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.

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.

scholarly journals A Novel Penalty Function Approach to Constrained Optimization Problems with Genetic Algorithms

1998 ◽  
Vol 2 (6) ◽  
pp. 208-213 ◽  
Author(s):  
Xinghuo Yu ◽  
◽  
Weixing Zheng ◽  
Baolin Wu ◽  
Xin Yao ◽  
...  
Keyword(s):  
Constrained Optimization ◽  
Unconstrained Optimization ◽  
Penalty Function ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Function Approach ◽  
Constrained Optimization Problem ◽  
Constrained Optimization Problems ◽  
Unconstrained Optimization Problem ◽  
Penalty Function Approach

In this paper, a novel penalty function approach is proposed for constrained optimization problems with linear and nonlinear constraints. It is shown that by using a mapping function to "wrap" up the constraints, a constrained optimization problem can be converted to an unconstrained optimization problem. It is also proved mathematically that the best solution of the converted unconstrained optimization problem will approach the best solution of the constrained optimization problem if the tuning parameter for the wrapping function approaches zero. A tailored genetic algorithm incorporating an adaptive tuning method is then used to search for the global optimal solutions of the converted unconstrained optimization problems. Four test examples were used to show the effectiveness of the approach.

Sign in / Sign up

Export Citation Format

Share Document