Joint reactions in rigid or flexible body mechanisms with redundant constraints

Open access

Abstract

The problem of joint reactions indeterminacy, in engineering simulations of rigid body mechanisms is most often caused by redundant constraints which are defined as constraints that can be removed without changing the kinematics of the system. In order to find a unique set of all joint reactions in an overconstrained system, it is necessary to reject the assumption that all bodies are rigid. Flexible bodies introduce additional degrees of freedom to the mechanism, which usually makes the constraint equations independent. Quite often only selected bodies are modelled as the flexible ones, whereas the other remain rigid. In this contribution it is shown that taking into account flexibility of selected mechanism bodies does not guarantee that unique joint reactions can be found. Problems typical for redundant constraints existence are encountered in partially flexible models, which are not overconstrained. A case study of a redundantly constrained spatial mechanism is presented. Different approaches to the mechanism modelling, ranging from a purely rigid body model to a fully flexible one, are investigated and the obtained results are compared and discussed.

[1] E.J. Haug, Intermediate Dynamics, Prentice Hall, New Jersey, 1992.

[2] J. Garcia de Jalon and E. Bayo, Kinematic and Dynamic Simulation of Multibody Systems: the Real-Time Challenge, Springer, Berlin, 1994.

[3] A.A. Shabana, Computational Dynamics, John Wiley & Sons, 2nd edition, New York, 2001.

[4] K. Arczewski and J. Frączek, “Friction models and stress recovery methods in vehicle dynamics modelling”, Multibody System Dynamics 14, 205-224 (2005).

[5] E.J. Haug, Computer Aided Kinematics and Dynamics of Mechanical Systems, Allyn and Bacon, Boston, 1989.

[6] P. Malczyk and J. Frączek, “Cluster computing of mechanisms dynamics using recursive formulation”, Multibody System Dynamics 20, 177-196 (2008).

[7] P.E. Nikravesh, Computer-Aided Analysis of Mechanical Systems, Prentice Hall, London, 1988.

[8] L.J. Corwin and R.H. Szczarba, Multivariable Calculus, Marcel Dekker, New York, 1982.

[9] F. E. Udwadia and R. E. Kalaba, Analytical Dynamics: a New Approach, Cambridge University Press, Cambridge, 1996.

[10] E. Bayo and R. Ledesma, “Augmented lagrangian and massorthogonal projection methods for constrained multibody dynamics”, Nonlinear Dynamics 9, 113-130 (1996).

[11] W. Blajer, “Augmented Lagrangian formulation: geometrical interpretation and application to systems with singularities and redundancy”, Multibody Systems Dynamics 8, 141-159, (2002).

[12] M. Wojtyra, “Joint reactions in rigid body mechanisms withdependent constraints”, Mechanism and Machine Theory 44, 2265-2278 (2009).

[13] M. Wojtyra, “Joint reaction forces in multibody systems with redundant constraints”, Multibody System Dynamics 14, 23-46 (2005).

[14] J. Frączek and M. Wojtyra “On the unique solvability of a direct dynamics problem for mechanisms with redundant constraints and Coulomb friction in joints”, Mechanism and MachineTheory 46, 312-334 (2011).

[15] K. Mianowski and M. Wojtyra, “Virtual prototype of a 6-DOF parallel robot”, Eleventh World Congress in Mechanism andMachine Science 1, 1604-1608 (2004).

[16] Z. Dziopa, I. Krzysztofik, and Z. Koruba, “An analysis of the dynamics of a launcher-missile system on a moveable base”, Bull. Pol. Ac.: Tech. 58, 651-656 (2010).

[17] W. Ostapski, “Analysis of the stress state in the harmonic drive generator-flexspline system in relation to selected structural parameters and manufacturing deviations”, Bull. Pol. Ac.: Tech. 58, 683-698 (2010).

[18] S.-M. Song and X. Gao, “The mobility equation and the solvability of joint forces/torques in dynamic analysis”, ASME J.Mechanical Design 114, 257-262 (1992).

[19] G. Strang, Linear Algebra and Its Applications, Academic Press, New York, 1980.

[20] M. Wojtyra and J. Frączek, “Comparison of selected methods of handling redundant constraints in multibody systems simulations”, ASME J. Computational and Nonlinear Dynamics 8, 021007 (1-9), DOI: 10.1115/1.4006958 (2013).

[21] A.A. Shabana, Dynamics of Multibody Systems, Cambridge University Press, Cambridge, 2010.

[22] R.R. Craig and M.C. Bampton, “Coupling of substructure in dynamic analysis”, American Institute of Aeronautics and AstronauticsJ. 6, 1313-1319 (1968).

[23] Theory of Flexible Bodies, MD.ADAMS.R3 Documentation, 2008.

Bulletin of the Polish Academy of Sciences Technical Sciences

The Journal of Polish Academy of Sciences

Journal Information


IMPACT FACTOR 2016: 1.156
5-year IMPACT FACTOR: 1.238

CiteScore 2016: 1.50

SCImago Journal Rank (SJR) 2016: 0.457
Source Normalized Impact per Paper (SNIP) 2016: 1.239

Metrics

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 42 42 13
PDF Downloads 8 8 1