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, UK, EH14 4AS

Xiuyun He

School of Engineering and Physical, Sciences, Heriot-Watt University, Edinburgh, UK, EH14 4AS

Duanling Li

Automation School, Beijing University of Posts and Telecommunications, Beijing 100876, China

1Corresponding author.

ASME 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 is also presented in this paper. These formulas will be useful for the analysis of multi-loop overconstrained mechanisms involving plane symmetric spatial RRR triads.

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