Summary
In the present paper, a numerical method for generating the equations of motion of planar mechanisms with only revolute joints is presented. The method rests upon the idea of replacing the rigid body by a dynamically equivalent constrained system of particles. For the open loop case, the equations of motion are generated recursively along the open chains. Geometric constraints that fix the distance between the particles are introduced. For the closed loop case, the system is transformed to open loops by cutting suitable kinematic joints with the addition of kinematic constraints. The method is conceptually easy and suitable for computer implementation. It eliminates the necessity of distributing the external forces and moments over the particles and uses the concepts of linear and angular momentums to generate the rigid body equations of motion without introducing any rotational coordinates. An example with closed loops is chosen to demonstrate the generality and simplicity of the proposed method.
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References
Denavit, J., Hartenberg, R. S.: A kinematic notation for lower-pair mechanisms based on matrices. ASME J. Appl. Mech.22, 215–221 (1955).
Sheth, P. N., Uicker, J. J. Jr.: IMP (Integrated Mechanisms Program), A computer-aided design analysis system for mechanisms linkages. ASME J. Engng Industry94, 454 (1972).
Dix, R. C., Lehman, T. J.: Simulation of the dynamics of machinery. ASME J. Engng Industry94, 433–438 (1972).
Orlandea, N., Chace, M. A., Calahan, D. A.: A sparsity-oriented approach to dynamic analysis and design of mechanical systems, Part I and II. ASME J. Engng Industry99, 773–784 (1977).
Nikravesh, P. E.: Computer aided analysis of mechanical systems. Englewood Cliffs, N. J.: Prentice-Hall 1988.
Jerkovsky, W.: The transformation operator approach to multi-body dynamics. Aerospace Corp., El Segundo, Calif., Rept. TR-0076 (6901-03)-5, 1976; also: The Matrix and Tensor Quarterly, Part 1 in Vol.27, 48–59 (1976).
Kim, S. S., Vanderploeg, M. J.: A general and efficient method for dynamic, analysis of mechanical systems using velocity transformation. ASME J. Mechanisms, Transmissions and Automation in Design108, 176–182 (1986).
Nikravesh, P. E., Gim, G.: Systematic, construction of the equations of motion for multibody systems containing closed kinematic loop. ASME Design Conference 1989.
Wittaker, E. T.: A treatise on the analytical dynamics of particles and rigid bodies. Dover Publications 1937.
Attia, H. A.: A computer-oriented dynamical formulation with applications to multibody systems. Ph. D. Dissertation, Department of Engineering Mathematics and Physics, Faculty of Engineering, Cairo University 1993.
Nikravesh, P. E., Attia, H. A.: Construction of the equations of motion for multibody dynamics using point and joint coordinates. Computer-aided analysis of rigid and flexible mechanical systems. Kluwer Academic Publications, NATO ASI, Series E: Applied Sciences268, 31–60 (1994).
Attia, H. A.: Dynamic analysis of the multi-link five-point suspension system using point and joint coordinates. Acta Mech.119, 221–228 (1996).
Attia, H. A.: Formulation of the equations of motion for the RRRR robot manipulator. Trans. Canadian Soc. Mech. Engng22, 83–93 (1998).
Schiehlen, W.: Computational aspects in multibody system dynamics. Computer Meth. Appl. Mech. Engng90, 569–582 (1991).
Goldstein, H.: Classical mechanics. Reading, Mass: Addison-Wesley 1950.
Gear, C. W.: Differential-algebraic equations index transformations. SIAM Journal of Scientific and Statistical Computing9, 39–47 (1988).
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Attia, H.A. A simplified recursive formulation for the dynamic analysis of planar mechanisms. Acta Mechanica 149, 11–21 (2001). https://doi.org/10.1007/BF01261660
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DOI: https://doi.org/10.1007/BF01261660