Forward kinematic problem of 5-RPUR parallel mechanisms (3T2R) with identical limb structures

This paper investigates the formulation of the forward kinematic problem of the 5-DOF parallel mechanisms performing three translation and two independent rotations with identical limb structures. The mathematical framework used in this paper is based on algebraic geometry where the forward kinemati...

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Vydané v:Mechanism and machine theory Ročník 46; číslo 7; s. 945 - 959
Hlavní autori: Masouleh, Mehdi Tale, Gosselin, Clément, Husty, Manfred, Walter, Dominic R.
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Kidlington Elsevier 01.07.2011
Predmet:
Algorithms
Applied sciences
Design engineering
Drives
Exact sciences and technology
Fundamental areas of phenomenology (including applications)
Kinematics
Limbs
Linkage mechanisms, cams
Mathematical analysis
Mathematical models
Mechanical engineering. Machine design
Physics
Resultants
Solid dynamics (ballistics, collision, multibody system, stabilization...)
Solid mechanics
Translations
Forward kinematic problem (FKP)
Euclidean theory
Three translations and two rotations motion pattern (3T2R)
Solid dynamic
Parallel mechanism
Study parameters
Modeling
Linear implicitization algorithm
Direct problem
Linear system
5-DOF parallel mechanisms
Homotopy
Kinematics
Linkage mechanism
Elimination method
Algebraic geometry
ISSN:0094-114X
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Popis
Shrnutí:This paper investigates the formulation of the forward kinematic problem of the 5-DOF parallel mechanisms performing three translation and two independent rotations with identical limb structures. The mathematical framework used in this paper is based on algebraic geometry where the forward kinematic problem is explored in a seven-dimensional kinematic space by the means of the so-called Study parameters. In this paper, the algorithms proposed for obtaining the forward kinematic expression is based on two approaches which differ by their concept of eliminating passive variables. The first one is based on the application of the so-called resultant method and the second one, as a novel approach referred to as linear implicitization algorithm, uses an elimination procedure based on solving several systems of linear equations. The forward kinematic problem is solved using the homotopy continuation and it is revealed that it has 1680 finite solutions. Moreover, the forward kinematic problem is studied in three-dimensional Euclidean space where a class of simplified designs are proposed which admit a simpler formulation for the forward kinematic problem. Finally, based on the simplified designs, for a nearly general design a univariate expression of degree 220 is obtained.
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ISSN:0094-114X
DOI:10.1016/j.mechmachtheory.2011.02.005