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Research Papers: Mechanisms and Robotics

A Virtual Cam Method for Locating Instant Centers of Kinematically Indeterminate Linkages

[+] Author and Article Information
Yin-Ping Chang

Mechanical Engineering Department, Oakland University, Rochester, MI 48309

Innchyn Her

Electro-Mechanical Engineering Department, National Sun Yat-sen University, Taiwan 804, R.O.C.

J. Mech. Des 130(6), 062304 (Apr 15, 2008) (7 pages) doi:10.1115/1.2900720 History: Received June 15, 2007; Revised October 18, 2007; Published April 15, 2008

Kinematically indeterminate linkages are those whose complete set of instant centers cannot be obtained by Kennedy’s theorem. A linkage of this kind is often characterized as having no four-bar loop, or even if one exists, it does not lead to the finding of all other instant centers in the multiple-loop chain. This paper presents a simple graphical method for dealing with many of these linkages. While not altering the total degrees of freedom of the linkage, a virtual cam is introduced to help locate some key instant centers. This method also lends itself to applications along with Pennock’s method to achieve greater usability.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 1

The basic concept of the virtual cam method

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Figure 2

To construct ΔI26I12I2i similar to ΔI26I16I6i by graphical method: (a) when I26 is on Line I12I16 and (b) when I26 is on the extension part of Line I12I16

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Figure 3

(a) Finding the locus of the key instant center, L15, from the original mechanism and (b) Locating the key instant center, I15, via kinematic inversion

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Figure 4

(a) An eight-bar single butterfly mechanism and (b) virtual cam application on the eight-bar mechanism in (a)

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Figure 5

(a) A geared nine-bar mechanism and (b) virtual cam application on the geared nine-bar mechanism in (a)

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Figure 6

(a) A ten-bar mechanism, (b) virtual cam application on the ten-bar mechanism in (a)—to find L16, and (c) virtual cam application on the ten-bar mechanism in (a)—to find L19

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Figure 7

Combining virtual-cam-and-Pennock’s approach on the ten-bar mechanism: (a) locate I46(1) by Pennock’s method, (b) locate I46(2) by Pennock’s method, and (c) I46 found by the virtual-cam-and-Pennock joint approach

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