Computer-Aided Synthesis of Mechanisms Using Nonlinear Programming

1973 ◽  
Vol 95 (1) ◽  
pp. 339-344 ◽  
Author(s):  
V. K. Gupta
Keyword(s):  
Nonlinear Programming ◽  
Mathematical Programming ◽  
Penalty Function ◽  
Inequality Constraints ◽  
Mathematical Programming Problem ◽  
Spatial Mechanisms ◽  
Synthesis Of Mechanisms ◽  
Computer Aided ◽  
Equality And Inequality Constraints ◽  
Penalty Function Approach

The synthesis of spatial mechanisms is formulated as a mathematical programming problem and solved using a penalty function approach. The objective function as well as the equality and inequality constraints are determined explicitly from conditions such as those required for linkage closure, mobility, and transmissibility.

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.

A Class of Augumented Lagrangian Function for Nonlinear Programming

2011 ◽  
Vol 271-273 ◽  
pp. 1955-1960
Author(s):  
Mei Xia Li
Keyword(s):  
Nonlinear Programming ◽  
Programming Problem ◽  
Inequality Constraints ◽  
Unconstrained Minimization ◽  
Lagrangian Function ◽  
Point Of View ◽  
Theoretical Point ◽  
Non Linear Programming ◽  
Global Minimizers ◽  
Equality And Inequality Constraints

In this paper, we discuss an exact augumented Lagrangian functions for the non- linear programming problem with both equality and inequality constraints, which is the gen- eration of the augmented Lagrangian function in corresponding reference only for inequality constraints nonlinear programming problem. Under suitable hypotheses, we give the relation- ship between the local and global unconstrained minimizers of the augumented Lagrangian function and the local and global minimizers of the original constrained problem. From the theoretical point of view, the optimality solution of the nonlinear programming with both equality and inequality constraints and the values of the corresponding Lagrangian multipli- ers can be found by the well known method of multipliers which resort to the unconstrained minimization of the augumented Lagrangian function presented in this paper.

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.

scholarly journals Lagrange duality and saddle point optimality conditions for semi-infinite mathematical programming problems with equilibrium constraints

2019 ◽  
Vol 29 (4) ◽  
pp. 433-448
Author(s):  
Kunwar Singh ◽  
J.K. Maurya ◽  
S.K. Mishra
Keyword(s):  
Mathematical Programming ◽  
Saddle Point ◽  
Optimality Conditions ◽  
Optimization Problems ◽  
Inequality Constraints ◽  
Mathematical Programming Problem ◽  
Dual Model ◽  
Equilibrium Constraints ◽  
Convexity Assumptions ◽  
Mathematical Programming Problems

In this paper, we consider a special class of optimization problems which contains infinitely many inequality constraints and finitely many complementarity constraints known as the semi-infinite mathematical programming problem with equilibrium constraints (SIMPEC). We propose Lagrange type dual model for the SIMPEC and obtain their duality results using convexity assumptions. Further, we discuss the saddle point optimality conditions for the SIMPEC. Some examples are given to illustrate the obtained results.

Optimum Design of Curve-Generating Linkages With Inequality Constraints

1967 ◽  
Vol 89 (1) ◽  
pp. 144-151 ◽  
Author(s):  
R. L. Fox ◽  
K. D. Willmert
Keyword(s):  
Mathematical Programming ◽  
Inequality Constraints ◽  
Problem Area ◽  
Mathematical Programming Problem ◽  
Iterative Technique ◽  
Circular Arc ◽  
Open Questions ◽  
Design Variables ◽  
Straight Line ◽  
Four Bar Linkage

The problem of synthesizing a four-bar linkage is presented as a mathematical programming problem. The objective is to synthesize a four-bar linkage whose coupler point will generate, as closely as possible, a given curve, and whose crank rotations will be as close as possible to desired values. Constraints are imposed on the design variables which force the result to be a four-bar linkage, limit the forces and torques within the linkage, restrict the location of the pivot points, limit the lengths of the links, and so on. The solution is found using an iterative technique with the aid of a digital computer. Several examples are presented which demonstrate the effectiveness of this approach. They include generation of a straight line, a figure eight, and a portion of a circular arc (previously investigated using a method developed by Freudenstein and Sandor). The work on this problem area is still in progress and there remain a number of open questions and unexplored alternatives.

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