Interval-analysis-based determination of the singularity-free workspace of Gough-Stewart parallel robots

Kaloorazi, Mohammad Hadi Farzaneh; Masouleh, Mehdi Tale; Caro, Stéphane

doi:10.1109/iraniancee.2013.6599740

Cited by 8 publications

(8 citation statements)

References 29 publications

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“…Upon resorting to screw theory [7] and following the reasoning given in the study conducted in [14], the Jacobian matrix of actuated constraints system of a 6-UPS parallel robot can be written as:…”

Section: Case Study 2: Gough-stewartmentioning

confidence: 99%

A statistical weighted method for kinematic sensitivity analysis of parallel robots

Mehrafrooz

Mohammadi

Masouleh

2018

J Braz. Soc. Mech. Sci. Eng.

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Many efforts have been devoted to propose effective methods and indices of kinematic sensitivity, but all of them have considered equal proportion of errors in the actuated joint coordinates and generally entail several drawbacks. Therefore, all of previous studies conducted in the literature ignored the difference in sensitivity of manipulator to the active joints uncertainties. Solving this issue requires a deep understanding of mathematical modeling of kinematic sensitivity and its interpretations. In this paper, a synergy between kinematic concepts and statistics approaches is employed in order to propose a more reasonable index for the kinematic performance measurement of the robotic mechanical systems, with a more emphasis on parallel mechanisms.To this end, from kinematic stand point, the kinematic sensitivity is adopted as kinematic index performance. In turn, the so-called Sobol's method is used as the statistics framework of this paper. To do so, first, weighted kinematic sensitivity is introduced and its mathematical formulation is presented. Then, the application of the proposed method is illustrated by implementing the proposed method on two case studies, namely 3-RPR and 6-DOF Gough-Stewart parallel robots. Weighted kinematic sensitivity is calculated over the robot workspace, and consequently, weighted kinematic sensitivity and conventional methods and indices are compared. From the obtained results, it can be inferred that conventional methods predict sensitivity more conservative and the proposed method is more realistic and closer to the reality.

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Section: Case Study 2: Gough-stewartmentioning

confidence: 99%

A statistical weighted method for kinematic sensitivity analysis of parallel robots

Mehrafrooz

Mohammadi

Masouleh

2018

J Braz. Soc. Mech. Sci. Eng.

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“…Recently, upon revealing some remarkable features of interval analysis, such as finding the solution of a problem within some finite domains and taking into account the numerical computer round-off errors, it has stimulated the interests of many researchers in the robotic community to deal with complicated problems such as FKP and inverse kinematic problem (IKP), 18,35 calibration 36,37 and the determination of the singularity-free workspace of parallel manipulators. 16,19 In the evolutionary techniques, the chance of being trapped in a local optimum is highly dependent of the initial population and initial search space. However, in the case of interval analysis, the only parameter to obtain the global optimum is to choose the proper search space.…”

Section: Interval Analysis and Mathematical Frameworkmentioning

confidence: 99%

Collision-free workspace of parallel mechanisms based on an interval analysis approach

FarzanehKaloorazi¹,

Masouleh²,

Caro³

2016

Robotica

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SUMMARYThis paper proposes an interval-based approach in order to obtain the obstacle-free workspace of parallel mechanisms containing one prismatic actuated joint per limb, which connects the base to the end-effector. This approach is represented through two cases studies, namely a 3-RPR planar parallel mechanism and the so-called 6-DOF Gough–Stewart platform. Three main features of the obstacle-free workspace are taken into account: mechanical stroke of actuators, collision between limbs and obstacles and limb interference. In this paper, a circle(planar case)/spherical(spatial case) shaped obstacle is considered and its mechanical interference with limbs and edges of the end-effector is analyzed. It should be noted that considering a circle/spherical shape would not degrade the generality of the problem, since any kind of obstacle could be replaced by its circumscribed circle/sphere. Two illustrative examples are given to highlight the contributions of the paper.

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“…Interval arithmetic, proposed by Moore [14], has been used for PKM property analysis, such as accuracy [15], [16], sensitivity [17], force workspace [18], existence of singularities [19], among others. It deals with continuous intervals instead of discrete points, thus allowing a continuous evaluation of the entire workspace of the PKM as well as the entire range of its design parameters.…”

Section: Introductionmentioning

confidence: 99%

Performance analysis and design of parallel kinematic machines using interval analysis

Viegas

Daney

Tavakoli

et al. 2017

Mechanism and Machine Theory

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. Performance analysis and design of parallel kinematic machines using interval analysis. Mechanism and Machine Theory, Elsevier, 2017, 115, pp.218 -236 Abstract-Some design methodologies for Parallel Kinematic Machines (PKM) have been proposed but with limitations regarding two main problems: how to improve multiple properties of different nature such as accuracy, force or singularity poses, and how to check these properties for all poses inside the PKM workspace. To address these problems, this work proposes to formulate the design problem as a feasibility problem and use a data representation which takes into account the uncertainty or variation of the involved parameters. This method, based on interval analysis, allows to evaluate several performance indexes of a PKM design. For validation purposes, this methodology is applied to a PKM, obtaining a continuous set of possible kinematic parameters values for its architecture which is capable of fulfilling several performance requirements over a desired workspace.

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Interval-analysis-based determination of the singularity-free workspace of Gough-Stewart parallel robots

Cited by 8 publications

References 29 publications

A statistical weighted method for kinematic sensitivity analysis of parallel robots

A statistical weighted method for kinematic sensitivity analysis of parallel robots

Collision-free workspace of parallel mechanisms based on an interval analysis approach

Performance analysis and design of parallel kinematic machines using interval analysis

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