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Computational kinematics for robotic manipulators: Jacobian problems

Computational kinematics for robotic manipulators: Jacobian problems Purpose – This paper aims to provide tools for the complete Jacobian analysis of robotic manipulators of general topology, using a comprehensive velocity equation. Design/methodology/approach – First, a modelling process is made in order to build the velocity equation using simple constraint equations: i.e. length restriction, relative motion and rigid body constraints. Then the motion space is solved, i.e. the space that spans all feasible motions of the manipulator. Findings – The velocity equation is comprehensive, i.e. it relates all kinematic variables, not only input and output. The Jacobian related to the comprehensive velocity equation is a square dimensionless matrix. This characteristic has great importance when evaluating manipulability or closeness to singularities. Employing the motion space, any kinematic entity can be studied: i.e. velocities and accelerations of any active/passive joints, screw axis, axodes, and so on. Also a comprehensive singularity analysis can be made. Research limitations/implications – The approach presented is focused on the kinetostatic analysis of manipulators and, therefore, subjected to rigid body assumption. Practical implications – The paper presents a proposal of effective codes for engineering analysis of manipulators. Originality/value – This approach is based on a pure computational kinematic analysis that unifies all kinetostatic analysis for any manipulator topology (i.e. serial, parallel, hybrid manipulators, complex mechanisms, redundant‐or non‐redundant‐actuated). The characteristic Jacobian matrix is dimensionless and provides the means for a complete singularity analysis and an effective use of indicators. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Engineering Computations: International Journal for Computer-Aided Engineering and Software Emerald Publishing

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References (19)

Publisher
Emerald Publishing
Copyright
Copyright © 2008 Emerald Group Publishing Limited. All rights reserved.
ISSN
0264-4401
DOI
10.1108/02644400810841396
Publisher site
See Article on Publisher Site

Abstract

Purpose – This paper aims to provide tools for the complete Jacobian analysis of robotic manipulators of general topology, using a comprehensive velocity equation. Design/methodology/approach – First, a modelling process is made in order to build the velocity equation using simple constraint equations: i.e. length restriction, relative motion and rigid body constraints. Then the motion space is solved, i.e. the space that spans all feasible motions of the manipulator. Findings – The velocity equation is comprehensive, i.e. it relates all kinematic variables, not only input and output. The Jacobian related to the comprehensive velocity equation is a square dimensionless matrix. This characteristic has great importance when evaluating manipulability or closeness to singularities. Employing the motion space, any kinematic entity can be studied: i.e. velocities and accelerations of any active/passive joints, screw axis, axodes, and so on. Also a comprehensive singularity analysis can be made. Research limitations/implications – The approach presented is focused on the kinetostatic analysis of manipulators and, therefore, subjected to rigid body assumption. Practical implications – The paper presents a proposal of effective codes for engineering analysis of manipulators. Originality/value – This approach is based on a pure computational kinematic analysis that unifies all kinetostatic analysis for any manipulator topology (i.e. serial, parallel, hybrid manipulators, complex mechanisms, redundant‐or non‐redundant‐actuated). The characteristic Jacobian matrix is dimensionless and provides the means for a complete singularity analysis and an effective use of indicators.

Journal

Engineering Computations: International Journal for Computer-Aided Engineering and SoftwareEmerald Publishing

Published: Jan 4, 2008

Keywords: Velocity; Numerical analysis; Robotics; Kinematics

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