Dynamic Modeling of a Generalized Stewart Platform by Bond Graph Method Utilizing a Novel Spatial Visualization Technique

Abstract

This paper represents dynamic modeling of generalized Stewart Platform Manipulator by Bond Graph method with a new spatial visualization method and the state-space representation of the dynamic equations of the system. Dynamic model includes all the dynamics and gravity effects, linear motor dynamics as well as the viscous friction at the joints. Following modeling of actuation system and of main structure, unification of these two is accomplished. Linear DC motors are utilized and are modeled as the actuation system. Since overall system consists of high nonlinearity originated from geometric nonlinearity and gyroscopic forces, resultant derivative causality problem caused by rigidly coupled inertia elements is addressed and consequential system state-space equations are presented. A spatial visualization method is developed based on classic vector bond-graph method, due to the lack of representing overall kinematic bonds of the Stewart Platform Mechanism using classic vector bond-graph visualization.