A parametric model of 3-PPR planar parallel manipulators for optimum shape design of platforms

Xiaoyong Wu, Zhijiang Xie, Jørgen Asbøll Kepler, Shaoping Bai*

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

16 Citations (Scopus)


This work presents a parametric model of 3-PPR1 P and R represent prismatic and revolute joints, and an underline letter indicates an actuated joint planar parallel manipulators, aiming to optimize shape design of the base and mobile platforms. The kinematic model is established with shape parameters and motion variables. With the model, the inverse and forward position analyses are carried out, upon which the dexterity performance in terms of conditioning index is evaluated and analyzed. The analysis of global dexterity reveals a number of platform shapes, which lead to singularity in all configurations and must be avoided in design. Further performance evaluation in terms of transmission quality is also presented. Finally, two optimal configurations for the considered manipulators are obtained from the numerical simulation results. A case study is included to demonstrate the dynamics performance with an optimal platform shape design.

Original languageEnglish
JournalMechanism and Machine Theory
Pages (from-to)139-153
Number of pages15
Publication statusPublished - 1 Dec 2017


  • Dexterity
  • Motion/force transmission quality
  • Optimum shape design
  • Planar parallel manipulator
  • Shape singularity


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