Utilization of the Moore-Penrose inverse in the modeling of overconstrained mechanisms with frictionless and frictional joints

Marek Wojtyra , Marcin Pękal , Janusz Frączek

Abstract

The indeterminate equations that describe overconstrained mechanisms are often solved using the Moore-Penrose inverse. Some limitations of this approach are investigated here. Firstly, frictionless systems are considered. The problem of solvability of accelerations and joint reactions is studied—the non-uniqueness of reactions and uniqueness of accelerations is discussed. Next, the dependence of the results on the selection of the physical units is examined. It is checked which elements of the solution are physically non-equivalent after changing the units; relationships between different solutions are derived. Secondly, frictional systems are considered. Joint friction dependent and independent on normal load is studied. Fixed point iterations and Newton's method are applied to solve nonlinear equations of motion. The Moore-Penrose inverse is employed to conduct calculations. The null space solution components are considered, and necessary amendments in the iterative processes termination criteria are discussed. The origins of non-uniqueness of accelerations and Lagrange multipliers are analyzed. The unit-sensitivity of frictional system models is addressed. Finally, an illustrative example is given, and conclusions are drawn—limitations and possible improvements of the Moore-Penrose inverse approach are discussed.
Author Marek Wojtyra (FPAE / IAAM)
Marek Wojtyra,,
- The Institute of Aeronautics and Applied Mechanics
, Marcin Pękal (FPAE / IAAM)
Marcin Pękal,,
- 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
Issue year2020
Vol153
Pages1-19
Publication size in sheets5199.95
Article number103999
Keywords in EnglishEquations of motion, Friction, Lagrange multipliers, Newton-Raphson method, Nonlinear equations, Fixed point iteration, Frictionless system, Iterative process, Moore-Penrose inverse, Newton's methods, Overconstrained mechanism, Solution components, Termination criteria, Inverse problems
ASJC Classification1502 Bioengineering; 1706 Computer Science Applications; 2210 Mechanical Engineering; 2211 Mechanics of Materials
DOIDOI:10.1016/j.mechmachtheory.2020.103999
Languageen angielski
Score (nominal)200
Score sourcejournalList
ScoreMinisterial score = 200.0, 18-09-2020, ArticleFromJournal
Publication indicators Scopus Citations = 0; GS Citations = 1.0; Scopus SNIP (Source Normalised Impact per Paper): 2016 = 2.433; WoS Impact Factor: 2018 = 3.535 (2) - 2018=3.632 (5)
Citation count*1 (2020-09-25)
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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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