Coupler Cognates for the Double Flier Eight-Bar Linkage

[+] Author and Article Information
Gordon R. Pennock

School of Mechanical Engineering,  Purdue University, West Lafayette, IN 47907-2088pennock@ecn.purdue.edu

Nihar N. Raje

School of Mechanical Engineering,  Purdue University, West Lafayette, IN 47907-2088

J. Mech. Des 127(6), 1145-1151 (Feb 14, 2005) (7 pages) doi:10.1115/1.1992508 History: Received October 21, 2004; Revised February 14, 2005

This paper presents a graphical technique to construct the coupler cognate linkages for the double flier eight-bar linkage. The technique is based on the skew pantograph construction which converts the double flier linkage into a second eight-bar linkage by applying the concepts of stretch rotation and kinematic inversion. Since a stretch-rotation operation preserves the angular velocities of corresponding links of the two linkages then the second linkage has the same input-output motion as the original double flier linkage. Another stretch rotation is performed on the intermediate eight-bar linkage and a third eight-bar linkage, which duplicates the motion of the coupler link of the original linkage, is obtained. This graphical approach, to investigating coupler cognates, is believed to be an original contribution to the study of cognate linkages. The technique can be applied in a straightforward manner, requiring few constructions, and offers significant advantages over well-known analytical techniques which use the locus equation. For the double flier eight-bar linkage, the locus equation is of a high degree and the coefficients can only be obtained from a very laborious procedure. This paper shows the existence of two coupler cognates for each of the two floating binary links of the double flier eight-bar linkage that are connected to the ternary link which is pinned to ground.

Copyright © 2005 by American Society of Mechanical Engineers
Topics: Linkages , Rotation
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Figure 1

(a) The skew pantograph. (b) The two dyads forming a skew pantograph.

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Figure 2

The double flier eight-bar linkage and angular notation

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Figure 3

(a) Points U and V fixed in the coupler link 4. (b) Skew pantograph EF′G′BFG and eight-bar linkage 1′−2−3−4−5′−6′−7′−8′. (c) Points G″, O8″, O5″, E″, F″, B″, C″, A″ and O2″.

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Figure 4

The coupler cognate linkage

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Figure 5

The triangles O5EO5′, O5DO5′ and CDC

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Figure 6

(a) Graphical programming of the first set of stretch rotations. (b) Graphical programming of the second set of stretch rotations.

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Figure 7

(a) The coupler curve traced by point U. (b) The coupler curve traced by point U″.

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Figure 8

Coupler curves traced by points U and U″ and points V and V″




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