Optimum Design of a Four-Bar Linkage Whose Coupler Path Has Specified Extremes

1972 ◽  
Vol 94 (2) ◽  
pp. 483-487 ◽  
Author(s):  
M. Tranquilla
Keyword(s):  
Mathematical Programming ◽  
Optimum Design ◽  
Trial Design ◽  
Graphical Method ◽  
Synthesis Problem ◽  
Programming Technique ◽  
Initial Trial ◽  
Four Bar Linkage ◽  
Mathematical Programming Technique

The synthesis problem of specifying the extremes of a coupler path of a four-bar linkage is presented. Equations are derived to specify that a precision point be an extreme of the coupler path. Other portions of the path are considered as well. Constraints are imposed which limit the width of the coupler path, the locations of the crankshaft and rockshaft, and which guarantee that the input crank will make a full revolution. This suggests using a mathematical programming technique (i.e., optimization) to solve the synthesis problem. A graphical method is developed to obtain an initial trial design for the mathematical programming technique. An example problem is then solved.

A Mathematical Programming Technique for the Evaluation of Load Distribution and Optimal Modifications for Gear Systems

1973 ◽  
Vol 95 (4) ◽  
pp. 1115-1122 ◽  
Author(s):  
T. F. Conry ◽  
A. Seireg
Keyword(s):  
Mathematical Programming ◽  
Load Distribution ◽  
Effective Means ◽  
Uniform Load ◽  
Programming Technique ◽  
Type Algorithm ◽  
Gear Systems ◽  
Selection Of ◽  
Mathematical Programming Technique

A generalized technique is presented in this paper for evaluation of load distribution in gear systems and automated selection of optimal modification for the best possible distribution based on any prespecified type of modification. The procedure which utilizes a simplex-type algorithm provides an efficient and effective means for the design of gears with uniform load distribution.

scholarly journals Applications of mathematical programming in graceful labeling of graphs

2004 ◽  
Vol 2004 (1) ◽  
pp. 1-8 ◽  
Author(s):  
Kourosh Eshghi ◽  
Parham Azimi
Keyword(s):  
Mathematical Programming ◽  
Graph Labeling ◽  
Computational Results ◽  
Programming Technique ◽  
New Approach ◽  
Graceful Labeling ◽  
Applications Of Mathematical Programming ◽  
The Subject ◽  
Mathematical Programming Technique ◽  
Special Classes

Graceful labeling is one of the best known labeling methods of graphs. Despite the large number of papers published on the subject of graph labeling, there are few particular techniques to be used by researchers to gracefully label graphs. In this paper, first a new approach based on the mathematical programming technique is presented to model the graceful labeling problem. Then a “branching method” is developed to solve the problem for special classes of graphs. Computational results show the efficiency of the proposed algorithm for different classes of graphs. One of the interesting results of our model is in the class of trees. The largest tree known to be graceful has at most 27 vertices but our model can easily solve the graceful labeling for trees with 40 vertices.

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