Alternative methods for direct kinematic analysis of a parallel robot for ankle rehabilitation

Erick D. Flores-Salazar; Manuel Arias-Montiel; Esther Lugo-González; Jaime Gallardo-Alvarado; Ricardo Tapia-Herrera

doi:10.1007/978-3-030-58104-6_7

Alternative methods for direct kinematic analysis of a parallel robot for ankle rehabilitation

Erick D. Flores-Salazar, Manuel Arias-Montiel, Esther Lugo-González, Jaime Gallardo-Alvarado, Ricardo Tapia-Herrera

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

This work deals with the direct kinematic analysis of a parallel robot for ankle rehabilitation. The problem consists of solving a set of nonlinear equations derived from the closure equations of the closed kinematic chains which form the parallel architecture of the robot. The Newton-Rhapson method is often used for this kind of problem. However, the convergency of this method strongly depends on the initial conditions chosen for the iterative algorithm. Moreover, this method converges to only one of particular solution where many are possible. To overcome these disadvantages, two alternative numerical methods are proposed. Newton-Homotopy and Sylvester dialytic methods are implemented and the obtained results are discussed.

Original language	English
Pages (from-to)	53-61
Number of pages	9
Journal	Mechanisms and Machine Science
Volume	93
DOIs	https://doi.org/10.1007/978-3-030-58104-6_7
State	Published - 2021
Externally published	Yes

Keywords

Direct kinematics
Numerical methods
Parallel robot

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10.1007/978-3-030-58104-6_7

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title = "Alternative methods for direct kinematic analysis of a parallel robot for ankle rehabilitation",

abstract = "This work deals with the direct kinematic analysis of a parallel robot for ankle rehabilitation. The problem consists of solving a set of nonlinear equations derived from the closure equations of the closed kinematic chains which form the parallel architecture of the robot. The Newton-Rhapson method is often used for this kind of problem. However, the convergency of this method strongly depends on the initial conditions chosen for the iterative algorithm. Moreover, this method converges to only one of particular solution where many are possible. To overcome these disadvantages, two alternative numerical methods are proposed. Newton-Homotopy and Sylvester dialytic methods are implemented and the obtained results are discussed.",

keywords = "Direct kinematics, Numerical methods, Parallel robot",

author = "{D. Flores-Salazar}, Erick and Manuel Arias-Montiel and Esther Lugo-Gonz{\'a}lez and Jaime Gallardo-Alvarado and Ricardo Tapia-Herrera",

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AU - D. Flores-Salazar, Erick

AU - Arias-Montiel, Manuel

AU - Lugo-González, Esther

AU - Gallardo-Alvarado, Jaime

AU - Tapia-Herrera, Ricardo

PY - 2021

Y1 - 2021

N2 - This work deals with the direct kinematic analysis of a parallel robot for ankle rehabilitation. The problem consists of solving a set of nonlinear equations derived from the closure equations of the closed kinematic chains which form the parallel architecture of the robot. The Newton-Rhapson method is often used for this kind of problem. However, the convergency of this method strongly depends on the initial conditions chosen for the iterative algorithm. Moreover, this method converges to only one of particular solution where many are possible. To overcome these disadvantages, two alternative numerical methods are proposed. Newton-Homotopy and Sylvester dialytic methods are implemented and the obtained results are discussed.

AB - This work deals with the direct kinematic analysis of a parallel robot for ankle rehabilitation. The problem consists of solving a set of nonlinear equations derived from the closure equations of the closed kinematic chains which form the parallel architecture of the robot. The Newton-Rhapson method is often used for this kind of problem. However, the convergency of this method strongly depends on the initial conditions chosen for the iterative algorithm. Moreover, this method converges to only one of particular solution where many are possible. To overcome these disadvantages, two alternative numerical methods are proposed. Newton-Homotopy and Sylvester dialytic methods are implemented and the obtained results are discussed.

KW - Direct kinematics

KW - Numerical methods

KW - Parallel robot

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VL - 93

SP - 53

EP - 61

JO - Mechanisms and Machine Science

JF - Mechanisms and Machine Science

ER -

Alternative methods for direct kinematic analysis of a parallel robot for ankle rehabilitation

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Keywords

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