Determination of closed form solution to the 2-D orientation workspace of Gough-Stewart parallel manipulators

1999 ◽  
Vol 15 (6) ◽  
pp. 1121-1125 ◽  
Author(s):  
T. Huang ◽  
J. Wang ◽  
C.M. Gosselin ◽  
D. Whitehouse
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Parallel Manipulators ◽  
Form Solution ◽  
Orientation Workspace

Closed-Form Solution for Constant-Orientation Workspace and Workspace-Based Design of Radially Symmetric Hexapod Robots

2014 ◽  
Vol 6 (3) ◽  
Author(s):  
Mahdi Agheli ◽  
Stephen S. Nestinger
Keyword(s):  
Closed Form ◽  
Structural Parameters ◽  
Closed Form Solution ◽  
Form Solution ◽  
Axially Symmetric ◽  
Kinematic Chains ◽  
Design And Optimization ◽  
Hexapod Robots ◽  
Iterative Optimization Algorithm ◽  
Orientation Workspace

The workspace of hexapod robots is a key performance parameter which has attracted the attention of numerous researchers during the past decades. The selection of the hexapod parameters for a desired workspace generally employs the use of numerical methods. This paper presents a general methodology for solving the closed-form constant orientation workspace of radially symmetric hexapod robots. The closed-form solution facilitates hexapod robot design and minimizes numerical efforts with on-line determination of stability and workspace utilization. The methodology can be used for robots with nonsymmetric and nonidentical kinematic chains. In this paper, the methodology is used to derive the closed-form equations of the boundary of the constant-orientation workspace of axially symmetric hexapod robots. Several applications are provided to demonstrate the capability of the presented closed-form solution in design and optimization. An approach for workspace-based design optimization is presented using the provided analytical solution by applying an iterative optimization algorithm to the find optimized structural parameters and an optimized workspace.

Determination of a closed-form solution for the multidimensional transport equation using a fractional derivative

2002 ◽  
Vol 29 (10) ◽  
pp. 1141-1150 ◽  
Author(s):  
Jorge Zabadal ◽  
Marco Túllio Vilhena ◽  
Cynthia Feijó Segatto ◽  
Rúben Panta Pazos
Keyword(s):  
Fractional Derivative ◽  
Transport Equation ◽  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution

scholarly journals Use of a Strongly Nonlinear Gambier Equation for the Construction of Exact Closed Form Solutions of Nonlinear ODEs

2007 ◽  
Vol 2007 ◽  
pp. 1-25
Author(s):  
M. P. Markakis
Keyword(s):  
Closed Form ◽  
Initial Conditions ◽  
Closed Form Solution ◽  
Form Solution ◽  
Nonlinear Odes ◽  
Analytical Technique ◽  
Closed Form Solutions ◽  
Strongly Nonlinear ◽  
Parameter Values

We establish an analytical method leading to a more general form of the exact solution of a nonlinear ODE of the second order due to Gambier. The treatment is based on the introduction and determination of a new function, by means of which the solution of the original equation is expressed. This treatment is applied to another nonlinear equation, subjected to the same general class as that of Gambier, by constructing step by step an appropriate analytical technique. The developed procedure yields a general exact closed form solution of this equation, valid for specific values of the parameters involved and containing two arbitrary (free) parameters evaluated by the relevant initial conditions. We finally verify this technique by applying it to two specific sets of parameter values of the equation under consideration.

Determination of Closed Form Solution for Acceptance Sampling Using ANN

2005 ◽  
Vol 11 (1) ◽  
pp. 43-61 ◽  
Author(s):  
D. Vasudevan ◽  
V. Selladurai ◽  
P. Nagaraj
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Acceptance Sampling

On the Analytical Solution of Externally Pressurized Porous Gas Journal Bearings

1978 ◽  
Vol 100 (3) ◽  
pp. 442-444 ◽  
Author(s):  
B. C. Majumdar
Keyword(s):  
Analytical Solution ◽  
Pressure Distribution ◽  
Closed Form ◽  
Closed Form Solution ◽  
Journal Bearings ◽  
Form Solution ◽  
Performance Characteristics ◽  
Gas Bearing ◽  
Good Agreement

A closed form solution of pressure distribution which leads to the determination of bearing performance characteristics of an externally pressurized porous gas bearing without journal rotation is obtained. A good agreement with a similar available solution confirms the validity of the method.

Closed form solution to the position workspace of Stewart parallel manipulators

1998 ◽  
Vol 41 (4) ◽  
pp. 393-403 ◽  
Author(s):  
Tian Huang ◽  
Jinsong Wang ◽  
D. J. Whitehouse
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Parallel Manipulators ◽  
Form Solution

Determination of Eigenstresses from Curvature Data

1992 ◽  
Vol 276 ◽  
Author(s):  
Mauro Ferrari ◽  
Marie Weber
Keyword(s):  
Structural Analysis ◽  
Closed Form ◽  
Mechanical Systems ◽  
Closed Form Solution ◽  
Form Solution ◽  
Curvature Measurements

ABSTRACTCurvature measurements are generally employed in conjunction with elementary structural analysis to estimate deposition stresses in miniaturized electro-mechanical systems. In this paper the validity of this procedure is discussed by presenting a closed form solution for a bilayer subject to nonuniform intrinsic straining, and comparing the exact stress-curvature relations with the oft-used formulae of Stoney and Brenner-Senderoff.

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