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Analytic Formulation of Kinematics for a Planar Continuum Parallel Manipulator with Large-Deflection Links

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Abstract

This paper presents the analytic formulation of kinematics for a planar continuum parallel manipulator with large-deflection links. This development is motivated by the need for object manipulation with light-weight mechanisms in small spaces or human-machine collaborative environments. The manipulator contains two independent branch chains with links formed by highly flexible panels, and the moving platform is driven by the bending deflections of the links. For kinematic analysis, the Euler-Bernoulli beam theory is applied to model the continuous deflections of the links. Then, the relationship between the internal force/moment and the deflection of each branch is formulated via elliptic integrals. By establishing the equilibrium equations for the internal force and moment, analytic formulations can be derived for the forward and inverse kinematics, respectively. The proposed method can account for the nonlinearity and inflection points due to large deformations and the inherent coupling between the closed-loop chain kinematics and the static characteristics of the chains. Numerical simulation has been carried out for the kinematic analysis to reveal how the link deflections generate planar motion for the moving platform. The proposed method has been validated by comparing the simulation results with finite element analysis. Under large deflections, the links can have two inflection points close to both ends and the occurrence of inflection points has a large effect on the distribution of the internal moment along the link. Stress checking confirms that the deformations of the links are still within their elastic region.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China under Grant 51775322.

Funding

Partial financial support was received from the National Natural Science Foundation of China under Grant 51775322.

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Authors and Affiliations

  1. Shanghai Key Laboratory of Intelligent Manufacturing and Robotics, School of Mechatronic Engineering and Automation, Shanghai University, Shangda Road, 200444, Shanghai, China

    Yuwen Li, Ying Liu, Ping Zhang, Yinjun Zhao & Yingzhong Tian

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  1. Yuwen Li
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  3. Ping Zhang
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  4. Yinjun Zhao
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  5. Yingzhong Tian
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Contributions

All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by Yuwen Li, Ying Liu, Ping Zhang, Yinjun Zhao and Yingzhong Tian. The first draft of the manuscript was written by Yuwen Li.

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Correspondence to Yuwen Li.

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Li, Y., Liu, Y., Zhang, P. et al. Analytic Formulation of Kinematics for a Planar Continuum Parallel Manipulator with Large-Deflection Links. J Intell Robot Syst 107, 58 (2023). https://doi.org/10.1007/s10846-023-01847-w

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