# Kinematic analysis of conventional and multi-mode spatial mechanisms using dual quaternions

*Corresponding author for this work

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

6 Citations (Scopus)

## Abstract

Although kinematic analysis of conventional mechanisms is a well-documented fundamental issue in mechanisms and robotics, the emerging reconfigurable mechanisms and robots (or mechanisms and robots with multiple operation modes) require reexamining this fundamental issue. Recent advances in mathematics, especially algebraic geometry and numerical algebraic geometry, make it possible to develop an efficient method for the kinematic analysis of not only conventional mechanisms and robots but also reconfigurable mechanisms and robots. This paper first presents a method for setting up a set of kinematic loop equations for mechanisms using dual quaternions. Using this approach, a set of kinematic loop equations of a spatial mechanism is composed of six equations. The effectiveness of the proposed kinematic loop equations is then demonstrated by deriving the explicit input-output equations of a line symmetric 1-DOF (degree-of-freedom) 7R single-loop spatial mechanism, the reconfiguration analysis of a novel multi-mode 1-DOF 7R spatial mechanism. In the former case, an explicit input-output equation of degree 8 is derived. In the latter case, it is found that the 7R multi-mode mechanism has three motion modes, including a planar 4R mode, an orthogonal Bricard 6R mode, and a plane symmetric 6R mode. Unlike the 7R multi-mode mechanisms in the literature, the 7R multi-mode mechanism presented in this paper does not have a 7R mode in which all the seven R joints can move simultaneously.

Original language English ASME 2016 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference American Society of Mechanical Engineers 5B 9780791850169 https://doi.org/10.1115/DETC2016-59194 Published - 2016 40th Mechanisms and Robotics Conference 2016 - Charlotte, United StatesDuration: 21 Aug 2016 → 24 Aug 2016

### Conference

Conference 40th Mechanisms and Robotics Conference 2016 United States Charlotte 21/08/16 → 24/08/16

## Keywords

• Algebraic geometry
• Dual quaternions
• Kinematic analysis
• Multi-mode mechanisms
• Reconfiguration analysis

## ASJC Scopus subject areas

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

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