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The kinematics and kinetics of multi-closed-chain mechanisms in the impact and non-impact stages

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Abstract

The chief objective of the current research is to outline an automated technique for deriving the governing equations and also simulating the motions of the multi-closed-chain mechanisms. To this end, the behavior of a mechanical system, whose straight and rigid links are hinged together by perfect rotary joints to make an array of closed loops, will be studied in the two phases of impact and non-impact. For the non-impact phase, in which the said mechanism is only affected by the Earth’s gravity, the relevant differential equations will be derived by the recursive Gibbs–Appell (G–A) methodology (which is a simple approach with fewer partial derivatives to worry about, especially when dealing with the holonomic systems); while for the impact phase, in which at least one joint of the mechanism collides with the surrounding curved wall, the algebraic equations of the system will be obtained by the Newton’s kinematic impact law. One of the most formidable challenges in the current research is the presence of the holonomic constraints that govern the kinematics of the problem. The number of these constraints goes up linearly with the increase in the number of system loops. The other challenges and issues that have been successfully addressed by the presented technique include the oblique impact of the joints of the said mechanism with the surrounding curved wall and the relatively large number of the dependent generalized coordinates needed to define the system configuration. In the suggested approach, after deriving the inverse kinetic equations of the considered mechanism, they are converted to the forward dynamics form in a graphical procedure to simulate the system’s dynamic responses. To demonstrate the capability and the efficacy of the presented technique in deriving the kinetic equations of multi-closed-loop systems, the dynamic behavior of a 5RRR mechanism with 4 closed loops and 10 rigid links is simulated. The simulation results are then validated by means of the work and energy principles.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Shahid Bahonar University of Kerman, Kerman, Iran

    A. M. Shafei & Z. Sadeghi

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  1. A. M. Shafei
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Shafei, A.M., Sadeghi, Z. The kinematics and kinetics of multi-closed-chain mechanisms in the impact and non-impact stages. Meccanica 57, 2591–2608 (2022). https://doi.org/10.1007/s11012-022-01582-w

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  • DOI: https://doi.org/10.1007/s11012-022-01582-w

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