Equations of motion of serial chains in spatial motion using a recursive algorithm

• Autorzy: Attia H. A.
• Języki publikacji: EN

Abstrakty

EN

In the present study, a recursive algorithm for generating the equations of motion of serial chains that undergo spatial motion is presented. The method is based on treating each rigid body as a collection of constrained particles. Then, the force and moment equations are used to generate the rigid body equations of motion in terms of the Cartesian coordinates of the dynamically equivalent constrained system of particles, without introducing any rotational coordinates and the corresponding rotation matrices. For the open loop case, the equations of motion are generated recursively along the serial chains. Closed loop systems are transformed to open loop systems by cutting suitable kinematic joints and introducing cut-joint constraints. The method is simple and suitable for computer implementation. An example is chosen to demonstrate the generality and simplicity of the developed formulation.

Słowa kluczowe

EN

equation of motion; mechanisms; multibody system dynamics

PL

równanie ruchu; mechanizm

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Computer Assisted Mechanics and Engineering Sciences
• Rocznik: 2004
• Tom: Vol. 11, No. 1
• Strony: 35--46
• Opis fizyczny: Bibliogr. 15 poz., rys., tab., wykr.

Twórcy

autor

Attia H. A.

• King Saud University, Department of Mathematics, PO Box 237, Buraidah 81999, KSA

Bibliografia

• [1] J. Denavit, R. S. Hartenberg. A kinematic notation for lower-pair mechanisms based on matrices. ASME Journal of Applied Mechanics, 215- 221, 1955.
• [2] P. N. Sheth, J. J. Uicker, Jr. IMP (Integrated Mechanisms Program), A computer-aided design analysis system for mechanisms linkages. ASME Journal of Engineering for Industry, 94: 454, 1972.
• [3] N. Oriandea, M. A. Chace, D. A. Calahan. A sparsity-oriented approach to dynamic analysis and design of mechanical systems, Part I and II. ASME Journal of Engineering for Industry, 99: 773- 784, 1977.
• [4] P. E. Nikravesh. Computer aided analysis of mechanical systems. Prentice-Hall, Englewood Cliffs N.J., 1988.
• [5] S. S. Kim, M. J . Vanderploeg. A general and efficient method for dynamic analysis of mechanical systems using velocity transformation. ASME Journal of Mechanisms, Transmissions and Automation in Design, 108:(2) 176-182, 1986.
• [6] P.E. Nikravesh, G. Gim. Systematic construction of the equations of motion for multibody systems containing closed kinematic loop. Journal of Mechanical Design, 115:(1) 143-149, 1993.
• [7] J. Garcia de Jalon, et al. A simple numerical method for the kinematic analysis of spatial mechanisms. ASME Journal on Mechanical! Design, 104: 78-82, 1982.
• [8] G. de Jalon, J. Unda, A. Avello, J. M. Jimenez. Dynamic analysis of three-dimensional mechanisms in 'natural' coordinates. ASME, 86-DET-137, 1986.
• [9] J. Unda, G. de Jalon, F. Losantos, R. Enparantza. A comparative study on some different formulations of the dynamic equations of constrained mechanical systems. ASME, No. 86-DET-138, 1986.
• [10] H.A. Attia. 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.
• [11] P.E. Nikravesh, H. A. Afff. Construction of the equations of motion for multibody dynamics using point and joint coordinates. Computer-Aided Analysis of Rigid and Flezible Mechanical Systems, Kluwer Academic Publications, NATO ASI, Series E: Applied Sciences, 268: 31-60, 1994.
• [12] H.A. Attia. Formulation of the equations of motion for the RRRR robot manipulator. Transactions of the Canadian Society for Mechanical Engineers, 22:(1) 83-93, 1998.
• [13] H. A. Attia. A recursive method for the dynamic analysis of a system of rigid bodies in plane motion. Computer Assisted Mechanics and Engineering Sciences (CAMES), 8:(4) 557-566, 2001.
• [14] H. Goldstein. Classical mechanics. Addison- Wesley, Reading, Mass, 1950.
• [15] C. W. Gea. Differential-algebraic equations index transformations. SIAM Journal of Scientific and Statistical Computing 9, 39-47, 1988.