Reconfiguration analysis of a two degrees-of-freedom 3-4R parallel manipulator with planar base and platform

Xianwen Kong*, Jingjun Yu, Duanling Li

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

15 Citations (Scopus)


This paper deals with a 2-DOF (degrees-of-freedom) 3-4R parallel manipulator (PM) with planar base and platform-a novel PM with multiple operation modes (or disassembly free reconfigurable PM) that can use the minimum number of actuated joints. At first, a set of constraint equations of the 3-4R PM are derived with the orientation of the moving platform represented using a Euler parameter quaternion (also Euler-Rodrigues quaternion) and then solved using the algebraic geometry method. It is found that this 3-4R PM has six 2-DOF operation modes, including the two expected spherical translation mode and sphere-on-sphere rolling mode when the PM was synthesized. The motion characteristics of the moving platform are obtained using the kinematic interpretation of Euler parameter quaternions with certain number of constant zero components, which was presented in a recent paper by the first author of this paper, instead of the eigenspace-based approach in the literature. The transition configurations, which are constraint singular configurations, among different operation modes are also presented. This work provides a solid foundation to the development and control of the 2-DOF 3-4R PM with both 2-DOF spherical translation mode and 2-DOF sphere-on-sphere rolling mode.

Original languageEnglish
Article number011019
JournalJournal of Mechanisms and Robotics
Issue number1
Early online date18 Aug 2015
Publication statusPublished - Feb 2016


  • Algebraic geometry
  • Euler parameters
  • Parallel manipulator with multiple operation modes
  • Quaternion
  • Singularity

ASJC Scopus subject areas

  • Mechanical Engineering


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