Published 6 issues per year
ISSN Print: 1543-1649
ISSN Online: 1940-4352
Indexed in
A Generalized Recursive Coordinate Reduction Method for Multibody System Dynamics
ABSTRACT
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.
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Schutte Aaron, Udwadia Firdaus, New Approach to the Modeling of Complex Multibody Dynamical Systems, Journal of Applied Mechanics, 78, 2, 2011. Crossref
-
Weinstein R., Teran J., Fedkiw R., Dynamic simulation of articulated rigid bodies with contact and collision, IEEE Transactions on Visualization and Computer Graphics, 12, 3, 2006. Crossref
-
Bhalerao K.D., Crean C., Anderson K., Hybrid complementarity formulations for robotics applications, ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 91, 5, 2011. Crossref
-
Jain Abhinandan, Multibody graph transformations and analysis, Nonlinear Dynamics, 67, 3, 2012. Crossref
-
Jain Abhinandan, Multibody graph transformations and analysis, Nonlinear Dynamics, 67, 4, 2012. Crossref
-
Koul Majid, Shah Suril V., Saha S. K., Manivannan M., Reduced-order forward dynamics of multiclosed-loop systems, Multibody System Dynamics, 31, 4, 2014. Crossref
-
Khan I.M., Anderson K.S., Performance investigation and constraint stabilization approach for the orthogonal complement-based divide-and-conquer algorithm, Mechanism and Machine Theory, 67, 2013. Crossref
-
Annicchiarico Claudio, Capitani Renzo, Testi Riccardo, Stress Analysis of a CVT Belt Transmission, SAE Technical Paper Series, 1, 2010. Crossref
-
Tomcin Robin, Sibbing Dominik, Kobbelt Leif, Efficient enforcement of hard articulation constraints in the presence of closed loops and contacts, Computer Graphics Forum, 33, 2, 2014. Crossref
-
Pasparakis G.D., Fragkoulis V.C., Beer M., Harmonic wavelets based response evolutionary power spectrum determination of linear and nonlinear structural systems with singular matrices, Mechanical Systems and Signal Processing, 149, 2021. Crossref
-
Shabana Ahmed A., Dynamics of Multibody Systems, 2020. Crossref
-
Dabiri Arman, Poursina Mohammad, Machado J. A. Tenreiro, Dynamics and optimal control of multibody systems using fractional generalized divide-and-conquer algorithm , Nonlinear Dynamics, 102, 3, 2020. Crossref
-
Fragkoulis Vasileios C., Kougioumtzoglou Ioannis A., Pantelous Athanasios A., Linear Random Vibration of Structural Systems with Singular Matrices, Journal of Engineering Mechanics, 142, 2, 2016. Crossref
-
Ni Peihua, Fragkoulis Vasileios C., Kong Fan, Mitseas Ioannis P., Beer Michael, Response Determination of Nonlinear Systems with Singular Matrices Subject to Combined Stochastic and Deterministic Excitations, ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering, 7, 4, 2021. Crossref
-
Fragkoulis Vasileios C., Kougioumtzoglou Ioannis A., Pantelous Athanasios A., Statistical Linearization of Nonlinear Structural Systems with Singular Matrices, Journal of Engineering Mechanics, 142, 9, 2016. Crossref
-
Pantelous Athanasios A., Pirrotta Antonina, Modal Analysis of Multi-Degrees-of-Freedom Systems with Singular Matrices: Analytical Dynamics Approach, Journal of Engineering Mechanics, 143, 6, 2017. Crossref