On the unique solvability of a direct dynamics problem for mechanisms with redundant constraints and Coulomb friction in joints

Janusz Frączek , Marek Wojtyra


The uniqueness of simulated motion of an overconstrained rigid body mechanism with joint friction is studied. The investigated issue originates in the problem of joint reactions solvability. It is known that in case of redundant constraints existence the constraint reaction forces cannot be — in general — uniquely determined. It can be proved, however, that — under certain conditions — selected reactions can be specified uniquely. Analytical and numerical methods for reactions solvability analysis are available. It is shown in this paper that indeterminacy of normal reactions results in indeterminacy of friction forces, and moreover, non-uniqueness of friction forces results in non-uniqueness of simulated motion. A method of finding these joints, for which friction forces are unique, is presented. It is also proved that if only uniquely solvable friction effects are introduced, then simulated motion of the mechanism is unique, otherwise it is not. Finally, examples of dynamic analysis of overconstrained mechanisms with joint friction are presented; unique and non-unique results are obtained.
Author Janusz Frączek (FPAE / IAAM)
Janusz Frączek,,
- The Institute of Aeronautics and Applied Mechanics
, Marek Wojtyra (FPAE / IAAM)
Marek Wojtyra,,
- The Institute of Aeronautics and Applied Mechanics
Journal seriesMechanism and Machine Theory, ISSN 0094-114X, (A 35 pkt)
Issue year2011
Publication size in sheets1.1
Keywords in EnglishCoulomb friction, Dependent constraints, Direct dynamics, Joint reactions, Multibody system
ASJC Classification1706 Computer Science Applications; 2210 Mechanical Engineering; 2211 Mechanics of Materials; 1502 Bioengineering
URL http://dx.doi.org/10.1016/j.mechmachtheory.2010.11.003
Languageen angielski
Score (nominal)35
Publication indicators WoS Citations = 30; Scopus Citations = 47; Scopus SNIP (Source Normalised Impact per Paper): 2014 = 2.951; WoS Impact Factor: 2011 = 1.366 (2) - 2011=1.54 (5)
Citation count*57 (2020-01-07)
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