THE SYNTHESIS OF THE PLANAR LINKAGES WITH SYMMETRICAL CONFIGURATIONS

The mechanisms that employ symmetrical configurations can be found in the steering mechanisms, double open refrigerator, roof boxes, and double open windows, among others. They are useful for some special applications with kinematic symmetry. There have been studies about the linkage synthesis, especially in the research of planar closed chains, from as early as 1960s. However, no study has focused on the symmetry of planar linkages. Thus, the purpose of this paper is to present a methodology to synthesize the configurations of planar linkages. The systematic methodology can be divided into structure synthesis, configuration synthesis and results produced from three major processes. Finally, four suitable results of up to six-bar linkages can be obtained, for example. The four results include one four-bar linkage and three six-bar linkages.

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A Design Methodology for System Parameters Synthesis of Elastic Planar Linkages: Theory

Journal of Mechanical Design ◽

10.1115/1.2917040 ◽

1992 ◽

Vol 114 (4) ◽

pp. 536-541 ◽

Cited By ~ 2

Author(s):

Zine-Eddine Boutaghou ◽

A. G. Erdman

Keyword(s):

Design Methodology ◽

Design Sensitivity ◽

Element Analysis ◽

System Parameters ◽

Sensitivity Equations ◽

The Finite Element Analysis ◽

Planar Linkages ◽

Multi Body ◽

Four Bar Linkage ◽

Theoretical Considerations

Existing formulations predict the displacement and stresses in multi-body systems that result from known system parameters. In contrast, the proposed design methodology enables structured selection of system parameters necessary to produce desired elastic displacements, stresses, and frequencies. This design process involves the development of inverse design equations, the finite element analysis, and the design sensitivity equations to obtain converged solutions satisfying desired design constraints. Part 1 (Theory) considers the theoretical considerations involved. Part 2 (Applications) applies the methodology to design a four-bar linkage and a six-bar linkage.

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Four-Bar Linkage Synthesis Using Non-convex Optimization

Lecture Notes in Computer Science - Principles and Practice of Constraint Programming ◽

10.1007/978-3-319-44953-1_39 ◽

2016 ◽

pp. 618-635 ◽

Cited By ~ 5

Author(s):

Vincent Goulet ◽

Wei Li ◽

Hyunmin Cheong ◽

Francesco Iorio ◽

Claude-Guy Quimper

Keyword(s):

Convex Optimization ◽

Four Bar Linkage ◽

Linkage Synthesis

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Linkage Synthesis of a Four-Bar Mechanism for N Precision Points Using Simulated Annealing

Volume 1B: 25th Biennial Mechanisms Conference ◽

10.1115/detc98/mech-5942 ◽

1998 ◽

Author(s):

Horacio Martínez-Alfaro ◽

Homero Valdez ◽

Jaime Ortega

Keyword(s):

Simulated Annealing ◽

Computational Intelligence ◽

Simulated Annealing Algorithm ◽

Alternative Synthesis ◽

Computational Intelligence Technique ◽

Annealing Algorithm ◽

Four Bar Linkage ◽

Generation Problem ◽

Intelligence Technique ◽

Linkage Synthesis

Abstract This paper presents an alternative way of linkage synthesis by using a computational intelligence technique: Simulated Annealing. The technique allows to define n precision points of a desired path to be followed by a four-bar linkage (path generation problem). The synthesis problem is transformed into an optimization one in order to use the Simulated Annealing algorithm. With this approach, a path can be better specified since the user will be able to provide more “samples” than the usual limited number of five allowed by the classical methods. Several examples are shown to demonstrate the advantages of this alternative synthesis technique.

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Finding All Solutions to Unconstrained Nonlinear Optimization for Approximate Synthesis of Planar Linkages Using Continuation Method

Journal of Mechanical Design ◽

10.1115/1.2829469 ◽

1999 ◽

Vol 121 (3) ◽

pp. 368-374 ◽

Cited By ~ 8

Author(s):

A.-X. Liu ◽

T.-L. Yang

Keyword(s):

Continuation Method ◽

Optimization Method ◽

Global Optimum ◽

Kinematic Synthesis ◽

All Solutions ◽

Approximate Synthesis ◽

Unconstrained Nonlinear Optimization ◽

Optimum Solution ◽

Planar Linkages ◽

Four Bar Linkage

Generally, approximate kinematic synthesis of planar linkage is studied using optimization method. But this method has two defects: i) the suitable 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 three examples are given to illustrate the advantages of the proposed method.

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Performance of EAs for four-bar linkage synthesis

Mechanism and Machine Theory ◽

10.1016/j.mechmachtheory.2009.03.003 ◽

2009 ◽

Vol 44 (9) ◽

pp. 1784-1794 ◽

Cited By ~ 77

Author(s):

S.K. Acharyya ◽

M. Mandal

Keyword(s):

Four Bar Linkage ◽

Linkage Synthesis

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A new method for torque balancing of planar linkages using non-circular gears

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1243/095440603765226786 ◽

2003 ◽

Vol 217 (5) ◽

pp. 495-503 ◽

Cited By ~ 18

Author(s):

Y-A Yao ◽

H-S Yan

Keyword(s):

Optimization Model ◽

Design Method ◽

Gear Ratio ◽

New Method ◽

Transmission Ratio ◽

Gear Pair ◽

Novel Concept ◽

Planar Linkages ◽

Driving Torque ◽

Linkage Synthesis

This paper proposes a novel concept for reducing driving torque fluctuations of planar linkages by the application of non-circular gears. The circular gears normally used in gear linkage mechanisms are replaced by a pair of non-circular gears. The design method includes two individual stages: linkage synthesis and gear ratio synthesis. An optimization model is developed for determining the appropriate transmission ratio function of the non-circular gear pair to meet user-specified requirements and constraints. Two examples are given to demonstrate this method and to verify its feasibility.

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Four-Bar Linkage Synthesis Methods for Two Precision Positions Combined With N Quasi-Positions

Volume 1: 21st Design Automation Conference ◽

10.1115/detc1995-0063 ◽

1995 ◽

Author(s):

John A. Mirth

Keyword(s):

Synthesis Method ◽

Synthesis Methods ◽

Bounded Motion ◽

Transmission Angle ◽

Pass Through ◽

Position Synthesis ◽

Four Bar Linkage ◽

Exact Positions ◽

Linkage Synthesis

Abstract Mechanisms seldom need to pass through more than one or two exact positions. The method of quasi-position synthesis combines a number of approximate or “quasi” positions with two exact positions to design four-bar linkages that will produce a specified, bounded motion. Quasi-position synthesis allows for the optimization of some linkage characteristic (such as link lengths or transmission angles) by using the three variables that describe a single quasi-position. Procedures for circuit and transmission angle rectification are also easily incorporated into the quasi-position synthesis method.

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A Numerical Method and Automatic Generation for Determining the Assemblage Configurations of Complex Planar Linkages Based on the Ordered Single-Opened-Chains

Volume 2A: 24th Biennial Mechanisms Conference ◽

10.1115/96-detc/mech-1030 ◽

1996 ◽

Author(s):

Shen Hui-Ping ◽

Yang Ting-Li

Keyword(s):

Numerical Method ◽

Numerical Evaluation ◽

Evaluation Method ◽

Automatic Generation ◽

Structural Theory ◽

Structure Synthesis ◽

Planar Linkages

Abstract This paper presents a simple numerical evaluation method for solving all possible assembly configurations on an any position of the input link of some complex planar linkages according to the structural theory of mechanism based on the ordered Single-Opened-Chains (S.O.Cs). This method can simultaneously checks on whether the input link is a crank of the linkage. This paper also discovers that full-cycle ratability (F.C.R) of a linkage depends on not only the length of links of the linkage but also the different assembly configurations of the linkage after analysis of assemblage configurations. The illustration for solution and analysis of assembly configurations of a complex planar linkage is given in detail. This paper provides the actual assembly of linkages and the optimization of structure synthesis of linkages with some important information.

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A Unified Algorithm for Analysis and Simulation of Planar Four-Bar Motions Defined With R- and P-Joints

Volume 5B: 38th Mechanisms and Robotics Conference ◽

10.1115/detc2014-35203 ◽

2014 ◽

Author(s):

Xiangyun Li ◽

Xin Ge ◽

Anurag Purwar ◽

Q. J. Ge

Keyword(s):

Linkage Analysis ◽

Least Squares ◽

Efficient Algorithm ◽

Image Space ◽

Loop Closure ◽

Closure Equation ◽

Unified Algorithm ◽

Four Bar Linkage ◽

Best Fit ◽

Linkage Synthesis

This paper presents a single, unified and efficient algorithm for animating the motions of the coupler of all four-bar mechanisms formed with revolute (R) and prismatic (P) joints. This is achieved without having to formulate and solve the loop closure equation associated with each type of four-bar linkages separately. In our previous paper on four-bar linkage synthesis, we map the planar displacements from Cartesian to image space using planar quaternion. Given a set of image points that represent planar displacements, the problem of synthesizing a planar four-bar linkage is reduced to finding a pencil of Generalized- or G-manifolds that best fit the image points in the least squares sense. The three planar dyads associated with Generalized G-manifolds are RR, PR and RP which could construct six types of four-bar mechanisms. In this paper, we show that the same unified formulation for linkage synthesis leads to a unified algorithm for linkage analysis and simulation as well. Both the unified synthesis and analysis algorithms have been implemented on Apple’s iOS platform.

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Towards the appropriate synthesis of the four-bar linkage

Transactions of the Canadian Society for Mechanical Engineering ◽

10.1139/tcsme-2017-0001 ◽

2018 ◽

Vol 42 (1) ◽

pp. 1-9 ◽

Cited By ~ 2

Author(s):

Joshua K. Pickard ◽

Juan A. Carretero ◽

Jean-Pierre Merlet

Keyword(s):

Design Methodology ◽

Design Parameters ◽

Geometrical Parameters ◽

Assembly Process ◽

Multiple Descriptions ◽

Complete Set ◽

Design Solutions ◽

Four Bar Linkage ◽

Linkage Synthesis

Uncertainties are an inherent element in all mechanisms, arising from the manufacturing and assembly process or even from the operation of the device. In terms of synthesis routines for mechanisms, uncertainties are generally neglected since they are difficult to account for. In this work, the concept of appropriate design is utilized to develop routines that can more easily account for uncertainties in the geometrical parameters. These routines have been developed for linkages, specifically the four-bar linkage, and are capable of synthesizing the complete set of design solutions, referred to as allowable regions, for a set of desired coupler curve characteristics. The description of the desired coupler curve may contain any number of precision points and (or) trajectories. Several problems are solved in this work, including obtaining a representation of the coupler curve corresponding to a set of design parameters containing uncertainties, and synthesizing the appropriate designs for multiple descriptions of desired coupler curves. The results are quite promising and show great potential for using the appropriate design methodology for linkage synthesis.

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