Reconfiguration Analysis of Multimode Single-Loop Spatial Mechanisms Using Dual Quaternions

被引:38
作者
Kong, Xianwen [1 ]
机构
[1] Heriot Watt Univ, Sch Engn & Phys Sci, Edinburgh EH14 4AS, Midlothian, Scotland
来源
JOURNAL OF MECHANISMS AND ROBOTICS-TRANSACTIONS OF THE ASME | 2017年 / 9卷 / 05期
基金
英国工程与自然科学研究理事会;
关键词
kinematic analysis; multimode mechanisms; dual quaternions; algebraic geometry; reconfiguration analysis; INVERSE KINEMATICS;
D O I
10.1115/1.4037111
中图分类号
TH [机械、仪表工业];
学科分类号
0802 ;
摘要
Although kinematic analysis of conventional mechanisms is a well-documented fundamental issue in mechanisms and robotics, the emerging reconfigurable mechanisms and robots pose new challenges in kinematics. One of the challenges is the reconfiguration analysis of multimode mechanisms, which refers to finding all the motion modes and the transition configurations of the multimode mechanisms. Recent advances in mathematics, especially algebraic geometry and numerical algebraic geometry, make it possible to develop an efficient method for the reconfiguration analysis of reconfigurable mechanisms and robots. This paper first presents a method for formulating a set of kinematic loop equations for mechanisms using dual quaternions. Using this approach, a set of kinematic loop equations of spatial mechanisms is composed of six polynomial equations. Then the reconfiguration analysis of a novel multimode single-degree-of-freedom (1DOF) 7R spatial mechanism is dealt with by solving the set of loop equations using tools from algebraic geometry. It is found that the 7R multimode mechanism has three motion modes, including a planar 4R mode, an orthogonal Bricard 6R mode, and a plane symmetric 6R mode. Three (or one) R (revolute) joints of the 7R multimode mechanism lose their DOF in its 4R (or 6R) motion modes. Unlike the 7R multimode mechanisms in the literature, the 7R multimode mechanism presented in this paper does not have a 7R mode in which all the seven R joints can move simultaneously.
引用
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页数:8
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