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Research Papers: Design of Mechanisms and Robotic Systems

Geometric Method of Spatial Linkages Synthesis for Function Generation With Three Finite Positions

[+] Author and Article Information
Song Lin

Sino-German College for Postgraduate Studies,
Tongji University,
Shanghai 201804, China
e-mail: slin@tongji.edu.cn

Hanchao Wang

School of Mechanical Engineering,
Tongji University,
Shanghai 201804, China
e-mail: whc120005@126.com

Jingshuai Liu

School of Mechanical Engineering,
Tongji University,
Shanghai 201804, China
e-mail: 1210295@tongji.edu.cn

Yu Zhang

School of Mechanical Engineering,
Tongji University,
Shanghai 201804, China
e-mail: sjzzy1991@163.com

1Corresponding author.

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received November 23, 2017; final manuscript received April 19, 2018; published online June 1, 2018. Assoc. Editor: Ettore Pennestri.

J. Mech. Des 140(8), 082303 (Jun 01, 2018) (11 pages) Paper No: MD-17-1785; doi: 10.1115/1.4040171 History: Received November 23, 2017; Revised April 19, 2018

This paper presents a geometric method as a unified synthesis process of function generation for spatial linkages. The synthesis method utilizes the mapping relationship between spatial kinematic geometric model and two-plane projection system to transform the problem from spatial geometry to plane geometry. In this way, the synthesis process of mechanisms can be simplified through the corresponding transformation. Afterward, the line-guidance model is built up. Combining the kinematic inversion in two-plane projection system, this model can be used to realize the spatial linkages synthesis for function generation with three finite positions. Finally, revolute–sphere–sphere–revolute (RSSR) and revolute–sphere–sphere–prism (RSSP) mechanisms are offered to illustrate the application of this method.

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Figures

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Fig. 1

Spatial kinematic rules of a line with two positions

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Fig. 2

The relationship between three positions of a line and three rotation axes

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Fig. 3

The quadratic surface consists of central point axes

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Fig. 4

Dimensionality transformation: (a) two-plane projections of a line with two positions and (b) the conversion of the projection system

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Fig. 5

The projection of a line with two positions in planes III and IV

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Fig. 6

The projection of a spatial line with three positions and three rotation axes

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Fig. 7

The transformation process of finding the projection of central point axis

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Fig. 8

The establishment of line-guidance model with three positions

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Fig. 9

Unified synthesis process for function generation of spatial linkages

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Fig. 10

RSSR mechanism for the function generation with three positions

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Fig. 11

Construction of projection plane III−IV: (a) constructing process and (b) constructing result

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Fig. 12

The synthesis result for the function generation with three positions of RSSR mechanism: (a) in the two-plane projection system and (b) in the space

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Fig. 13

RSSP mechanism for the function generation with three positions

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Fig. 14

The transformation of projection system: (a) transformation process and (b) transformation result

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Fig. 15

The synthesis result for the function generation with three positions of RSSP mechanism: (a) in the two-plane projection system and (b) in the space

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