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DINAME 2017
XVII International Symposium on Dynamic Problems of Mechanics
DYNAMIC MODELING AND SIMULATION OF A PARALLEL PLANAR MECHANISM USING BOND GRAPH (POWER FLOW) APPROACH
Submission Author:
Allan Nogueira de Albuquerque , RJ
Co-Authors:
Allan Nogueira de Albuquerque, Mauro Speranza Neto, Marco Antonio Meggiolaro
Presenter: Allan Nogueira de Albuquerque
doi://10.26678/ABCM.DINAME2017.DIN17-0090
Abstract
This work presents the analytical form determination of the dynamic model of a parallel planar mechanism with three degrees of freedom through the characterization of the power flow between its components. From the geometrical relations associated to the displacement of their degrees of freedom, the kinematic relations associated to their speeds are determined. Considering the power flow between the degrees of freedom, and also between these and the actuating elements (linear electric actuators) the equilibrium relations of the forces and torques are obtained. Accounting for inertial effects of system components, the stiffness and damping effects, the equations of motion or the state equations are analytically determined and represented in any reference frame, local or global. Besides, the relation between the inverse kinematics and the direct dynamics is presented. This approach adopts the same fundamentals, concepts and elements of the Bond Graph Technique, with its symbolic notation and graphical representation. The proposed methodology is generalized and applicable in any type of mechanism (open or closed, planar or spatial). The inverse kinematic model of the closed chain mechanism, which has easy solution when compared to the direct model, can be developed by any known methodology. In this work, the vector loop technique is used to determine the inverse geometric model, and with its derivation, the kinematic relations are obtained, and therefore the inverse Jacobian matrix. Thereby, the inverse kinematics bond graph is built and, from the cause and effect relations, the direct dynamic model of the mechanism is found. Thus, this methodology (bond graphs or power flow) is more efficient and secure to achieve the dynamic analytical (closed) models of parallel mechanisms. A set of simulations are performed to validate this approach, using the real data (geometry, inertia, damping, actuators forces, etc) from a planar mechanism designed and built especially for the purpose to compare the simulated and experimental results. Finally, a closed-loop control strategy using the inverse kinematic and the direct dynamic models is proposed. The analytical equations lead to a more efficient simulation process and real-time control of these systems.
Keywords
Parallel Mechanisms, Inverse Kinematic, Direct Dynamic, Power Flow, Causal Relations, Bond Graphs
