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Research Papers

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

[+] Author and Article Information
Xianwen Kong

School of Engineering and Physical Sciences,
Heriot-Watt University,
Edinburgh EH14 4AS, UK
e-mail: X.Kong@hw.ac.uk

Manuscript received September 17, 2016; final manuscript received May 28, 2017; published online August 4, 2017. Assoc. Editor: Venkat Krovi.

J. Mechanisms Robotics 9(5), 051002 (Aug 04, 2017) (8 pages) Paper No: JMR-16-1273; doi: 10.1115/1.4037111 History: Received September 17, 2016; Revised May 28, 2017

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.

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Figures

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Fig. 2

A multimode 7R mechanism

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Fig. 3

Motion modes of the multimode 7R mechanism: (a) motion mode 1: planar 4R mode in circuit 1, (b) motion mode 1: planar 4R mode in circuit 2, (c) motion mode 2: orthogonal bricard 6R mode in circuit 1, (d) motion mode 2: orthogonal bricard 6R mode in circuit 2, (e) motion mode 3: plane symmetric 6R mode in circuit 1, and (f) motion mode 3: plane symmetric 6R mode in circuit 2

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Fig. 4

Transition configurations between the planar 4R mode and the orthogonal bricard 6R mode of the multimode 7R mechanism: (a) transition configuration 1 between motion modes 1 and 2 in circuit 1 and (b) transition configuration 2 between motion modes 1 and 2 in circuit 2

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Fig. 5

Transition configurations between the planar 4R mode and the plane symmetric 6R mode of the multimode 7R mechanism: (a) transition configuration 3 between motion modes 1 and 3 in circuit 1 and (b) transition configuration 4 between motion modes 1 and 3 in circuit 2

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Fig. 6

Reconfiguration of the multimode 7R mechanism: (a) motion modes 1, 2, and 3 in circuit 1 and (b) motion modes 1, 2, and 3 in circuit 2

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Fig. 7

A 3D-printed prototype of the multimode 7R mechanism in transition configuration 2

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