Simulation of Planar Mechanism Dynamics with Index-I Formulation and Projection Method Solution of Differential Algebraic Equations

Dogruer C. U., YILDIRIM B.

ARABIAN JOURNAL FOR SCIENCE AND ENGINEERING, vol.47, no.7, pp.9305-9317, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 47 Issue: 7
  • Publication Date: 2022
  • Doi Number: 10.1007/s13369-022-07062-3
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Aerospace Database, Communication Abstracts, Metadex, Pollution Abstracts, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.9305-9317
  • Keywords: Differential algebraic equations, Multi-body systems, Index-I formulation, Projection method, NUMERICAL-SIMULATION, INTEGRATION METHOD, MULTIBODY, ELIMINATION, STRATEGIES, VIOLATION, SYSTEMS
  • Hacettepe University Affiliated: Yes


This paper presents the application details of a methodology, which can be used to simulate any planar mechanism having revolute, prismatic and ground joints. To this end, in this article, Index-I formulation and Projection method, which are used to solve differential algebraic equations representing the dynamics of a multi-body system, were discussed. Constraint violation elimination method was also studied within this framework. The tangent and null space concepts were discussed, and it was shown that these spaces can be determined by the singular value decomposition of constraint Jacobian matrix. In this context, application details of both Index-I formulation and Projection method were illustrated on an example; in this example, off-set slider-crank mechanism dynamics was simulated.