Classification of a class of 3-rer parallel manipulators using Gröbner cover and primary decomposition of ideals

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Recent studies have revealed that the type/number of operation modes of a parallel manipulator (PM) may vary with the link parameters of the PM. However, current research on the impact of link parameters on the type/number of operation modes of a PM is usually based on intuition. This paper deals with the systematic classification of a 3-RER PM. The 3-RER PM is composed of a base and a moving platform connected by three RER legs, each of which is a serial kinematic chain composed of a revolute (R) joint, a planar (E) joint and an R joint in sequence. The axes of the R joints on the base (or moving platform) are all parallel. At first, a set of constraint equations of the 3-RER PM is first derived. Then using a method called Gröbner cover to calculate the comprehensive Gröbner system of parametric polynomial systems, the 3-RER PM is classified into 21 types. The operation modes of all the types of 3-RER PMs are determined using primary decomposition of ideals. Besides the two 4-DOF (degree-of-freedom) 3T1R operation modes, different types of 3-RER PMs may have up to two more 3-DOF or other types of 4-DOF operation modes. This work is the first systematic study on the impact of link parameters on the operation modes of the 3-RER PM and will contribute to the design and control of 3-RER PMs and research on multi-mode (or reconfigurable) PMs.

Original languageEnglish
Title of host publication43rd Mechanisms and Robotics Conference
PublisherAmerican Society of Mechanical Engineers
ISBN (Electronic)9780791859247
DOIs
Publication statusPublished - 25 Nov 2019
Event43rd Mechanisms and Robotics Conference 2019 - Anaheim, United States
Duration: 18 Aug 201921 Aug 2019

Publication series

NameProceedings of the IDETC/CIE Conferences
Volume5B

Conference

Conference43rd Mechanisms and Robotics Conference 2019
CountryUnited States
CityAnaheim
Period18/08/1921/08/19

Keywords

  • Euler parameters
  • Gröbner Cover
  • Multi-mode mechanism
  • Operation mode
  • Quaternion

ASJC Scopus subject areas

  • Mechanical Engineering
  • Computer Graphics and Computer-Aided Design
  • Computer Science Applications
  • Modelling and Simulation

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