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Dynamic modelling of planar mechanisms using point coordinates

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In the present study, the dynamic modelling of planar mechanisms that consist of a system of rigid bodies is carried out using point coordiantes. 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 with the addition of 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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  1. Attia, H. A., 1993, A Computer-Oriented Dynamical Formulation with Applications to Multibody Systems, Ph. D. Dissertation, Department of Engineering Mathematics and Physics, Faculty of Engineering, Cairo University.

  2. Denavit, J. and Hartenberg, R. S., 1955, “A Kinematic Notation for Lower-Pair Mechanisms Based on Matrices,”ASME Journal of Applied Mechanics, pp. 215-221.

  3. Dix, R. C. and Lehman, T. J., 1972, “Simulation of the Dynamics of Machinery,”ASME Journal of Engineering for Industry, Vol. 94, pp. 433–438.

  4. Goldstein, H., 1950, Classical mechanics, Ad-dison-Wesley, Reading, Mass.

  5. Hairer, E. and Wanner, G., 2001, Solution of Ordinary Differential Equations II. Stiff and Differential-Algebraic Problems, Springer-Verlag.

  6. Jerkovsky, W., 1976, “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, pp. 48-59.

  7. Kim. S. S. and Vanderploeg, M. J., 1986, “A General and Efficient Method for Dynamic Analysis of Mechanical Systems Using Velocity Transformation.”ASME Journal of Mechanisms, Transmissions and Automation in Design, Vol. 108, No. 2. pp. 176–182.

  8. Nikravesh P. E., 1988, Computer Aided Analysis of Mechanical Systems, Prentice-Hall. Englewood Cliffs, N.J.

  9. Nikravesh, P. E. and Gim, G.. 1989. “Systematic Construction of the Equations of Motion for Multibody Systems Containing Closed Kinematic Loop,”ASME Design Conference.

  10. Nikravesh, P. E. and Attia. H. A., 1994, “Construction of the Equations of Motion for Multi- body Dynamics Using Point and Joint Coordinates,” Computer-Aided Analysis of Rigid and Flexible Mechanical Systems, Kluwer Academic Publications, NATO ASI, Series E: Applied Sciences -Vol. 268, pp. 31–60.

  11. Orlandea, N., Chace, M. A. and Calahan, D. A., 1977, “A Sparsity-Oriented Approach to Dynamic Analysis and Design of Mechanical Systems, Part I and II,”ASME Journal of Engineering for Industry, Vol. 99, pp. 773–784.

  12. Sheth, P. N. and Uicker, J. J. Jr., 1972, “IMP (Integrated Mechanisms Program), A Computer-Aided Design Analysis System for Mechanisms Linkages,”ASME Journal of Engineering for Industry, Vol. 94, p. 454.

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Correspondence to Hazem Ali Attia.

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Attia, H.A. Dynamic modelling of planar mechanisms using point coordinates. KSME International Journal 17, 1977–1985 (2003). https://doi.org/10.1007/BF02982437

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Key Words

  • Dynamic Analysis
  • Recursive Formulation
  • Equations of Motion
  • System of Rigid Bodies
  • Open-Chain
  • Closed-Chains