A General Method for Direct Kinematic Equation Computation of Closed Link Mechanisms
Zaiquan Sheng and Kazuo Yamafuji
Department of Mechanical and Control Engineering, University of Electro-Communications, 1-5-1 Chofugaoka, Chofu Tokyo, 182 Japan
This paper proposes a general and systematic computational scheme for the dynamic motion of closed link mechanisms. The scheme can also be extended to multiple closed kinematic mechanisms. The closed link mechanism is essentially, treated as if it were cut at one of joints. The closed link mechanism is then equivalent to an open tree structure mechanism with constraints at the cut joint: By applying d’Alembert’s principle, the dynamic motion for the equivalent open tree structure mechanism with constraints is established. Based on the constraints condition of the original closed link mechanism, we can obtain the constraint equations about the acceleration of the original closed link mechanism. Using these constraints, we derive a simple and general scheme for the dynamic motion computation of the original non-redundant and controllable closed link mechanism. The scheme avoids direct computation of Lagrangian multipliers; instead Lagrangian multipliers are treated as a part of the variables of the closed link mechanism. As shown by an example of a four-bar closed link mechanism in this paper, the scheme is simple and efficient.
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