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FZU-OPU-NTOU joint symposium on Advanced Mechanical Science & Technology for Industrial Revolution 4.0

FZU 2016: Advanced Mechanical Science and Technology for the Industrial Revolution 4.0 pp 71–84Cite as

A General Kinetostatic Model Based Stiffness Estimation for Tripod Parallel Kinematic Machines with Prismatic Actuators

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Abstract

A general stiffness modeling methodology for tripod parallel kinematic machines (PKMs) with prismatic actuators is proposed in this paper. With the technique of substructure synthesis, the whole system of a tripod is divided into a platform, a base and three kinematic limb substructures. Each limb assemblage is modeled as a spatial beam constrained by two sets of six degree-of-freedom (6-DOF) virtual lumped springs with equivalent stiffness at their geometric centers. The equilibrium equation of each individual limb assemblage is derived through finite element formulation, while that of the platform is derived with the Newton’s 2nd law. The governing stiffness matrix is synthesized by introducing the deformation compatibility conditions between the platform and the limbs. By extracting a 6x6 block matrix from the inversion of the governing compliance matrix, a stiffness matrix of the platform is formulated. Taking the Sprint Z3 Head and the A3 Head as examples, the distributions of stiffness values of these two types of PKM modules are predicted and discussed. It is worth mentioning that the proposed methodology of stiffness modeling can further be applied to other types of PKMs for evaluating the global rigidity performance over entire workplace efficiently with minor revisions.

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Acknowledgements

This work was supported by the Open Fund of the State Key Laboratory for Manufacturing Systems Engineering (Xi’an Jiaotong University) with Grant No. sklms2015004 and Open Fund of Shanghai Key Laboratory of Digital Manufacture for Thin-walled Structures with Grant No. 2014001. The second author would like to acknowledge for Innovation Research Fund for Postgraduates of Anhui University of Technology (Grant No. 2015032).

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Authors and Affiliations

  1. School of Mechanical Engineering and Automation, Fuzhou University, Fuzhou, China

    Jun Zhang

  2. School of Mechanical Engineering, Anhui University of Technology, Ma’anshan, China

    Tengfei Tang

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  1. Jun Zhang
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  2. Tengfei Tang
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Corresponding author

Correspondence to Jun Zhang .

Editor information

Editors and Affiliations

  1. Fuzhou University , Fuzhou, Fujian, China

    Ligang Yao

  2. Fuzhou University , Fuzhou, Fujian, China

    Shuncong Zhong

  3. Osaka Prefecture University , Sakai, Osaka, Japan

    Hisao Kikuta

  4. National Taiwan Ocean University , Taipei, Taiwan

    Jih-Gau Juang

  5. Fuzhou University , Fuzhou, China

    Masakazu Anpo

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Zhang, J., Tang, T. (2018). A General Kinetostatic Model Based Stiffness Estimation for Tripod Parallel Kinematic Machines with Prismatic Actuators. In: Yao, L., Zhong, S., Kikuta, H., Juang, JG., Anpo, M. (eds) Advanced Mechanical Science and Technology for the Industrial Revolution 4.0. FZU 2016. Springer, Singapore. https://doi.org/10.1007/978-981-10-4109-9_8

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  • DOI: https://doi.org/10.1007/978-981-10-4109-9_8

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-10-4108-2

  • Online ISBN: 978-981-10-4109-9

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