parallel, which makes the calculation seamless in application to any type of link system regardless of its boundary conditions or stiffness values. The scheme is revised and the calculation time is shortened by applying Bernoulli-Euler beam elements, and the scheme is then combined with a kinematics solution scheme that calculates target trajectories for flexible models. The calculation flow of inverse dynamics is shown for a 5-link system, and some feed-forward control experiments are carried out on a 2-link system with different stiffness members. The accuracies of trajectories and torque curves are verified by applying the system to a sensorless, model-based vibration control.
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