Spatial Kinematic Synthesis of Adaptive Hard-Automation Modules: An RS-SRR-SS Adjustable Spatial Motion Generator

1986 ◽  
Vol 108 (3) ◽  
pp. 292-299 ◽  
Author(s):  
G. N. Sandor ◽  
S. P. Yang ◽  
L. J. Xu ◽  
P. De
Keyword(s):  
Numerical Methods ◽  
Nonlinear System ◽  
Analytical Methods ◽  
Robotic Manipulators ◽  
Optimization Techniques ◽  
System Of Equations ◽  
Spatial Motion ◽  
Nonlinear System Of Equations ◽  
Kinematic Synthesis ◽  
Motion Generator

Purely mechanical, single-actuator adaptive hard-automation modules can perform highly repetitive simple tasks much more economically, energy-efficiently and accurately than multi-degree-of-freedom, multiple-actuator robotic manipulators. As an example, an RS-SRR-SS adjustable spatial motion generator is synthesized by analytical methods with two exact prescribed positions (including orientations) for each of two different motion tasks, by numerical methods to solve a nonlinear system of equations and by optimization techniques to minimize the motion errors at additional, approximately prescribed positions.

A Full-System Approach of the Elastohydrodynamic Line/Point Contact Problem

2008 ◽  
Vol 130 (2) ◽  
Author(s):  
W. Habchi ◽  
D. Eyheramendy ◽  
P. Vergne ◽  
G. Morales-Espejel
Keyword(s):  
Finite Element ◽  
Nonlinear System ◽  
System Approach ◽  
Jacobian Matrix ◽  
Point Contact ◽  
System Of Equations ◽  
Nonlinear System Of Equations ◽  
Full System ◽  
Element Discretization ◽  
Fully Coupled

The solution of the elastohydrodynamic lubrication (EHL) problem involves the simultaneous resolution of the hydrodynamic (Reynolds equation) and elastic problems (elastic deformation of the contacting surfaces). Up to now, most of the numerical works dealing with the modeling of the isothermal EHL problem were based on a weak coupling resolution of the Reynolds and elasticity equations (semi-system approach). The latter were solved separately using iterative schemes and a finite difference discretization. Very few authors attempted to solve the problem in a fully coupled way, thus solving both equations simultaneously (full-system approach). These attempts suffered from a major drawback which is the almost full Jacobian matrix of the nonlinear system of equations. This work presents a new approach for solving the fully coupled isothermal elastohydrodynamic problem using a finite element discretization of the corresponding equations. The use of the finite element method allows the use of variable unstructured meshing and different types of elements within the same model which leads to a reduced size of the problem. The nonlinear system of equations is solved using a Newton procedure which provides faster convergence rates. Suitable stabilization techniques are used to extend the solution to the case of highly loaded contacts. The complexity is the same as for classical algorithms, but an improved convergence rate, a reduced size of the problem and a sparse Jacobian matrix are obtained. Thus, the computational effort, time and memory usage are considerably reduced.

Kinematic Synthesis of an RS-SRR-SS Adjustable Spatial Motion Generator for Three Alternate Tasks

1993 ◽  
Author(s):  
Jin Yao ◽  
Liju Xu ◽  
Shou-wen Fan
Keyword(s):  
Mathematical Model ◽  
Spatial Motion ◽  
Kinematic Synthesis ◽  
Inversion Theory ◽  
Constant Distance ◽  
And Inversion ◽  
Distance Conditions ◽  
Motion Generator

Abstract A method is presented for kinematical synthesis of an RS-SRR-SS adjustable spatial motion generator for three alternate tasks. Three separate systems of synthesis equations to exactly generate the first and the last positions for each task are obtained for the R-S by co-plane and constant distance conditions, for the S-R-R by co-plane, constant distance conditions and inversion theory, and for S-S by constant distance condition. Based on these equations, mathematical model for approximately generating the intermediate positions for each task is formulated. This method is characterized by reduction of the unknowns and equations in both exact and approximate syntheses. As a result, computing work is to be decreased obviously.

Nonlinear System Of Equations For Multicomponent Analysis Of Artificial Food Coloring

2010 ◽  
Author(s):  
I. E. Santosa ◽  
L. K. Budiasih ◽  
Khairurrijal ◽  
Mikrajuddin Abdullah ◽  
Wahyu Srigutomo ◽  
...  
Keyword(s):  
Nonlinear System ◽  
System Of Equations ◽  
Nonlinear System Of Equations ◽  
Multicomponent Analysis ◽  
Artificial Food

scholarly journals A Quartically Convergent Jarratt-Type Method for Nonlinear System of Equations

Algorithms ◽  
2015 ◽  
Vol 8 (3) ◽  
pp. 415-423 ◽  
Author(s):  
Mohammad Ghorbanzadeh ◽  
Fazlollah Soleymani
Keyword(s):  
Nonlinear System ◽  
System Of Equations ◽  
Nonlinear System Of Equations ◽  
Type Method
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