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Workspace analysis and size optimization of planar 3-DOF redundantly actuated parallel mechanism

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Parallel mechanism is widely used due to its high stiffness, strong bearing capacity, small accumulated error, and good dynamic performance. In this paper, a planar three-degree-of-freedom (3-DOF) redundantly actuated parallel mechanism is proposed. Firstly, the position constraint equation is investigated and the inverse position solution is derived. The center velocity mapping model of the moving platform is established and the Jacobian matrix of the mechanism is obtained. The theoretical model based on Mathematica and the simulation model based on ADAMS are compared to validate the correctness of the theoretical results, and the peak deviation of the results is within 5 %. Then, the constraint conditions are conducted, and the workspace of the mechanism is solved by numerical method. Finally, the influence relationship curves of rod parameters on the proportion of workspace are obtained respectively. And the size parameters are optimized to carry out a comparative analysis of the workspace.

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Degrees of freedom


Computer numerical control


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This work was supported by Open R&D Program of Haian Taiyuan University of Technology Advanced Manufacturing and Intelligent Equipment Industry Research Institute (Project No. 2023HA-TYUTKFYF026), National Key R&D Program of China (Project No. 2018YFB1307900), National Natural Science Foundation of China (Project No. 51835002).

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Correspondence to Jing Zhang.

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Jing Zhang, Ph.D., is an Associate Professor in Yanshan University. Her research interests include robotics and mechanism theory and mechatronics.

Dongbao Wang studied at Taiyuan University of Technology, Taiyuan. His research interests include robotic and control.

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Zhang, J., Wang, D., Song, Z. et al. Workspace analysis and size optimization of planar 3-DOF redundantly actuated parallel mechanism. J Mech Sci Technol 38, 957–967 (2024).

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