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Research Papers

Spatial Generalizations of Planar Point-Angle and Path Generation Problems

[+] Author and Article Information
Chintien Huang

Department of Mechanical Engineering, National Cheng Kung University, Tainan 701, Taiwanchuang@mail.ncku.edu.tw

Ching-Lung Lai

Department of Mechanical Engineering, National Cheng Kung University, Tainan 701, Taiwan

J. Mechanisms Robotics 4(3), 031010 (Jul 02, 2012) (6 pages) doi:10.1115/1.4006742 History: Received February 20, 2011; Revised October 18, 2011; Published June 29, 2012; Online July 02, 2012

This paper deals with the spatial generalizations of two classical planar synthesis problems: the point-angle and the path generation problems. The two planar synthesis problems involve the guidance of a point through specified positions by using planar four-bar linkages. In spatial generalizations, we are concerned with the guidance of an infinitely extended line by using spatial 4C linkages. The equivalent screw triangle is used to derive the synthesis equations of the spatial 4C linkage. By constraining the translational motion in the driving C joint, the RCCC linkage is synthesized. Our results show that the synthesis of the 4C linkage for line guidance yields the same maximum number of positions as the planar four-bar linkage for point guidance. The maximum number of positions of the path generation of a line is nine, while that of the line-angle problem is five. In addition to presenting the spatial generalizations of planar synthesis problems, the results in this paper can be used to design spatial four-bar linkages to match line specifications, in which only a line element, such as a laser beam, is of interest.

FIGURES IN THIS ARTICLE
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Copyright © 2012 by American Society of Mechanical Engineers
Topics: Linkages , Equations , Design
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References

Figures

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Figure 1

The planar 4R linkage for point guidance

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Figure 2

The displacement of a CC dyad

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Figure 3

The displacement of a line

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Figure 4

The spatial 4C linkage for line guidance

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Figure 5

The guidance of a line using the RCCC linkage

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Figure 6

A solution of the 4C linkage

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Figure 7

A solution of the RCCC linkage

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