Free-body-diagram method for the uniqueness analysis of reactions and driving forces in redundantly constrained multibody systems with nonholonomic constraints

Marcin Pękal , Marek Wojtyra , Janusz Frączek


Overconstrained and overactuated multibody systems are problematic in modeling. Under the rigid body assumption, redundantly constrained systems have, in general, nonunique reactions. However, despite this fact, some of the reactions may be unique. A similar problem pertains to driving forces. There are methods that may be used to check the uniqueness. One of them is the free-body-diagram-based approach considered in this paper. The former formulations of this method are unified and extended to the case of systems with affine nonholonomic constraints. Moreover, the previously proposed methods are partially reformulated to obtain a unified description. Four numerical approaches are considered—three based on the direct sum (namely, rank comparison, SVD and QR methods) and the nullspace approach. The numerical efficiency of these four methods is estimated and compared. In order to illustrate the reaction uniqueness analysis, a mobile platform with a trailer is examined in three actuation cases (non-actuated, fully actuated and overactuated). The obtained results are summarized and a brief guidance for exploiting the outcomes of the uniqueness analysis is provided.
Author Marcin Pękal (FPAE)
Marcin Pękal,,
- Faculty of Power and Aeronautical Engineering
, Marek Wojtyra (FPAE / IAAM)
Marek Wojtyra,,
- The Institute of Aeronautics and Applied Mechanics
, Janusz Frączek (FPAE / IAAM)
Janusz Frączek,,
- The Institute of Aeronautics and Applied Mechanics
Journal seriesMechanism and Machine Theory, ISSN 0094-114X, (N/A 200 pkt)
Issue year2019
Publication size in sheets0.85
Keywords in EnglishNonholonomic constraint, Redundantly constrained system, Uniqueness analysis, Free-body-diagram method, Direct sum Nullspace
ASJC Classification2210 Mechanical Engineering
Languageen angielski
Score (nominal)200
Score sourcejournalList
ScoreMinisterial score = 200.0, 05-03-2020, ArticleFromJournal
Publication indicators WoS Citations = 0; Scopus Citations = 1; GS Citations = 3.0; Scopus SNIP (Source Normalised Impact per Paper): 2016 = 2.433; WoS Impact Factor: 2018 = 3.535 (2) - 2018=3.632 (5)
Citation count*3 (2020-04-06)
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* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.
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