Forward Kinematics of the General 6–6 Fully Parallel Mechanism: An Exhaustive Numerical Approach Via a Mono-Dimensional-Search Algorithm

1993 ◽  
Vol 115 (4) ◽  
pp. 932-937 ◽  
Author(s):  
C. Innocenti ◽  
V. Parenti-Castelli
Keyword(s):  
Numerical Method ◽  
Parallel Mechanism ◽  
Search Algorithm ◽  
Numerical Approach ◽  
Forward Kinematics ◽  
The Real ◽  
Real Solutions ◽  
Position Analysis ◽  
General Geometry

A new numerical method for the solution of the direct position analysis of the six d.o.f. fully parallel mechanism with general geometry, often referred to as generalized Stewart platform mechanism, is presented. The main feature of the method, making it attractive with respect to the methods available in the literature, is the ability to find out all the real solutions of the direct position analysis. The effectiveness of the new algorithm relies upon the solution of only one equation in one unknown. That equation is strictly representative of the problem, i.e., it is free from extraneous roots and every solution of the direct position analysis entails the existence of a root for the equation. A case study is reported.

Forward Kinematics of the General 6-6 Fully Parallel Mechanism: An Exhaustive Numerical Approach via a Mono-Dimensional-Search Algorithm

1992 ◽  
Author(s):  
C. Innocenti ◽  
V. Parenti-Castelli
Keyword(s):  
Numerical Method ◽  
Parallel Mechanism ◽  
Search Algorithm ◽  
Numerical Approach ◽  
Forward Kinematics ◽  
The Real ◽  
Real Solutions ◽  
Position Analysis ◽  
General Geometry

Abstract A new numerical method for the solution of the direct position analysis of the six d.o.f. fully parallel mechanism with general geometry, often referred to as generalized Stewart platform mechanism, is presented. The main feature of the method, making it attractive with respect to the methods available in the literature, is the ability to find out all the real solutions of the direct position analysis. The effectiveness of the new algorithm relies upon the solution of only one equation in one unknown. That equation is strictly representative of the problem, i.e., it is free from extraneous roots and every solution of the direct position analysis entails the existence of a root for the equation. A case study is reported.

A New Algorithm Based on Two Extra-Sensors for Real-Time Computation of the Actual Configuration of the Generalized Stewart-Gough Manipulator

1998 ◽  
Author(s):  
V. Parenti-Castelli ◽  
R. Di Gregorio
Keyword(s):  
Real Time ◽  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Computational Burden ◽  
The Real ◽  
Position Analysis ◽  
Extra Information ◽  
Actual Configuration ◽  
General Geometry

Abstract It is well known that the direct position analysis of fully-parallel manipulators provides more than one solution, i.e., more than one configuration of the mechanism is possible for a given set of the actuated variables of motion. Extra information is, thus, necessary to find the actual configuration of the manipulator. This paper presents a new algorithm for the real-time computation of the actual configuration of the generalized Stewart-Gough manipulator, also known as 6-6 fully-parallel manipulator with general geometry. The proposed algorithm makes use of two extra rotary sensors in addition to the six normally implemented in the servosystems of the manipulator. A one-to-one correspondence between the sensor measurements and the manipulator configuration is provided. With respect to other algorithms recently presented in the literature, the proposed method greatly reduces the computational burden. Finally a case study shows the effectiveness of the proposed procedure.

A New Algorithm Based on Two Extra-Sensors for Real-Time Computation of the Actual Configuration of the Generalized Stewart-Gough Manipulator

1999 ◽  
Vol 122 (3) ◽  
pp. 294-298 ◽  
Author(s):  
Vincenzo Parenti-Castelli ◽  
Raffaele Di Gregorio
Keyword(s):  
Real Time ◽  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Computational Burden ◽  
The Real ◽  
Position Analysis ◽  
Extra Information ◽  
Actual Configuration ◽  
General Geometry

It is well known that the direct position analysis of fully-parallel manipulators provides more than one solution, i.e., more than one configuration of the mechanism is possible for a given set of the actuated variables of motion. Extra information is, thus, necessary to find the actual configuration of the manipulator. This paper presents a new algorithm for the real-time computation of the actual configuration of the generalized Stewart-Gough manipulator, also known as 6-6 fully-parallel manipulator with general geometry. The proposed algorithm makes use of two extra rotary sensors in addition to five out of the six sensors normally implemented in the servosystems of the manipulator. A one-to-one correspondence between the sensor measurements and the manipulator configuration is provided. With respect to other algorithms recently presented in the literature, the proposed method greatly reduces the computational burden. Finally a case study shows the effectiveness of the proposed procedure. [S1050-0472(00)01703-7]

Direct Position Analysis of a Reconfigurable 4-DOF Parallel Mechanism

2012 ◽  
Vol 562-564 ◽  
pp. 1168-1171
Author(s):  
Er Jiang Zhang ◽  
Yong Gang Li
Keyword(s):  
Parallel Mechanism ◽  
Structural Features ◽  
Graphical Representations ◽  
Elimination Method ◽  
Numerical Examples ◽  
The Real ◽  
Real Solutions ◽  
Position Analysis ◽  
Movable Platform ◽  
Absolute Coordinates

This article presents a direct position analysis of a reconfigurable 2PRS-2PUS parallel mechanism. Based on the structural features of this new mechanism, take the absolute coordinates of the four balls vice center on movable platform as the output variables, a direct position analysis which using elimination method is presented. The solution is verified by a group of numerical examples, which given by matlab. In addition, graphical representations of the real solutions are presented.

Forward Kinematics in Polynomial Form of the General Stewart Platform1

1998 ◽  
Vol 123 (2) ◽  
pp. 254-260 ◽  
Author(s):  
Carlo Innocenti
Keyword(s):  
Parallel Manipulator ◽  
Polynomial Equation ◽  
Polynomial Form ◽  
Floating Point ◽  
Forward Kinematics ◽  
Numerical Example ◽  
Univariate Polynomial ◽  
General Geometry ◽  
Floating Point Computation

The paper presents a new algorithm to solve, in polynomial form, the forward kinematics of the general-geometry 6-6 fully-parallel manipulator. The forty solutions that the problem at hand admits in the complex domain are found by determining the roots of a 40th-order univariate polynomial equation. Unlike the existing algorithm, the proposed one is suitable for implementation in a standard floating-point computation environment. A numerical example shows application of the new algorithm to a case study.

A New Method on the Position Analysis of 3-Dof 3-PC(RR)N Spherical Parallel Mechanism

2011 ◽  
Vol 101-102 ◽  
pp. 369-373
Author(s):  
Dong Lai Xu ◽  
Shuai Zhang ◽  
Jun Tao Si ◽  
Wei Yu
Keyword(s):  
Parallel Mechanism ◽  
Inverse Solution ◽  
New Method ◽  
Elimination Method ◽  
Real Solutions ◽  
Position Analysis ◽  
Sylvester Resultant ◽  
Spherical Parallel Mechanism

By applying quaternion and Sylvester resultant elimination method, and with the help of Mathematica 8.0 software, the 3-Dof 3-PC(RR)N spherical parallel mechanism location is analyzed. In solving inverse solution, there are 512-group input angle solutions, and 64-group real solutions. In the example of this paper, there are a total of 8-group real solutions by removing the extraneous roots.

Forward Kinematics in Polynomial Form of the General Stewart Platform

1998 ◽  
Author(s):  
Carlo Innocenti
Keyword(s):  
Parallel Manipulator ◽  
Polynomial Equation ◽  
Polynomial Form ◽  
Floating Point ◽  
Forward Kinematics ◽  
Numerical Example ◽  
Univariate Polynomial ◽  
General Geometry ◽  
Floating Point Computation

Abstract The paper presents a new algorithm to solve, in polynomial form, the forward kinematics of the general-geometry 6-6 fully-parallel manipulator. The forty solutions that the problem at hand admits in the complex domain are found by determining the roots of a 40th-order univariate polynomial equation. Unlike the existing algorithm, the proposed one is suitable for implementation in a standard floating-point computation environment. A numerical example shows application of the new algorithm to a case study.

scholarly journals Numerical solution of scattering problems using a Riemann–Hilbert formulation

2019 ◽  
Vol 475 (2229) ◽  
pp. 20190105 ◽  
Author(s):  
Stefan G. Llewellyn Smith ◽  
Elena Luca
Keyword(s):  
Numerical Solution ◽  
Numerical Method ◽  
Real Line ◽  
Plane Waves ◽  
Numerical Approach ◽  
Far Field ◽  
Infinite Plane ◽  
Scattering Problems ◽  
The Real ◽  
Field Behaviour

A fast and accurate numerical method for the solution of scalar and matrix Wiener–Hopf (WH) problems is presented. The WH problems are formulated as Riemann–Hilbert problems on the real line, and a numerical approach developed for these problems is used. It is shown that the known far-field behaviour of the solutions can be exploited to construct numerical schemes providing spectrally accurate results. A number of scalar and matrix WH problems that generalize the classical Sommerfeld problem of diffraction of plane waves by a semi-infinite plane are solved using the approach.

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