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Elastodynamics of a spatial redundantly actuated parallel mechanism constrained by two higher kinematic pairs

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Abstract

A spatial redundantly actuated parallel mechanism (RAPM) constrained by two point-contact higher kinematic pairs (HKPs) has been designed for food texture evaluation during the mastication process. To this end, the mechanism must be capable of reproducing complex mandibular behaviours of human subjects in a biomimetic manner with satisfied motion accuracy. In this paper, first, the mechanism is described in detail, then elastodynamic behaviours of this mechanism are investigated based on the kineto-elastodynamics (KED) method and are formulated as a system of stiff ordinary differential equations. Due to the constraints of two HKPs onto the mandible, the derived mass matrix contains unknown generalized coordinates. This matrix is significantly different from those of parallel mechanisms (PMs) via the KED method in the literature. Third, the distributed torque under five performance criteria is employed as a feedforward to investigate its elastodynamic performance in two case studies, namely, without and with bite force onto the molar, respectively, given that the mechanism is specified to track a real human mandibular movement. The role of the damping effect in influencing vibrations is also studied. Finally, to explore the role of redundant actuations in elastodynamics, a non-redundantly actuated counterpart is proposed, where the aforementioned procedure is implemented. Results illustrate that the RAPM owns the satisfied elastodynamic performance in small vibrations, large stiffness and high natural frequency. Meanwhile, the damping effect can change the vibration distribution among different optimal torque criteria. It also shows that the RAPM outperforms its counterpart in the elastodynamic performance.

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Acknowledgements

The authors sincerely appreciate the valuable time, suggestions and comments from editors and anonymous reviewers to improve this paper.

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Authors and Affiliations

  1. Lab of Mechatronics, Xi’an College of Technology, 710025, Xi’an, China

    Chen Cheng

  2. Northwest Institute of Nuclear Technology, 710024, Xi’an, China

    Hongbo Liao

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  1. Chen Cheng
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  2. Hongbo Liao
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Correspondence to Chen Cheng.

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Cheng, C., Liao, H. Elastodynamics of a spatial redundantly actuated parallel mechanism constrained by two higher kinematic pairs. Meccanica 56, 515–533 (2021). https://doi.org/10.1007/s11012-020-01304-0

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