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Research Papers

A Double-Faced 6R Single-Loop Overconstrained Spatial Mechanism

[+] 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

Xiuyun He

School of Engineering and Physical Sciences,
Heriot-Watt University,
Edinburgh EH14 4AS, UK
e-mail: xiuyunhe@gmail.com

Duanling Li

Automation School,
Beijing University of Posts
and Telecommunications,
Beijing 100876, China
e-mail: liduanling@163.com

1Corresponding author.

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANISMS AND ROBOTICS. Manuscript received October 1, 2017; final manuscript received December 23, 2017; published online April 5, 2018. Assoc. Editor: Raffaele Di Gregorio.

J. Mechanisms Robotics 10(3), 031013 (Apr 05, 2018) (10 pages) Paper No: JMR-17-1335; doi: 10.1115/1.4039224 History: Received October 01, 2017; Revised December 23, 2017

This paper deals with a 6R single-loop overconstrained spatial mechanism that has two pairs of revolute joints with intersecting axes and one pair of revolute joints with parallel axes. The 6R mechanism is first constructed from an isosceles triangle and a pair of identical circles. The kinematic analysis of the 6R mechanism is then dealt with using a dual quaternion approach. The analysis shows that the 6R mechanism usually has two solutions to the kinematic analysis for a given input and may have two circuits (closure modes or branches) with one or two pairs of full-turn revolute joints. In two configurations in each circuit of the 6R mechanism, the axes of four revolute joints are coplanar, and the axes of the other two revolute joints are perpendicular to the plane defined by the above four revolute joints. Considering that from one configuration of the 6R mechanism, one can obtain another configuration of the mechanism by simply renumbering the joints, the concept of two-faced mechanism is introduced. The formulas for the analysis of plane symmetric spatial triangle are also presented in this paper. These formulas will be useful for the design and analysis of multiloop overconstrained mechanisms involving plane symmetric spatial RRR triads.

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Figures

Grahic Jump Location
Fig. 2

D-H parameters of the 6R mechanism

Grahic Jump Location
Fig. 3

Wohlhart's double-Goldberg-5R 6R mechanism: (a) Wohlhart's 6R mechanism, (b) two compositional Goldberg 5R mechanisms, and (c) Bennett's linkages associated with Goldberg 5R mechanisms

Grahic Jump Location
Fig. 4

A plane symmetric spatial triangle: (a) general case and (b) degenerate case

Grahic Jump Location
Fig. 5

A special case of Wohlhart's double-Goldberg-5R 6R mechanism: (a) Wohlhart's 6R mechanism, (b) two compositional Goldberg 5R mechanisms, and (c) Bennett's linkages associated with Goldberg 5R mechanisms

Grahic Jump Location
Fig. 1

Construction of a 6R mechanism that has two pairs of R joints with intersecting axes and one pair of R joints with parallel axes: (a) step 1 and (b) step 2

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Fig. 6

Kinematic analysis of mechanism I: (a) plot of θ1θ2, (b) plot of θ1θ3, (c) plot of θ1θ4, (d) plot of θ1θ5, and (e) plot of θ1θ6

Grahic Jump Location
Fig. 7

Configurations of mechanism I in mode 1: (a) configuration A: θ1 = π, (b) configuration B: θ1 = 157.76 deg, and (c) configuration C: θ1 = π

Grahic Jump Location
Fig. 8

Configurations of mechanism I in mode 2: (a) configuration D: θ1 = 0, (b) configuration E θ1 = −82.24 deg, and (c) configuration F: θ1 = 0

Grahic Jump Location
Fig. 9

Kinematic analysis of mechanism II: (a) plot of θ1θ2, (b) plot of θ1θ3, (c) plot of θ1θ4, (d) plot of θ1θ5, and (e) plot of θ1θ6

Grahic Jump Location
Fig. 10

Configurations of mechanism II in mode 1: (a) configuration A: θ1 = 0, (b) configuration B: θ1 = π/2, and (c) configuration C: θ1 = π

Grahic Jump Location
Fig. 11

Configurations of mechanism II in mode 2: (a) configuration D: θ1 = 0, (b) configuration E: θ1 = π/2, and (c) configuration F: θ1 = π

Grahic Jump Location
Fig. 12

A prototype of 6R mechanism II: (a) computer-aided design model and (b) three-dimensional (3D)-printed prototype

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