Direct displacement analysis of parallel manipulators

Zhao, Xinhua; Peng, Shangxian

doi:10.1002/(sici)1097-4563(200006)17:6<341::aid-rob4>3.0.co;2-n

Cited by 10 publications

(5 citation statements)

References 21 publications

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“…A pioneering work in this regard has been done by Raghavan [30], who has used a continuation method to solve a system of equations and found 40 solutions in the complex domain, tracking 960 paths from the start point. A novel numerical method has been proposed [31] which uses the instantaneous velocity direction of the mobile platform to find its new position. This algorithm is faster than the Newton-Raphson and can converge to the accuracy of the order of 1e− 9 in two or more iterations.…”

Section: Methodsmentioning

confidence: 99%

Forward kinematics modelling of a parallel ankle rehabilitation robot using modified fuzzy inference

Jamwal

Xie

Tsoi

et al. 2010

Mechanism and Machine Theory

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Section: Methodsmentioning

confidence: 99%

Forward kinematics modelling of a parallel ankle rehabilitation robot using modified fuzzy inference

Jamwal

Xie

Tsoi

et al. 2010

Mechanism and Machine Theory

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“…However, it is known (Merlet 19901 Husty 1996) that this numerical inversion requires high-order polynomial 678 THE INTERNATIONAL JOURNAL OF ROBOTICS RESEARCH / July 2007 root determination, with several possible solutions (up to 40 real solutions (Dietmaier 1998) for a Gough-Stewart platform (Gough and Whitehall 19621 Stewart 1965). Much of the work is thus devoted to solving this problem accurately and in real time (see, for instance, Zhao and Peng 2000), or to designing parallel mechanisms with an algebraic forward kinematic model (Kim and Tsai 20021 Gogu 2004). Alternatively, one of the promising paths lies in the use of the so-called metrological redundancy (Baron and Angeles 1998), which simplifies the kinematic models by introducing additional sensors into the mechanism and thus yields easier control (Marquet 2002).…”

Section: Introductionmentioning

confidence: 99%

Image-based Visual Servoing of a Gough—Stewart Parallel Manipulator using Leg Observations

Andreff

Dallej

Martinet

2007

The International Journal of Robotics Research

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In this paper, a tight coupling between computer vision and parallel robotics is exhibited through the projective line geometry. Indeed, contrary to the usual methodology where the robot is modeled independently from the control law that will be implemented, the proposed method takes into account, from the early modeling stage, the fact that vision will be used for control. Hence, kinematic modeling and projective geometry are fused into a control-devoted projective kinematic model. Thus, starting from a vision-based kinematic modeling of a Gough-Stewart manipulator, a visual servoing scheme is presented, where the image projection (edges) of the non-rigidly linked legs are servoed, rather than the end-effector pose or the leg directions.

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“…However, it is known [4], [5] that this numerical inversion requires high-order polynomial root determination, with several possible solutions (up to 40 real solutions [6] for a Gough-Stewart platform [7], [8]). Much of the work is thus devoted to solving this problem accurately and in real time (see, for instance, [9]), or to designing parallel mechanisms with algebraic forward kinematic model [10], [11]. Alternately, one of the promising paths lies in the use of the so-called metrological redundancy [12], which simplifies the kinematic models by introducing additional sensors into the mechanism, and thus yields easier control [13].…”

Section: Introductionmentioning

confidence: 99%

Unifying Kinematic Modeling, Identification, and Control of a Gough–Stewart Parallel Robot Into a Vision-Based Framework

Andreff

Martinet

2006

IEEE Trans. Robot.

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In this paper, it is shown that computer vision, used as an exteroceptive redundant metrology mean, simplifies the control of a Gough-Stewart parallel robot. Indeed, contrary to the usual methodology, where the robot is modeled independently from the control law which will be implemented, we take into account that vision will be used for control, from the early modeling stage. Hence, kinematic modeling and projective geometry are fused into a control-devoted projective kinematic model. Thus, a novel vision-based kinematic modeling of such a robot is proposed through the observation of its legs. Inspired by the geometry of lines, this model unifies and simplifies both identification and control. Indeed, it has a reduced parameter set, and allows us to propose a linear solution to its calibration. Using the same model, a visual servoing scheme is presented, where the attitudes of the nonrigidly linked legs are servoed, rather than the end-effector pose. Finally, theoretical results concerning the stability of this control law are provided.

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Direct displacement analysis of parallel manipulators

Cited by 10 publications

References 21 publications

Forward kinematics modelling of a parallel ankle rehabilitation robot using modified fuzzy inference

Forward kinematics modelling of a parallel ankle rehabilitation robot using modified fuzzy inference

Image-based Visual Servoing of a Gough—Stewart Parallel Manipulator using Leg Observations

Unifying Kinematic Modeling, Identification, and Control of a Gough–Stewart Parallel Robot Into a Vision-Based Framework

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