A single-loop 7R spatial mechanism that has three motion modes with the same instantaneous DOF but different finite DOF

Xianwen Kong, Andreas Müller

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

Abstract

Multi-mode mechanisms, including kinematotropic mechanisms, are a class of reconfigurable mechanisms that can switch motion modes with the same or different DOF (degree-of-freedom). For most of the multi-mode mechanisms reported in the literature, the instantaneous (or differential) DOF and finite DOF in a motion mode are equal. In this paper, we will discuss the construction, reconfiguration analysis, and higher-order mobility analysis of a multi-mode single-loop 7R mechanism that has three motion modes with the same instantaneous DOF but different finite DOF. Firstly, the novel multi-mode single-loop 7R spatial mechanism is constructed by inserting one revolute (R) joint into a plane symmetric Bennett joint-based 6R mechanism for circular translation. The reconfiguration analysis is then carried out in the configuration space by solving a set of kinematic loop equations based on dual quaternions and the natural exponential function substitution using tools from algebraic geometry. The analysis shows that the multi-mode single-loop 7R spatial mechanism has three motion modes, including a 2-DOF planar 5R mode and two 1-DOF spatial 6R modes and can transit between each pair of motion modes through two transition configurations. The higher-order mobility analysis shows that the 7R mechanism has two-instantaneous DOF at a regular configuration of any motion mode and three instantaneous DOF in a transition configuration. The infinitesimal motions that are not tangential to finite motions are of second-order in transition configurations between 2-DOF motion mode 1 and 1-DOF motion modes 2 or 3 or first-order in transition configurations between 1-DOF motion modes 2 and 3.

Original languageEnglish
Title of host publicationASME 2018 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
PublisherAmerican Society of Mechanical Engineers
Volume5B
ISBN (Electronic)9780791851814
DOIs
Publication statusPublished - 2018
Event42nd Mechanisms and Robotics Conference 2018 - Quebec City, Canada
Duration: 26 Aug 201829 Aug 2018

Conference

Conference42nd Mechanisms and Robotics Conference 2018
CountryCanada
CityQuebec City
Period26/08/1829/08/18

Keywords

  • Configuration space
  • Multi-mode mechanism
  • Reconfiguration analysis
  • Singularity
  • Tangent cone

ASJC Scopus subject areas

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

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