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Research Papers

Synthesis of Spatial Mechanism UR-2SS for Path Generation

[+] Author and Article Information
Wen-Yeuan Chung

Department of Mechanical Engineering,
Chinese Culture University,
Taipei 11114, Taiwan
e-mail: wchung@faculty.pccu.edu.tw

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANISMS AND ROBOTICS. Manuscript received December 3, 2013; final manuscript received December 16, 2014; published online March 23, 2015. Assoc. Editor: Andrew P. Murray.

J. Mechanisms Robotics 7(4), 041009 (Nov 01, 2015) (9 pages) Paper No: JMR-13-1243; doi: 10.1115/1.4029438 History: Received December 03, 2013; Revised December 16, 2014; Online March 23, 2015

This article presents a new spatial mechanism with single degree of freedom (DOF) for three-dimensional path generation. The path can be defined by prescribing at most seven precision points. The moving platform of the mechanism is supported by a U-R (universal-revolute) leg and two S–S (spherical–spherical) legs. The driving unit is the first axis of the universal pair. The U-R leg is synthesized first with the problem of order defects being considered. Precision points then lead to prescribed poses of the moving platform. Two S–S legs are then synthesized to meet these poses. This spatial mechanism with a given input is analogous to a planar kinematic chain so that all possible configurations of the spatial mechanism can be constructed. A strategy consisting of three stages for evaluating branch defects is developed with the aid of the characteristic of double configurations and the technique of coding three constituent four-bar linkages. Two numerical examples are presented to illustrate the design, the evaluation of defects, and the performance of the mechanism.

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Figures

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Fig. 3

Illustration of fixed and moving frames

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Fig. 4

Illustration for analogous four-bar linkage

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Fig. 5

Analogous Assur five links

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Fig. 6

Two branches for a planar four-bar linkage

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Fig. 7

Examples of planar Assur kinematic chain with five links. (a) Configuration 1, (b) configuration 2, and (c) double configurations.

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Fig. 8

Coding of a four-bar linkage at four positions. (a) Code = 1, (b) code = 2, (c) code = 3, and (d) code = 4.

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Fig. 9

Results of example 1. (a) Plot of Δ versus θ1, (b) plot of θ2 versus θ1, and (c) trajectory of point P.

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Fig. 10

Animation picture of the mechanism

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Fig. 11

Results of mechanism CD. (a) Values of criterion and (b) trajectory of point P.

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Fig. 12

Results of mechanism BC. (a) Values of criterion, (b) trajectory of point P, and (c) animation picture.

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Fig. 13

Results of mechanism BD. (a) Values of criterion, (b) trajectory of point P, and (c) animation picture.

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