Structural synthesis of articulated manipulators with non-fractionated or fractionated kinematic chains without isomorphism

Ho Sung Park, Jae Kyung Shim, Woon Ryong Kim, Tae Woong Yun

Research output: Contribution to journalArticlepeer-review


As the kinematic structure of an articulated manipulator affects the characteristics of its motion, rigidity, vibration, and force transmissibility, finding the most suitable kinematic structure for the desired task is important in the conceptual design phase. This paper proposes a systematic method for generating non-isomorphic graphs of articulated manipulators that consist of a fixed base, an end-effector, and a two-degree-of-freedom (DOF) intermediate kinematic chain connecting the two. Based on the analysis of the structural characteristics of articulated manipulators, the con-ditions that must be satisfied for manipulators to have a desired DOF is identified. Then, isomor-phism-free graph generation methods are proposed based on the concepts of the symmetry of a graph, and the number of graphs generated are determined. As a result, 969 graphs of articulated manipulators that have two-DOF non-fractionated intermediate kinematic chains and 33,438 graphs with two-DOF fractionated intermediate kinematic chains are generated, including practical articulated manipulators widely used in industry.

Original languageEnglish
Article number9658
JournalApplied Sciences (Switzerland)
Issue number20
Publication statusPublished - 2021 Oct 1

Bibliographical note

Publisher Copyright:
© 2021 by the authors. Licensee MDPI, Basel, Switzerland.


  • Articulated manipulator
  • Graph theory
  • Kinematic structure
  • Structural synthesis

ASJC Scopus subject areas

  • General Materials Science
  • Instrumentation
  • General Engineering
  • Process Chemistry and Technology
  • Computer Science Applications
  • Fluid Flow and Transfer Processes


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