On the regularity of the inverse Jacobian of parallel robots

Merlet, Jean‐Pierre; Donelan, Peter

doi:10.1007/978-1-4020-4941-5_5

Cited by 16 publications

(15 citation statements)

References 6 publications

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“…i.e., the matrix of Plücker coordinates of the six leg lines (for details, see [17]), where a i are the global coordinates of the attachment point of leg l i to the base of the Gough-Stewart platform, and n i is the unit free vector anchored at a i and defining the orientation of leg l i . Note that, in order to simplify notation, the same symbol is used to represent a point and its position vector.…”

Section: Singularities Of Gough-stewart Platformsmentioning

confidence: 99%

On $\Delta$-Transforms

2009

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Abstract-Any set of two legs in a Gough-Stewart platform sharing an attachment is defined as a ∆component. This component links a point in the platform (base) to a line in the base (platform). Thus, if the two legs, which are involved in a ∆ component, are rearranged without altering the location of the line and the point in their base and platform local reference frames, the singularity locus of the Gough-Stewart platform remains the same, provided that no architectural singularities are introduced. Such leg rearrangements are defined as ∆-transforms, and they can be applied sequentially and simultaneously. Although it may seem counterintuitive at first glance, the rearrangement of legs using simultaneous ∆-transforms does not necessarily lead to leg configurations containing a ∆component. As a consequence, the application of ∆-transforms reveals itself as a simple, yet powerful, technique for the kinematic analysis of large families of Gough-Stewart platforms. It is also shown that these transforms shed new light on the characterization of architectural singularities and their associated self-motions.

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Section: Singularities Of Gough-stewart Platformsmentioning

confidence: 99%

On $\Delta$-Transforms

2009

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“…In this system, the machining station is a parallel machine tool. Considering the real time and stability of the system, the control system of this unit is developed by EVC also [5][6][7][8], the main interface is depicted as fig.4. L L = , then Z coordinate change of B i can be determined, this is the length that the linkage should move, thus the inverse solution can be solved by the given output position.…”

Section: Training Tasksmentioning

confidence: 99%

Practical Application of Training tasks Based on Flexible Manufacturing System

Fan¹

2014

Proceedings of the 3rd International Conference on Science and Social Research

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Abstract. Aiming at the characteristics of the flexible manufacturing system, the equipment composition and the hardware architecture of the flexible manufacturing system is described in this paper. Taking the parallel machine fabrication process as an example, the automated production process is elaborated. Combined with laboratory equipment and the professional knowledge and different teaching characteristics, the teaching programs of flexible manufacturing system is presented. The laboratory project is planned and is implemented in specific engineering training tasks, the professional knowledge of students on both the breadth and depth has been expanded, the experimental skills and innovative capacity to improve teaching effectiveness has been significantly improved as well.

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“…Using both filters algorithm A is very efficient: checking the regularity of J −1 over a large workspace requires less than one second [11].…”

Section: Singularity Analysismentioning

confidence: 99%

Interval Analysis and Robotics

Merlet

2010

Springer Tracts in Advanced Robotics

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Interval analysis is a relatively new mathematical tools that allows one to deal with problems that may have to be solved numerically with a computer. Examples of such problems are system solving and global optimization but numerous other problems may be addressed as well. This approach has the following general advantages:• it allows to find solutions of a problem only within some finite domain• numerical computer round-off errors are taken into account so that the solutions are guaranteed A further inherent property that is of interest for robotics problems is that this approach allows one to deal with the uncertainties that are unavoidable in robotics. Although the basic principles of interval analysis are easy to understand and to implement, this approach will be efficient only if additional methods are used and if the problem at hand is formulated appropriately. In this paper we will emphasize various robotics problems that have been solved with interval analysis, many of which are currently beyond the reach of other mathematical approaches.

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On the regularity of the inverse Jacobian of parallel robots

Cited by 16 publications

References 6 publications

On $\Delta$-Transforms

On $\Delta$-Transforms

Practical Application of Training tasks Based on Flexible Manufacturing System

Interval Analysis and Robotics

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