Branching solutions and Lie series

1993 ◽  
Vol 57 (4) ◽  
pp. 517-536 ◽  
Author(s):  
F. V�radi
Keyword(s):  
Lie Series ◽  
Branching Solutions

Five Position Synthesis of a Slider-Crank Function Generator

2011 ◽  
Author(s):  
Mark M. Plecnik ◽  
J. Michael McCarthy
Keyword(s):  
Full Range ◽  
Linear Actuator ◽  
Tolerance Zone ◽  
Function Generator ◽  
Front End ◽  
Input And Output ◽  
Function Generators ◽  
Synthesis Procedure ◽  
Position Synthesis ◽  
Branching Solutions

In this paper, we present a synthesis procedure for the coupler link of a planar slider-crank linkage in order to coordinate input by a linear actuator with the rotation of an output crank. This problem can be formulated in a manner similar to the synthesis of a five position RR coupler link. It is well-known that the resulting equations can produce branching solutions that are not useful. This is addressed by introducing tolerances for the input and output values of the specified task function. The proposed synthesis procedure is then executed on two examples. In the first example, a survey of solutions for tolerance zones of increasing size is conducted. In this example we find that a tolerance zone of 5% of the desired full range results in a number of useful task functions and usable slider-crank function generators. To demonstrate the use of these results, we present an example design for the actuator of the shovel of a front-end loader.

DEVELOPMENT OF NEW METHODS FOR THE SOLUTION OF DIFFERENTIAL EQUATIONS BY THE METHOD OF LIE SERIES

1969 ◽  
Author(s):  
W. Groebner ◽  
K. H. Kestlunger ◽  
H. Reitberger ◽  
R. Saely ◽  
G. Wanner
Keyword(s):  
Differential Equations ◽  
Lie Series ◽  
New Methods
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