Polynomial Solution to the Five-Position Synthesis of Spatial CC Dyads via Dialytic Elimination

2000 ◽  
Author(s):  
Chintien Huang ◽  
Yu-Jui Chang
Keyword(s):  
Polynomial Solution ◽  
Polynomial Equation ◽  
Elimination Method ◽  
Real Solutions ◽  
Numerical Example ◽  
Univariate Polynomial ◽  
Position Synthesis

Abstract This paper presents a polynomial solution to the five-position synthesis of spatial cylindrical-cylindrical dyads. The solution procedures start with the simplification of the synthesis equations derived by Tsai and Roth. The simplified equations are solved by Sylvester’s dialytic elimination method to obtain a univariate polynomial equation of degree six, which gives at most 6 CC dyads for the five-position synthesis. A numerical example with six real solutions is provided.

The Position Analysis of Spherical Seven-Bar Mechanism

2011 ◽  
Vol 101-102 ◽  
pp. 193-196
Author(s):  
Zhao Feng Zhang ◽  
Zhi Huan Zhang
Keyword(s):  
Mathematical Model ◽  
Analytical Solutions ◽  
Polynomial Equation ◽  
Constraint Equations ◽  
Position Analysis ◽  
Numerical Example ◽  
Location Parameters ◽  
Sylvester Resultant ◽  
Univariate Polynomial

In this paper, we turn plane seven-bar mechanism into spherical seven-bar mechanism, using quaternion to construct mathematical model for spherical seven-bar mechanism. Three constraint equations are obtained according to the angles constraint. Using Sylvester resultant elimination by two steps, a 32 degree univariate polynomial equation can be obtained. A numerical example confirms that analytical solutions of spherical seven-bar mechanism are 32 and with the help of Mathematic software to solve the location parameters.

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.

Polynomial Solution of the Spatial Burmester Problem

1995 ◽  
Vol 117 (1) ◽  
pp. 64-68 ◽  
Author(s):  
C. Innocenti
Keyword(s):  
Rigid Body ◽  
Polynomial Solution ◽  
Polynomial Equation ◽  
New Method ◽  
Algebraic Equations ◽  
Dimensional Synthesis ◽  
Connecting Rod ◽  
Elimination Procedure ◽  
Order Algebraic ◽  
Univariate Polynomial

This paper presents a new method for the dimensional synthesis of the spatial guidance linkage that features the guided body connected to the base by the interposition of five rods having spherical joints at both extremities. The linkage is required to index the guided body through seven arbitrarily-chosen rigid-body positions. Core of the proposed method is an original algebraic elimination procedure that allows five unknowns to be dropped from a set of six second-order algebraic equations in six unknowns. As a result, a final univariate polynomial equation of twentieth order is obtained whose twenty roots, in the complex domain, represent as many possible placements for a connecting rod. A numerical example is reported.

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.

Polynomial Solution of the Spatial Burmester Problem

1994 ◽  
Author(s):  
Carlo Innocenti
Keyword(s):  
Rigid Body ◽  
Polynomial Solution ◽  
Polynomial Equation ◽  
New Method ◽  
Algebraic Equations ◽  
Dimensional Synthesis ◽  
Connecting Rod ◽  
Elimination Procedure ◽  
Order Algebraic ◽  
Univariate Polynomial

Abstract The paper presents a new method for the dimensional synthesis of the spatial guidance linkage that features the guided body connected to the base by the interposition of five rods having spherical joints at both extremities. The linkage is required to index the guided body through seven arbitrarily-chosen rigid-body positions. Core of the proposed method is an original algebraic elimination procedure that allows five unknowns to be dropped from a set of six second-order algebraic equations in six unknowns. As a result, a final univariate polynomial equation of twentieth order is obtained whose twenty roots, in the complex domain, represent as many possible placements for a connecting rod. A numerical example is reported.

Closed-Form Displacement Relations of a Five-Link R-R-C-C-R Spatial Mechanism

1971 ◽  
Vol 93 (1) ◽  
pp. 221-226 ◽  
Author(s):  
A. H. Soni ◽  
P. R. Pamidi
Keyword(s):  
Closed Form ◽  
Polynomial Equation ◽  
Input Output ◽  
Degree Polynomial ◽  
Spatial Mechanism ◽  
Dual Number ◽  
Numerical Example

Using (3 × 3) matrices with dual-number elements, closed form displacement relationships are derived for a spatial five-link R-R-C-C-R mechanism. The input-output closed form displacement relationship is an eighth degree polynomial equation. A numerical example is presented.

On the Seven Position Synthesis of a 5-SS Platform Linkage

1997 ◽  
Vol 123 (1) ◽  
pp. 74-79 ◽  
Author(s):  
Qizheng Liao ◽  
J. Michael McCarthy
Keyword(s):  
Rigid Body ◽  
Reference Point ◽  
Polynomial Solution ◽  
Degree Of Freedom ◽  
Prismatic Joint ◽  
Movement Characteristics ◽  
Position Synthesis ◽  
Freedom Movement

This paper builds on Innocenti’s polynomial solution for the 5-SS platform that generates a one-degree of freedom movement through seven specified spatial positions of a rigid body. We show that his 60×60 resultant can be reduced to one that is 10×10. We then actuate the linkage using a prismatic joint on the sixth leg and determine the trajectory of the reference point through the specified positions. The singularity submanifold of this associated 6-SS platform provides information about the movement characteristics of the 5-SS linkage.

Forward Positional Analysis for the General 4–6 In-Parallel Platform

1995 ◽  
Vol 209 (1) ◽  
pp. 55-67 ◽  
Author(s):  
Q Liao ◽  
L D Seneviratne ◽  
S W E Earles
Keyword(s):  
Polynomial Equation ◽  
Unknown Variable ◽  
Real Solutions ◽  
Positional Analysis ◽  
Order Polynomial ◽  
Parallel Platform ◽  
New Equation ◽  
Published Paper ◽  
Special Case ◽  
Kinematic Solution

Presented is the forward positional (kinematic) solution for the general case of the 4–6 in-parallel platform mechanism; in particular, the spherical joints of the moving and base platforms are not restricted to lie in planes, but can be freely chosen. The forward positional analysis consists of 13 equations which are reduced to a single thirty-second order polynomial equation in one unknown variable. This new equation is numerically solved and validated by substituting the 32 roots into the 13 forward positional equations. The new analysis is also used to solve an example, with a set of known results from a previously published paper, in which a special case of the 4–6 in-parallel platform is considered; the results are in exact agreement. For a number of general platform and actuator inputs a maximum of 24 real solutions have been found. One example is illustrated.

Kinematics Analysis of a Parallel Robotic Manipulator

2010 ◽  
Vol 29-32 ◽  
pp. 956-960
Author(s):  
Xi Guang Huang ◽  
Guang Pin He ◽  
Duan Ling Li
Keyword(s):  
Algebraic Method ◽  
Robotic Manipulator ◽  
Kinematics Analysis ◽  
Analysis Problem ◽  
Numerical Example ◽  
Univariate Polynomial ◽  
Complete Sets ◽  
Direct Kinematics

The parallel robotic manipulator has attracted many researchers’ attention and it also has growing applications to different areas. In this paper an algebraic method for solving the direct kinematics analysis problem for a parallel robotic manipulator. Based on the presented algebraic method, the problem is derived into a 40th degree univariate polynomial. All complete sets of 40 solutions to the problem are obtained. The proposed method is exemplified by a numerical example.

Sign in / Sign up

Export Citation Format

Share Document