Synthesis of Plane Linkages With Use of the Displacement Matrix

1967 ◽  
Vol 89 (2) ◽  
pp. 206-214 ◽  
Author(s):  
C. H. Suh ◽  
C. W. Radcliffe
Keyword(s):  
Rigid Body ◽  
Two Dimensions ◽  
Path Generation ◽  
Function Generation ◽  
Generalized Matrix ◽  
Rigid Body Displacement ◽  
And Function

A generalized matrix for the description of rigid body displacement in two dimensions is developed. This displacement matrix is applied to the synthesis of plane linkages used for rigid body guidance, path generation, and function generation.

Synthesis of Spherical Linkages With Use of the Displacement Matrix

1967 ◽  
Vol 89 (2) ◽  
pp. 215-221 ◽  
Author(s):  
C. H. Suh ◽  
C. W. Radcliffe
Keyword(s):  
Rigid Body ◽  
Rigid Body Motion ◽  
Body Motion ◽  
Path Generation ◽  
Function Generation ◽  
Spherical Linkages ◽  
Spherical Rigid Body

Equations of synthesis are derived which are based upon rigid body motion expressed as a displacement matrix. Applications are shown in spherical rigid body guidance, function generation, and path generation.

Finding All Solutions to Approximate Synthesis of Planar Linkages for Function Generation, Rigid-Body Guidance and Path Generation

1996 ◽  
Author(s):  
An-Xin Liu ◽  
Ting-Li Yang
Keyword(s):  
Rigid Body ◽  
Continuation Method ◽  
Optimization Method ◽  
Global Optimum ◽  
Path Generation ◽  
Kinematic Synthesis ◽  
Function Generation ◽  
All Solutions ◽  
Approximate Synthesis ◽  
Optimum Solution

Abstract Generally, approximate kinematic synthesis of planar linkage is studied using optimization method. But this method has two defects: i) the initial guesses are hard to determine and ii) the global optimum solution is difficult to find. In this paper, a new method which can find all solutions to approximate kinematic synthesis of planar linkage is proposed. Firstly, we reduce the approximate synthesis problem to finding all solutions to polynomial equations. Polynomial continuation method is then used to find all solutions. Finally, all possible linkages can be obtained. Approximate syntheses of planar four-bar linkage for function generation, rigid-body guidance and path generation are studied in detail and 3 examples are given to illustrate the advantages of the proposed method.

On the Duality in the Existence of R-R Links for Three Positions

1969 ◽  
Vol 91 (1) ◽  
pp. 129-134 ◽  
Author(s):  
Chung Ha Suh
Keyword(s):  
Rigid Body ◽  
Point Of View ◽  
Geometric Invariant ◽  
Function Generation ◽  
And Function ◽  
First Time

The present paper intends to report a discovery of geometric invariant in finite synthesis of space mechanism called “the duality of R-R link.” The duality itself is first proven here by using the screw geometry to give it a simple and intuitive form. Second, proving the 4-bar mechanism made by the dual R-R links is a Bennett mechanism it is made possible to synthesize the Bennett mechanisms for rigid-body guidance and function generation. Synthesizing the Bennett mechanisms the first time, for these practical uses, is important in itself. However, from the point of view of “the duality” it is only one special application.

scholarly journals The Synthesis of Planar Four-Bar Linkage for Mixed Motion and Function Generation

Sensors ◽  
2021 ◽  
Vol 21 (10) ◽  
pp. 3504
Author(s):  
Bin Wang ◽  
Xianchen Du ◽  
Jianzhong Ding ◽  
Yang Dong ◽  
Chunjie Wang ◽  
...  
Keyword(s):  
Complex Plane ◽  
Path Generation ◽  
Motion Generation ◽  
Numerical Examples ◽  
Function Generation ◽  
Long Time ◽  
Synthesis Procedure ◽  
And Function ◽  
Four Bar Linkage ◽  
Numerical Synthesis

The synthesis of four-bar linkage has been extensively researched, but for a long time, the problem of motion generation, path generation, and function generation have been studied separately, and their integration has not drawn much attention. This paper presents a numerical synthesis procedure for four-bar linkage that combines motion generation and function generation. The procedure is divided into two categories which are named as dependent combination and independent combination. Five feasible cases for dependent combination and two feasible cases for independent combination are analyzed. For each of feasible combinations, fully constrained vector loop equations of four-bar linkage are formulated in a complex plane. We present numerical examples to illustrate the synthesis procedure and determine the defect-free four-bar linkages.

Evolutionary Based Optimal Synthesis of Four-Bar Mechanisms

2003 ◽  
Author(s):  
D. Koladiya ◽  
P. S. Shiakolas ◽  
J. Kebrle
Keyword(s):  
Optimization Techniques ◽  
Optimization Approach ◽  
Path Generation ◽  
Planar Mechanisms ◽  
Function Generation ◽  
Novel Technique ◽  
Optimum Synthesis ◽  
Design Variables ◽  
Accuracy Level ◽  
And Function

Graphical and analytical syntheses have been well applied to path, motion and function generation of planar mechanisms. Optimization techniques in common, require “good initial guesses” and do not necessarily converge to a solution. This paper presents a methodology to synthesize mechanisms employing an evolutionary optimization approach technique known as Differential Evolution. The initial bounds for the design variables are defined automatically using a newly developed and novel technique called the Geometric Centroid of Precision Points. Optimum synthesis of four-bar linkages for path generation with user defined accuracy level at required precision points is discussed.

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