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Simulation of Planar Mechanism Dynamics with Index-I Formulation and Projection Method

Solution of Differential Algebraic Equations

  • Research Article-Mechanical Engineering
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Abstract

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.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Hacettepe University, Ankara, Turkey

    C. U. Dogruer & Bora Yıldırım

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  1. C. U. Dogruer
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  2. Bora Yıldırım
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Correspondence to C. U. Dogruer.

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Dogruer, C.U., Yıldırım, B. Simulation of Planar Mechanism Dynamics with Index-I Formulation and Projection Method. Arab J Sci Eng 47, 9305–9317 (2022). https://doi.org/10.1007/s13369-022-07062-3

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