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An Interval Discretization Method for Workspace Determination of Parallel Mechanisms

  • Research Article-Mechanical Engineering
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Abstract

An interval discretization method (IDM) is proposed for the workspace determination of parallel mechanisms to address the fundamental problems of unreliable prediction and missing-points existing in the traditional point discretization method (PDM). The IDM involves two parts: the workspace prediction using interval analytical forward kinematics (AFK) and the workspace correction using interval analytical inverse kinematics (AIK). Three typical parallel mechanisms are adopted as illustrative examples, i.e., the planar four-bar mechanism, the spatial 9–3 and 12–6 parallel mechanisms. Firstly, the AFK and AIK of the mechanisms are derived and extended into interval-valued form. Then, the position and orientation workspaces are predicted and corrected in sequence. Finally, numerical behaviors of the proposed and traditional methods are compared. The numerical simulations in Matlab show that: (i) IDM is about 5.34 times faster than PDM; (ii) IDM is about 45.50 times more accurate than PDM; (iii) IDM is about 1.01 times more stable than PDM; and (iv) IDM can realize the prediction of position and orientation workspaces and has no missing-points, thereby demonstrating the effectiveness of the proposed method.

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Funding

This work was supported by an Oversea Study Fellowship from the China Scholarship Council (Grant No. 201908320035) and the National Natural Science Foundation of China (NSFC) (Grant No. 51405237).

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Authors and Affiliations

  1. College of Mechanical and Electronic Engineering, Nanjing Forestry University, Nanjing, 210037, China

    Pengda Ye, Jingjing You & Yu Ru

  2. Department of Aerospace Engineering, Ryerson University, Toronto, ON, M5B 2K3, Canada

    Fengfeng Xi & Jieyu Wang

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  1. Pengda Ye
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  2. Jingjing You
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  4. Jieyu Wang
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  5. Yu Ru
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Contributions

Jingjing You and Fengfeng Xi offered suggestions and reviewed the manuscript; Pengda Ye performed the simulation and wrote the manuscript; Jieyu Wang reviewed the manuscript; Yu Ru supervised all works.

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Correspondence to Jingjing You.

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Ye, P., You, J., Xi, F. et al. An Interval Discretization Method for Workspace Determination of Parallel Mechanisms. Arab J Sci Eng 47, 8805–8827 (2022). https://doi.org/10.1007/s13369-021-06310-2

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