Point-based Jacobian formulation for computational kinematics of manipulators

Altuzarra, Oscar; Salgado, Óscar; Petuya, V.; Hernández, A.

doi:10.1016/j.mechmachtheory.2006.01.011

Cited by 39 publications

(14 citation statements)

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“…The first one is to formulate a dimensionally homogeneous Jacobian in which all entries have the same physical units. The methods available for doing so include: (1) a length-based method, in which all translational elements in the Jacobian are normalized with the help of a "characteristic/natural length" [2][3][4][5][6][7][8]; however, this method depends on the choice of the characteristic length, and -although a "best" characteristic length can be defined by optimization notions [6] -the choice of an appropriate characteristic length and with this the combination of translational and rotational metrics for a particular operation is not unique; and (2) the point-based method, which makes use of linear maps between the joint rates and velocities of several points on the platform to overcome the problem of non-existence of a bi-invariant metric for combined rotation and translation [9][10][11][12][13]; however, defining good criteria for choosing proper points is an open issue needing investigation, as the locations of these points affect the algebraic characteristics of the Jacobian.…”

Section: Introductionmentioning

confidence: 99%

A generalized approach for computing the transmission index of parallel mechanisms

Liu

Huang

Kecskeméthy

et al. 2014

Mechanism and Machine Theory

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Copyright and reuse:The Warwick Research Archive Portal (WRAP) makes this work by researchers of the University of Warwick available open access under the following conditions. Copyright © and all moral rights to the version of the paper presented here belong to the individual author(s) and/or other copyright owners. To the extent reasonable and practicable the material made available in WRAP has been checked for eligibility before being made available.Copies of full items can be used for personal research or study, educational, or not-forprofit purposes without prior permission or charge. Provided that the authors, title and full bibliographic details are credited, a hyperlink and/or URL is given for the original metadata page and the content is not changed in any way. A note on versions:The version presented here may differ from the published version or, version of record, if you wish to cite this item you are advised to consult the publisher's version. Please see the 'permanent WRAP url' above for details on accessing the published version and note that access may require a subscription. AbstractThis paper presents a novel approach for computing the transmission index of parallel mechanisms. The approach is based on an extended concept to compute the maximal virtual coefficient, which is an important notion involved in the formulation of dimensionally homogeneous transmission indices for singularity analysis and dimensional optimization of parallel mechanisms. By exploiting the dual property of the virtual coefficient, two characteristic points instead of one as in the current state of the art are defined: one characteristic point is located on the 'floating' axis of the transmission wrench, as in existing approaches, while a second one is located on the floating axis of the output twist of the platform, which is a novel concept. This allows one to define two characteristic lengths, of which the larger is then used for the measure of the "distance" between the transmission wrench screw and the output twist screw. As shown in this paper, this new measure makes it possible to discern more finely the configuration-dependent properties of kinematic performance of parallel mechanisms, thus making it more suitable for dimensional optimization. Confidence in this statement is demonstrated through the comparative study of two in-parallel mechanisms using the new method and previously existing ones.

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Section: Introductionmentioning

confidence: 99%

A generalized approach for computing the transmission index of parallel mechanisms

Liu

Huang

Kecskeméthy

et al. 2014

Mechanism and Machine Theory

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“…The software solves the forward position problem of planar and spatial mechanisms with lower pairs, obtaining the trajectories of the selected points. Furthermore, the software includes other modules to analyse velocities [32] and likewise analyse of singular positions [33] and calculate workspace. The figures presented in this section are directly extracted from the simulation software.…”

Section: Preliminary Results On the Convergence Of Gimmentioning

confidence: 99%

A numerical procedure to solve non‐linear kinematic problems in spatial mechanisms

Petuya

Jiménez

Alonso

et al. 2007

Numerical Meth Engineering

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SUMMARYThis paper presents a numerical method to solve the forward position problem in spatial mechanisms. The method may be incorporated in a software for the kinematic analysis of mechanisms, where the procedure is systematic and can be easily implemented, achieving a high degree of automation in simulation. The procedure presents high computational efficiency, enabling its incorporation in the control loop to solve the forward position problem in the case of a velocity control scheme. Also, in this paper preliminary results on the convergence of the proposed procedure are shown, and efficiency results of the method applied to representative spatial mechanisms are presented.

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“…• Using natural length or characteristic length [27][28][29] • Using scaling matrix [30,31] • Using weighting factor [32] • By using power transition concept [33] • Point-based method [34][35][36][37] • General and systematic method [38] • Homogeneous extended Jacobian matrix [39]…”

Section: Jacobian Matrixmentioning

confidence: 99%

Kinematic Performance Measures and Optimization of Parallel Kinematics Manipulators: A Brief Review

Rosyid¹,

El‐Khasawneh²,

Alazzam³

2017

Kinematics

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This chapter covers a number of kinematic performance indices that are instrumental in designing parallel kinematics manipulators. These indices can be used selectively based on manipulator requirements and functionality. This would provide the very practical tool for designers to approach their needs in a very comprehensive fashion. Nevertheless, most applications require a more composite set of requirements that makes optimizing performance more challenging. The later part of this chapter will discuss single-objective and multi-objectives optimization that could handle certain performance indices or a combination of them. A brief description of most common techniques in the literature will be provided.

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Point-based Jacobian formulation for computational kinematics of manipulators

Cited by 39 publications

References 6 publications

A generalized approach for computing the transmission index of parallel mechanisms

A generalized approach for computing the transmission index of parallel mechanisms

A numerical procedure to solve non‐linear kinematic problems in spatial mechanisms

Kinematic Performance Measures and Optimization of Parallel Kinematics Manipulators: A Brief Review

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