Summary
Recursive methods represent a well-established and wide-spread technique for generation of dynamical equations of mechanical systems. Their main objective is to obtain computational schemes involving as few operations as possible. In this paper, we show that, besides the consideration of simplification resulting from a careful representation of geometric relationships between contiguous links, only two factors determine the overall efficiency of these methods. These factors are: the choice of an appropriate reference point for the kinematic and kinetic equations, and the frame of decomposition used to represent the involved vectors and tensors. Further, we derive a computational scheme which compares advantageously with existing methods. As only elementary laws of mechanics are applied, the exposition is also suitable for practising engineers seeking to understand the main differences between existing methods. A comparison with one of the reportedly most effective non-recursive method elucidates the advantages and bounds of the present approach.
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References
Vereschagin, A.: Computer simulation of the dynamics of complicated mechanisms of robot-manipulators. Eng. Cybern. 6 (1974) 65–70
Armstrong, W.: Recursive solution to the equations of motion of ann link manipulator. In: Proc. 5th World Congr. Theory of Machines and Mechanisms, Montreal, July 8–13, 1979, pp. 1343–1346. New York: ASME 1979
Featherstone, R.: The calculation of robot dynamics using articulated-body inertias. Int. J. Rob. Res. 2 (1983) 13–30
Featherstone, R.: Robot dynamics algorithms, Boston: Kluwer Academic Publishers 1987
Brandl, H.; Johanni, R.; Otter, M.: A very efficient algorithm for the simulation of robots and similar multibody systems without inversion of the mass matrix. In: Proc. IFAC/IFIP/IMACS Int. Symp. on Theory of Robots, Vienna, December 1986, pp. 95–100
Bae, D.-S.;Haug, E. J.: A recursive formulation for constrained mechanical system dynamics: Part I. Open loop systems. Mech. Struct. Mach. 15 (1987) 359–382
Jain, A.: Unified formulation of dynamics for serial rigid multibody systems. J. Guid. Contr. Dyn. 14 (1991) 531–542
Rodriguez, G.: Kalman filtering, smoothing, and recursive robot arm forward and inverse dynamics. J. Rob. Autom. 3 (1987) 624–639
Li, C. J.: A new Lagrangian formulation of dynamics for robot manipulators. Trans. ASME/J. Dyn. Syst. Meas. Control 111 (1989) 559–567
Valášek, M.: On the efficient implementation of multibody system formalisms. Institute report IB-17, Institute B of Mechanics, University of Stuttgart, 1990
Rosenthal, D.: Ordern formulation for equations of motions of multibody systems. In: SDIO/NASA Workshop on Multibody Simulation, pp. 1122–1150. JPL Pub. D-5190, Jet Propulsion Lab., Pasadena, CA, 1987
Wehage, R.: Application of matrix partitioning and recursive projection toO(n) solution of constrained equations of motion. In: Proc. 20th Biennal ASME Mechanism Conference, 1988
Angeles, J.: Rational kinematics, New York: Springer 1988
Duffy, J.: The fallacy of modern hybrid control theory that is based on “orthogonal complements” of twist and wrench spaces. Int. J. Rob. Res. 7 (1990) 139–144
Schwertassek, R.;Rulka, W.: Aspects of efficient and reliable multibody systems simulation. In: Haug, E. J.; Deyo, R. C. (eds.) Real-Time Integration Methods for Mechanical System Simulation, pp. 55–96. NATO ASI Series, Vol. F 69. Berlin: Springer 1990
Roberson, R.;Schwertassek, R.: Dynamics of multibody systems. Berlin: Springer 1988
Denavit, J.;Hartenberg, R.: A kinematic notation for lower-pair mechanisms based on matrices. J. Appl. Mech. 23 (1955) 215–221
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Stelzle, W., Kecskeméthy, A. & Hiller, M. A comparative study of recursive methods. Arch. Appl. Mech. 66, 9–19 (1995). https://doi.org/10.1007/BF00786685
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DOI: https://doi.org/10.1007/BF00786685