A Hybrid Approach to Solving the Position Equations for Planar Mechanisms

1995 ◽  
Vol 117 (4) ◽  
pp. 627-632 ◽  
Author(s):  
S. Bawab ◽  
G. L. Kinzel
Keyword(s):  
Closed Form ◽  
Hybrid Approach ◽  
Closed Form Solution ◽  
Iterative Solution ◽  
Form Solution ◽  
Planar Mechanisms ◽  
Solution Approach ◽  
Newton Raphson ◽  
Raphson Method ◽  
Straightforward Approach

In this paper, a straightforward approach is developed to solve the nonlinear position equations for a linkage when a closed-form solution to some of the equations can be obtained. This is done with the aid of dependency checking concepts that organizes a system 2n equations and 2n unknowns (variables) into smaller sets of equations. When a set of two equations and two unknowns is obtained, the variables are analyzed using a closed-form (non-iterative) solution approach. Otherwise, an iterative approach such as the Newton-Raphson method is used for the analysis.

The Contact Problem for a Rigid Cylinder Pressed Between Two Elastic Layers

1977 ◽  
Vol 44 (1) ◽  
pp. 36-40 ◽  
Author(s):  
G. M. L. Gladwell
Keyword(s):  
Approximate Solution ◽  
Closed Form ◽  
Closed Form Solution ◽  
Iterative Solution ◽  
Form Solution ◽  
Single Step ◽  
Space Problem ◽  
Rigid Cylinder ◽  
Elastic Layers ◽  
Layer Problem

The paper concerns the plane-strain problem of a rigid cylinder pressed between two identical elastic layers supported by rigid bases along which they may slide without friction. The essential difficulty of the problem is that there are three contact zones, one between the cylinder and the layers, and two, symmetrically placed, between the layers; the extent of these regions has first to be found. Alblas has given an iterative solution to the problem which reduces to a closed-form solution when the layers are half spaces. The purpose of the paper is to show that there is an elegant approximate solution of the half-space problem which is well suited to computation and which converges to the closed-form solution. The solution depends on some remarkable results obtained by extending the Chebyshev polynomials to the whole of the real line. The paper also provides a single-step approximate solution of the two-layer problem.

Finitely and Multiply Separated Synthesis of Link and Geared Mechanisms Using Symbolic Computing

1993 ◽  
Vol 115 (3) ◽  
pp. 560-567 ◽  
Author(s):  
A. K. Dhingra ◽  
N. K. Mani
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Iterative Solution ◽  
Form Solution ◽  
Motion Generation ◽  
Closed Form Solutions ◽  
Symbolic Computing ◽  
Manipulation Language ◽  
Solution Techniques

A computer amenable symbolic computing approach for the synthesis of six different link and geared mechanisms is presented. Burmester theory, complex number algebra, and loop closure equations are employed to develop governing equations for the mechanism to be synthesized. Closed-form and iterative solution techniques have been developed which permit synthesis of six-link Watt and Stephenson chains for function, path, and motion generation tasks with up to eleven precision points. Closed-form solution techniques have also been developed for the synthesis of geared five-bar, six-bar, and five-link cycloidal crack mechanisms, for synthesis tasks with up to six finitely and multiply separated precision points. The symbolic manipulation language MACSYMA is used to simplify the resulting synthesis equations and obtain closed-form solutions. A design methodology which demonstrates the feasibility and versatility of symbolic computing in computer-aided mechanisms design is outlined. A computer program which incorporates these synthesis procedures is developed. Two examples are presented to illustrate the role of symbolic computing in an automated mechanism design process.

On a Closed-Form Solution of Prandtl's System of Equations

2013 ◽  
Vol 40 (2) ◽  
pp. 106-114
Author(s):  
J. Venetis ◽  
Aimilios (Preferred name Emilios) Sideridis
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
System Of Equations
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