In this paper some existing codes for the determination of joint reactions in multibody mechanisms are first reviewed. The codes relate to the DAE (differential-algebraic equation) dynamics formulations in absolute coordinates and in relative joint coordinates, and to the ODE (ordinary differential equation) formulations obtained by applying the coordinate partitioning method to these both coordinate types. On this background a novel efficient approach to the determination of joint reactions is presented, naturally associated with the reduced-dimension formulations of mechanism dynamics. By introducing open-constraint coordinates to specify the prohibited relative motions in the joints, pseudoinverse matrices to the constraint Jacobian matrices are derived in an automatic way. The involvement of the pseudo-inverses leads to schemes in which the joint reactions are obtained directly in resolved forms—no matrix inversion is needed as it is required in the classical codes. This makes the developed schemes especially well suited for both symbolic manipulators and computer implementations. Illustrative examples are provided.
On the Determination of Joint Reactions in Multibody Mechanisms
Contributed by the Design Automation Committee for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received August 2002; revised August 2003. Associate Editor: A. A. Shabana.
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Blajer, W. (May 5, 2004). "On the Determination of Joint Reactions in Multibody Mechanisms ." ASME. J. Mech. Des. March 2004; 126(2): 341–350. https://doi.org/10.1115/1.1667944
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