Optimum Synthesis of Four-Bar and Offset Slider-Crank Planar and Spatial Mechanisms Using the Penalty Function Approach With Inequality and Equality Constraints

1975 ◽  
Vol 97 (3) ◽  
pp. 785-790 ◽  
Author(s):  
R. I. Alizade ◽  
A. V. Mohan Rao ◽  
G. N. Sandor
Keyword(s):  
Objective Function ◽  
Penalty Function ◽  
Optimization Technique ◽  
Equality Constraints ◽  
Function Approach ◽  
Numerical Examples ◽  
Optimum Synthesis ◽  
Spatial Mechanisms ◽  
Satisfying Inequality ◽  
Penalty Function Approach

This paper discusses the application of the logarithmic penalty function for the optimal synthesis of function generating mechanisms satisfying inequality and equality constraints. A new method of deriving the transmission ratio and the objective function is also presented. Numerical examples are used to illustrate the optimization technique.

Optimum Synthesis of Path-Generating Four-Bar Mechanisms

1975 ◽  
Vol 97 (1) ◽  
pp. 314-321 ◽  
Author(s):  
N. Bakthavachalam ◽  
J. T. Kimbrell
Keyword(s):  
Penalty Function ◽  
Gradient Method ◽  
Optimization Problem ◽  
Inequality Constraints ◽  
Unconstrained Minimization ◽  
Function Approach ◽  
Optimum Synthesis ◽  
Penalty Function Approach

Synthesis of path-generating four-bar mechanisms is considered as an optimization problem under inequality constraints. The penalty function approach is used. The effects of clearances and tolerances in manufacture are considered in order to make sure that the inequality constraints are within the acceptable tolerance during the required motion. Modifications are introduced in the gradient method, and sequential unconstrained minimization techniques are used in the process of minimization. A typical example under various conditions is presented in order to study the effectiveness of the technique.

Optimum Synthesis of Two-Degree-of-Freedom Planar and Spatial Function Generating Mechanisms Using the Penalty Function Approach

1975 ◽  
Vol 97 (2) ◽  
pp. 629-634 ◽  
Author(s):  
R. I. Alizade ◽  
A. V. Mohan Rao ◽  
G. N. Sandor
Keyword(s):  
Penalty Function ◽  
Initial Approximation ◽  
Inequality Constraints ◽  
Degree Of Freedom ◽  
Function Approach ◽  
Mathematical Programming Problem ◽  
Optimum Synthesis ◽  
Equality And Inequality Constraints ◽  
Two Degree Of Freedom ◽  
Penalty Function Approach

This paper presents the synthesis of two-degree-of-freedom function generating mechanisms as a mathematical programming problem. The optimum set of dimensions of a mechanism are determined using a penalty function approach. Also, a new algorithm is developed for finding the first mechanism satisfying all inequality constraints to serve as an initial approximation. A single objective function as well as the equality and inequality constraints are expressed explicitly from conditions of linkage closure, mobility, and transmissibility. The method is demonstrated through an example for a spatial RSSRP function generating mechanism.

Performance-Enhancing Techniques

2010 ◽  
pp. 133-148
Author(s):  
E. Parsopoulos Konstantinos ◽  
N. Vrahatis Michael
Keyword(s):  
Integer Programming ◽  
Objective Function ◽  
Penalty Function ◽  
Optimization Problems ◽  
Function Approach ◽  
Integer Optimization ◽  
Local Minimizers ◽  
Global Minimizers ◽  
Integer Programming Problems ◽  
Penalty Function Approach

This chapter presents techniques that have proved to be very useful in enhancing the performance of PSO in various optimization problem types. They consist of transformations of either the objective function or the problem variables, enabling PSO to alleviate local minimizers, detect multiple minimizers, handle constraints, and solve integer optimization problems. The chapter begins with a short discussion on the filled functions approach, and then presents the stretching technique as an alternative for alleviating local minimizers. Next, we present the deflection and repulsion techniques, as a means for detecting multiple global minimizers with PSO, followed by a penalty function approach for constraint handling. The chapter closes with the description of two rounding schemes that enable the continuous, real-valued PSO to solve integer programming problems. All techniques are thoroughly described and graphically illustrated whenever possible.

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