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.

An Elitist Ants-Search Based Method for Optimum Synthesis of Rigid-Linkage Mechanisms

2015 ◽  
Author(s):  
Nadim Diab ◽  
Ahmad Smaili
Keyword(s):  
Objective Function ◽  
Linear Constraints ◽  
Optimization Techniques ◽  
Path Generation ◽  
Generation Task ◽  
Optimum Synthesis ◽  
Structural Error ◽  
Constant Quantity ◽  
Future Work ◽  
Exploration Exploitation

Mechanical linkages are widely used in the industry and the synthesis of such mechanisms may require optimization depending on the number of precision positions required. Many intelligent optimization techniques (Genetic, Tabu, Simulated Annealing, etc) have been proposed in the literature, one of them being the Ant-Search which was first proposed by the authors in 2007. In this paper, a Modified Ant-Search (MAS) technique is proposed to optimize the synthesis of a four-bar mechanism with a path generation task. Two major improvements are applied over the previous algorithm: ants pheromone update and exploration/exploitation techniques are both modified. Unlike the previous work where a constant quantity of pheromones was added during each iteration, in this paper, the pheromone deposit rate is proportional to the error of the objective function. Such a modification in the pheromone update rule is expected to differentiate between the behaviors of different ants and better govern their motion in the subsequent iterations. Moreover, the second major improvement targets the exploration/exploitation techniques followed by the ants. Unlike the previous work where exploration dominates during the early iteration stages and exploitation during the late ones, this work implements a more dynamic strategy where ants enter and leave the exploration/exploitation processes as governed by parameters related to the objective function error and pheromone deposit levels. Such modifications applied to the Ant-Search (AS) technique are expected to ensure a better chance of converging to a global minimum. The MAS technique is applied for a few path generation tasks with prescribed timing along with a set of linear constraints. Results are compared with previous work in the literature where the newly proposed technique showed appreciable improvement as evaluated by the structural error objective function. Future work possibilities are also introduced.

Optimum Synthesis of Rigid Mechanisms Using a Dynamic Ant-Search Method With Sensitivity Analysis

2019 ◽  
Author(s):  
Nadim Diab ◽  
Omar Itani ◽  
Ahmad Smaili
Keyword(s):  
Sensitivity Analysis ◽  
Optimization Technique ◽  
Design Parameters ◽  
Neighborhood Search ◽  
Intensity Level ◽  
Path Generation ◽  
Exploration And Exploitation ◽  
Planar Mechanisms ◽  
Optimum Synthesis ◽  
Synthesis Of Mechanisms

Abstract Four-bar linkages are commonly used mechanisms in various mechanical systems and components. Several techniques for optimum synthesis of planar mechanisms have been suggested in literature such as the Genetic, Tabu, Simulated Annealing, Swarm-Based and many other algorithms. This paper covers optimization of four-bar mechanisms with path generation tasks using a Dynamic Ant Search (DAS) algorithm. Unlike the Modified Ant Search (MAS) technique where ants unanimously moved between the exploration and exploitation phases, in the proposed algorithm, each ant is free to travel between the two aforementioned phases independent of other ants and as governed by its own pheromone intensity level. Moreover, sensitivity analysis is conducted on the design parameters to determine their corresponding neighborhood search boundaries and thus improve the search while in the exploitation mode. These implemented changes demonstrated a remarkable impact on the optimum synthesis of mechanisms for path generation tasks. A briefing of the MAS based algorithm is first presented after which the proposed modified optimization technique and its implementation on four-bar mechanisms are furnished. Finally, three case studies are conducted to evaluate the efficiency and robustness of the proposed methodology where the performances of the obtained optimum designs are benchmarked with those previously reported in literature.

Optimum Synthesis of Planar Mechanisms for Path Generation Based on a Combined Discrete Fourier Descriptor

2015 ◽  
Vol 7 (4) ◽  
Author(s):  
Wen-Yi Lin
Keyword(s):  
Synthesis Method ◽  
Optimization Method ◽  
Path Generation ◽  
Fourier Descriptor ◽  
Planar Mechanisms ◽  
Two Phase ◽  
Phase Synthesis ◽  
Optimum Synthesis ◽  
Centroid Distance ◽  
The One

A two-phase synthesis method is described, which is capable of solving quite challenging path generation problems. A combined discrete Fourier descriptor (FD) is proposed for shape optimization, and a geometric-based approach is used for the scale–rotation–translation synthesis. The combined discrete FD comprises three shape signatures, i.e., complex coordinates (CCs), centroid distance (CD), and triangular centroid area (TCA), which can capture greater similarity of shape. The genetic algorithm–differential evolution (GA–DE) optimization method is used to solve the optimization problem. The proposed two-phase synthesis method, based on the combined discrete FD, successfully solves the challenging path generation problems with a relatively small number of function evaluations. A more accurate path shape can be obtained using the combined FD than the one-phase synthesis method. The obtained coupler curves approximate the desired paths quite well.

Multicriteria Optimization Model for a Containership Design

1994 ◽  
Vol 31 (04) ◽  
pp. 258-268
Author(s):  
Tapabrata Ray ◽  
Om Prakash Sha
Keyword(s):  
Multicriteria Optimization ◽  
Optimization Techniques ◽  
Time Span ◽  
Estimation Methods ◽  
Optimization Approach ◽  
Relative Importance ◽  
Decision System ◽  
Overall Design ◽  
Design Variables ◽  
Multi Attribute Decision Making

This paper describes a multicriteria optimization approach to ship design. The method incorporates accepted naval architectural estimation methods, a decision system handler and a nonlinear optimization tool. It allows the designer to identify different objectives, define prescribed limits on the design variables or define constraints on the design. The decision system identifies the weightages corresponding to different objectives based on the relative importance of the objectives using multi-attribute decision-making methods. The advantage of using optimization techniques along with a decision system handler allows the designer to develop new designs, while considering various interactions within the system, in a shorter time span. The proposed approach is illustrated by its application to a containership design. The effect of the weightages associated with the different objectives on the overall design is shown in the case studies.

Fuzzy Optimization of Complex Systems Using Approximation Concepts

1997 ◽  
Vol 50 (11S) ◽  
pp. S97-S104 ◽  
Author(s):  
Hector A. Jensen ◽  
Abdon E. Sepulveda
Keyword(s):  
Original Problem ◽  
Optimization Problems ◽  
Fuzzy Optimization ◽  
Optimization Techniques ◽  
System Response ◽  
Optimization Approach ◽  
Design Variables ◽  
Intermediate Response ◽  
Intermediate Variables ◽  
Approximation Concepts

This paper presents a methodology for the efficient solution of fuzzy optimization problems. Design variables, as well as system parameters are modeled as fuzzy numbers characterized by membership functions. An optimization approach based on approximation concepts is introduced. High quality approximations for system response functions are constructed using the concepts of intermediate response quantities and intermediate variables. These approximations are used to replace the solution of the original problem by a sequence of approximate problems. Optimization techniques for non-differentiable problems which arise in fuzzy optimization are used to solve the approximate optimization problems. Example problems are presented to illustrate the ideas set forth.

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.

Analysis and Optimum Synthesis of Planar Mechanisms With Clearances and Tolerances Using Interval Analysis

2006 ◽  
Author(s):  
Nadim Diab ◽  
Ahmad Smaili
Keyword(s):  
Interval Analysis ◽  
Optimization Approach ◽  
Membership Functions ◽  
Optimization Scheme ◽  
Planar Mechanisms ◽  
Fuzzy Membership Functions ◽  
Optimum Synthesis ◽  
Gradient Based ◽  
Joint Clearances

This paper presents an interval analysis based approach for analysis and optimization of planar mechanisms including the effect of link lengths tolerances and joint clearances. Mathematical models describing the effect of the mechanical errors on the desired output parameters of the mechanism are derived, followed by the commissioning of an ant-gradient based optimization scheme to find the maximum possible deviations in them. A new optimization approach is also devised to design a four bar mechanism with “minimal” sensitivity to clearances and tolerances. An analysis case study is presented and the results are displayed in the form of fuzzy membership functions and compared with results obtained using a similar approach. An example on optimum synthesis of a four-bar mechanism with joint clearances and link tolerances for hybrid exact/approximate points trajectory is also presented. Insights based on the assessment of the results are introduced.

An Integrated Kinematic-Kinetostatic Approach to Optimal Design of Planar Mechanisms Using Fuzzy Theories

1991 ◽  
Vol 113 (3) ◽  
pp. 306-311 ◽  
Author(s):  
A. K. Dhingra ◽  
S. S. Rao
Keyword(s):  
Nonlinear Programming ◽  
High Speed ◽  
Integrated Approach ◽  
Problem Formulation ◽  
Optimization Techniques ◽  
Motion Path ◽  
Programming Formulation ◽  
Planar Mechanisms ◽  
Motion Characteristics ◽  
And Function

A new integrated approach to the design of high speed planar mechanisms is presented. The resulting nonlinear programming formulation combines both the kinematic and kinetostatic synthesis aspects of mechanism design. The multiobjective optimization techniques presented in this work facilitate the design of a linkage to meet several kinematic and dynamic design criteria. The method can be used for motion, path, and function generation problems. The nonlinear programming formulation also permits an imposition of constraints to eliminate solutions which possess undesirable kinematic and motion characteristics. To model the vague and imprecise information in the problem formulation, the tools of fuzzy set theory have been used. A novel method of solving the resulting fuzzy multiobjective problem using mathematical programming techniques is presented. The outlined procedure is expected to be useful in situations where doubt arises about the exactness of permissible values, degree of credibility, and correctness of statements and judgements.

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.

On the Optimum Synthesis of Six-Bar Linkages Using Differential Evolution and the Geometric Centroid of Precision Positions Technique

2003 ◽  
Author(s):  
D. Koladiya ◽  
P. S. Shiakolas ◽  
J. Kebrle
Keyword(s):  
Differential Evolution ◽  
Evolutionary Optimization ◽  
Penalty Functions ◽  
Optimization Scheme ◽  
Constraint Violation ◽  
Initial Application ◽  
Optimum Synthesis ◽  
Design Variables ◽  
Transmission Angle ◽  
Accuracy Level

This paper presents the development of a methodology for the synthesis of six-bar dwell mechanisms combining Differential Evolution, an evolutionary optimization scheme, and the Geometric Centroid of Precision Positions technique for defining the initial bounds of the design variables. Two penalty functions are employed one for constraint violation and one for relative accuracy. The results of the initial application of this methodology were also used as “good initial guesses” for improving the desired accuracy level. The developed methodology is applied to the synthesis of six-bar linkages for dwell and dual-dwell mechanisms with prescribed timing and transmission angle constraints. The six-bar mechanism is synthesized using two different approaches: four-bar and extension to six-bar, direct six-bar. Results demonstrating the successful application of the developed methodology and the three approaches are presented.

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