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International Journal for Multiscale Computational Engineering
IF: 1.016 5-Year IF: 1.194 SJR: 0.554 SNIP: 0.68 CiteScore™: 1.18

ISSN Print: 1543-1649
ISSN Online: 1940-4352

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.v1.i23.50
20 pages

A Generalized Recursive Coordinate Reduction Method for Multibody System Dynamics

J. H. Critchley
Department of Mechanical, Aeronautical, and Nuclear Engineering, Rensselaer Polytechnic Institute, Troy, New York, USA
Kurt S. Anderson
Rensselaer Polytechnic Institute, USA


The method of recursive coordinate reduction (RCR) offers solutions to the forward problem of multibody dynamics at a cost in which the number of operations is linear in both the number of generalized coordinates, n, and the number of independent algebraic constraints, m (e.g., O(n + m)). However, the RCR is presently restricted in applicability (albeit broad) and susceptible to formulation singularities. This article develops two methods for avoiding formulation singularities as well as a recursive general coupled loop solution that extends the RCR to the complete set of multibody systems. Application of these techniques are further illustrated with a special five-bar linkage. The existing RCR coupled with these developments constitute a generalized recursive coordinate reduction method that should be used in place of the traditional "O(n)" constraint technique (truly O(n + nm2 + m3)) for superior O(n + m) computational performance.