Pareto optimal design of six-bar mechanism for path generation using evolutionary algorithms

abstract

Pareto optimal design of six-bar mechanism for route generation

Morteza Ilanlo

In this thesis, we present the dimensional optimal synthesis of six-bar mechanism with rotational constraints we pay The goal of synthesis is to produce a path that is as close as possible to the desired path. From the chains of six shafts, with seven rotational connections, known with one degree of freedom, we can mention the chain of Watt and Stephenson. Two types of mechanisms are obtained from the Watt chain and three types of mechanisms are obtained from the Stephenson chain, which are introduced and some of their applications are given in chapter 2 of the thesis.

In order to optimally synthesize the single objective of the mechanism, considering the path error function as the objective function, the combination of the genetic algorithm and the cumulative particle method has been used, and the accuracy of the path error results is compared with the latest results in the articles. NSGAII multi-objective algorithm is used for simultaneous minimization of two objective functions. Two objective functions with opposite behavior considered in this work are the path error function and the deviation of the transmission angle from . In two-objective optimization, by using the controlled reduction method, the allowable deviation of the transfer angle increases the convergence speed of the error function and tries to obtain the appropriate Pareto front. Six-bar mechanism, multi-objective optimization, evolutionary algorithms, Pareto front, particle aggregation method. rtl;"> Morteza ilanlou

In this thesis, we present the optimal dimensional synthesis of a six-bar mechanism with rotational constraints. The aim of the synthesis is to bring the generated path as close to the given path as possible. There are two types of well-known six-bar chains with one-degree-of-freedom namely, Watt chain and Stephenson chain. Two types of mechanisms are created from watt chain and three types of mechanisms from stephenson chain that will peresented with some applications in chapter tow of this thesis.

In order to single-objective optimal synthesis, considering tracking error as objective function, combination of geneti algorithm and particle swarm method is used and tracking error accuracy results are compared with those given in the literature.

Multi-objective NSGAII algorithm is used to minimize to objective functions. Two conflicting objective functions considered in this work are tracking error and transmission angle's deviation from . In multi-objective optimization, fast convergence of tracking error and optimum pareto front is achieved by using controlled decrease of transmission angle's deviation method.

Keywords: Six-bar Mechanism, Multi-Objective Optimization, Evolutionary Algorithms, Pareto front, Particle Swarm Optimization. A linkage consists of levers (or rods) that are generally considered rigid and are connected to each other by connections such as pins (hinges) or prismatic sliders to form open or closed chains (rings). Such kinematic chains, in which at least one lever remains fixed and at least two other levers are movable, is called a mechanism, and if all the levers are fixed, then it is called a structure. In other words, the mechanism allows its "rigid" levers to move relative to each other. While this is not the case for the structure.

Kinematic chains are an important part of mechanisms whose research is divided into two parts: 1-analysis and 2-synthesis.

Analysis: the process of checking the movement of all members or some members of the chain based on the geometric parameters of the mechanism.

Synthesis: finding a mechanism that can achieve a certain movement or desired path

Generally, the synthesis of mechanisms is divided into three different parts: 1- Type synthesis 2- Numerical synthesis 3- Dimensional synthesis. The first two syntheses are related to the type of mechanism and the number of members required for a particular mechanical movement. While the goal of dimensional synthesis is to find all the dimensional parameters of a mechanism to create a desired movement. Our goal in this research is dimensional synthesis for a desired route.

In the dimensional investigation, three important issues are investigated, which are:

Dimensional generation: the goal is to find a mechanism to create a set of pairs and a certain output.

Path generation: the goal is to find a mechanism for passing the intermediate member through certain points. is.

Rigid object guidance: The goal is to find a mechanism for the intermediate member to pass through the positions determined for it, as a rigid object.

For the synthesis of a mechanism, sometimes exact methods and sometimes approximate methods are used. Exact synthesis means solving the governing equations of the problem accurately, and in approximate synthesis, the goal is to minimize the error for these equations, and optimal synthesis is dedicated to this method. It is in car design. For this reason, the synthesis of mechanisms has attracted the attention of many designers for more than a hundred years. Although the initial methods for synthesis were sketchy, but later these methods were changed to exact solutions.

The nonlinear nature of synthesis equations hindered the development of these exact methods for various applications, which caused numerical techniques to help solve these nonlinear equations with the advent of powerful computers. Although the numerical methods lead to an approximate solution for these equations, the limitation for the number of design variables caused a fundamental problem. In the middle of the 60s, this basic problem was solved with the development of computational techniques and mechanisms optimization methods.

There are many benefits in using mechanisms optimization methods. For example, there is no restriction on the number of design variables. Therefore, features such as the ability to move, transfer angle, etc. can be formulated and calculated in the equation as design parameters. In the 19th century, Kemp (1876) and Burmeister [1] (1888) used dimensional synthesis in kinematic problems. But at that time, little progress was made in this field [1]. In the 20th century, some researchers applied their efforts in the field of kinematic synthesis with regard to a specific branch of the mechanism. After World War II, when the industry grew rapidly, the demand for special mechanism designs increased. The new needs made the design problems using the old methods very complicated and difficult. In (1954), Lutisky [2] and Shakozian [3] introduced the least squares method for the synthesis of spatial mechanisms of RSSR [2]. And in (1955), Freudenstein [4] introduced an approximate method for the synthesis of four-axis plane mechanisms for function generation [3]. These two works led to the creation of a new era of kinematics known as modern kinematics.

The famous Freudenstein equations and input-output equations for the planar RRRR mechanism were formed in (1995), which were later expanded for other planar mechanisms and created a key relationship in kinematic synthesis [3]. After this research, Freudenstein and others worked on a synthesis method, known as synthesis using precision points, and succeeded in introducing this method by using approximate polynomials obtained from precision points.