Symmetrical Coupler Curve and Singular Point Classification in Planar and Spherical Swinging-Block Linkages

[+] Author and Article Information
Kourosh H. Shirazi

Mechanical Engineering Department, Faculty of Engineering, Chamran University of Ahvaz, Ahvaz, Iranshirazi@cua.ac.ir

J. Mech. Des 128(2), 436-443 (Jul 12, 2005) (8 pages) doi:10.1115/1.2167651 History: Received April 14, 2005; Revised July 12, 2005

The purpose of the present paper is coupler curve synthesis and classification in planar and spherical swinging block linkages for path generation problem. It is shown that the swinging block mechanism, which is an inversion of the slider crank mechanism, can be classified into two types. The first type generates Lemniscate coupler curves consisting one or two loops. In this case, two double points, namely cusp and crunode, occur depending on the mechanism's dimension. The second type generates Cardioid and Limaçon type coupler-curves consisting of one, two, three, and four loops. In this case, three kinds of double points, namely cusp, crunode, and tacnode, occur. For the spherical swinging-block linkages, a parametric coupler curve equation is derived. Using a trigonometric similitude between the planar and spherical linkages, a symmetrical coupler curve and singular point classification is accomplished.

Copyright © 2006 by American Society of Mechanical Engineers
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Figure 5

Lines L1 and L2 are envelopes of all the possible paths in type 1

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Figure 1

The planar and the spherical SBL

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Figure 2

Two different locations of point C with respect to A and O

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Figure 3

The path of point C when b3−b1<a<b3+b1

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Figure 4

The path of point C when a⩽b3−b1 or a⩾b3+b1

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Figure 6

The two piecewise nearly straight closed paths

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Figure 7

The path when both conditions b1−b3<a<b1+b3 are satisfied

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Figure 8

Double points in type 2 when the condition b12−b32⩽a⩽b1 is satisfied

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Figure 9

The path of point C when a⩾b1+b3 or a⩽b1−b3

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Figure 10

The possible piecewise nearly straight paths for type 2

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Figure 11

The employed coordinates for deriving the coupler-curve equation

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Figure 12

The planar and the spherical right-angle triangle forming in the SBL



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