Abstract
In the present study, the equations of motion for generalized planar linkages that consist of a system of rigid bodies with all common types of kinematic joints are derived using a recursive approach. The system of rigid bodies is replaced by a dynamically equivalent constrained system of particles. Then for the resulting equivalent system of particles, the concepts of linear and angular momentums are used to generate the equations of motion without either introducing any rotational coordinates or distributing the external forces and force couples over the particles. For the open loop case, the equations of motion are generated recursively along the open chains. For the closed loop case, the system is transformed to open loops by cutting suitable kinematic joints and introducing cut-joints kinematic constraints. An example of a multi-branch closed-loop system is chosen to demonstrate the generality and simplicity of the proposed method.
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References
Dix, R.C. and Lehman, T.J., 'Simulation of the dynamics of machinery', ASME J. Eng. Industry 94 (1972) 433-438.
Orlandea, N., Chace, M.A. and Calahan, D.A., 'A sparsity-oriented approach to dynamic analysis and design of mechanical systems, Part I and II', ASME J. Eng. Industry 99 (1977) 773-784.
Nikravesh, P.E., Computer Aided Analysis of Mechanical Systems, Prentice-Hall, Englewood Cliffs, N.J., 1988.
Denavit, J. and Hartenberg, R.S., 'A kinematic notation for lower-pair mechanisms based on matrices', ASME J. Appl. Mech. (1955) 215-221.
Sheth, P.N. and Uicker Jr., J.J., 'IMP (Integrated mechanisms program), a computer-aided design analysis system for mechanisms linkages', ASME J. Eng. Industry 94 (1972) 454.
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, Vol. 27, (Dec. 1976), 48–59.
Kim, S.S. and Vanderploeg, M.J., 'A general and efficient method for dynamic analysis of mechanical systems using velocity transformation', ASME J. Mech. Transmiss. Automat. Design 108(2) (1986) 176-182.
Nikravesh, P.E. and Gim, G., 'Systematic construction of the equations of motion for multibody systems containing closed kinematic loop', in: ASME Design Conference, 1989.
Attia, H.A., A Computer-Oriented Dynamical Formulation with Applications to Multibody Systems, PhD Dissertation, Department of Engineering Mathematics and Physics, Faculty of Engineering, Cairo University, 1993.
Nikravesh, P.E. and Attia, H.A., 'Construction of the equations of motion for multibody dynamics using point and joint coordinates', in: Computer-Aided Analysis of Rigid and Flexible Mechanical Systems, Kluwer Academic Publications, NATO ASI, Series E: Applied Sciences, Vol. 268, 1994, pp. 31-60.
Attia, H.A., 'Dynamic analysis of the multi-link five-point suspension system using point and joint coordinates', Acta Mech. 119 (1996) 221-228.
Attia, H.A., 'Formulation of the equations of motion for the RRRR robot manipulator', T. Can. Soc. Mech. Eng. 22(1) (1998) 83-93.
Attia, H.A. and El-Mistikawy, M.A., 'A matrix formulation for the dynamic analysis of planar mechanisms using point coordinates and velocity transformation', Eur. J. Mech. A Solids. 20(6) (2001) 981-995.
Routh, E.J., Dynamics of a System of Rigid Bodies, 7th edn, Vol. 2, Dover, New York.
Smith, M.R. and Ye, Z., 'Complete balancing of planar linkages by an equivalent method', Mech. Mach. Theory 29(5) (1994) 701-712.
Goldstein, H., Classical Mechanics, Addison-Wesley, Reading, MA, 1950.
Gear, C.W., 'Differential-algebraic equations index transformations', SIAM J. Sci. Stat. Comp. 9 (1988) 39-47.
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Ali Attia, H. Dynamic Analysis of Planar Linkages: A Recursive Approach. Meccanica 38, 405–418 (2003). https://doi.org/10.1023/A:1024618603580
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DOI: https://doi.org/10.1023/A:1024618603580