Motion/structure mode analysis and classification of n-RR planar parallelogram mechanisms

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Planar parallelogram mechanisms (PPMs) have been used in many applications either as standalone pieces or as compositional joints of mechanisms, such as parallel mechanisms, remote center mechanisms and variable-DOF mechanisms. An n-RR PPM is composed of congruent base and moving platform connected with n RR links of equal link lengths. Although it is well known that an n-RR PPM has one 1-DOF circular translation mode, whether an n-RR PPM has structure/motion modes in addition to the 1-DOF motion mode and how the link parameters affect the number of extra motion/structure modes of the n-RR PPMs have not been well investigated. This paper is about the motion/structure mode analysis and classification of n-RR PPMs. Firstly, the motion/structure mode analysis of 3-RR PPMs is carried out. Then conditions for an n (n>3)-RR PPM to have the same motion/structure modes as a 3-RR PPM are revealed. Finally, n (n≥3)-RR PPMs are classified into three types. In addition to one 1-DOF motion mode, Types I, II and III PPMs have two, one or zero structure mode respectively. This work provides a foundation for the construction and analysis of several variable-DOF mechanisms composed of PPMs.

Original languageEnglish
Article number104623
JournalMechanism and Machine Theory
Early online date19 Nov 2021
Publication statusPublished - Mar 2022


  • Motion mode
  • Parallel mechanism
  • Planar parallelogram mechanism
  • Structure mode
  • Variable-DOF mechanism

ASJC Scopus subject areas

  • Bioengineering
  • Mechanics of Materials
  • Mechanical Engineering
  • Computer Science Applications


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