Dimensionally Homogeneous Jacobian and Condition Number

Latifah Nurahmi; Stéphane Caro

doi:10.4028/www.scientific.net/AMM.836.42

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HomeApplied Mechanics and MaterialsApplied Mechanics and Materials Vol. 836Dimensionally Homogeneous Jacobian and Condition...

Dimensionally Homogeneous Jacobian and Condition Number

Abstract:

This paper deals with the formulation of the dimensionally homogeneous extended Jacobian matrix, which is an important issue for the performance analysis of f degrees-of-freedom (f ≤6) parallel manipulators having coupled rotational and translational motions. By using the f independent coordinates to define the permitted motions and (6-f) independent coordinates to define the restricted motions of the moving platform, the 6×6 dimensionally homogeneous extended Jacobian matrix is derived for non-redundant parallel manipulators. The conditioning number of the parallel manipulators is computed to evaluate the homogeneous extended Jacobian matrix, the homogeneous actuation wrench matrix, and the homogeneous constraint wrench matrix to evaluate the performance of the parallel manipulators. By using these indices, the closeness of a pose to different singularities can be detected. An illustrative example with the 3-RPS parallel manipulator is provided to highlight the effectiveness of the approach and the proposed indices.

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Periodical:

Applied Mechanics and Materials (Volume 836)

Pages:

42-47

DOI:

https://doi.org/10.4028/www.scientific.net/AMM.836.42

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Online since:

June 2016

Authors:

Latifah Nurahmi*, Stéphane Caro

Keywords:

Condition Number, Dimensionally Homogeneous Extended Jacobian Matrix, Parallel Manipulators, Screw Theory, Singularities

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References

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