Singularity Analysis of a Six-Dof Parallel Manipulator Using Grassmann-Cayley Algebra and Gröbner Bases

Caro, Stéphane; Moroz, Guillaume; Gayral, Thibault; Chablat, Damien; Chen, Chao

doi:10.1007/978-3-642-16259-6_26

Cited by 20 publications

(30 citation statements)

References 16 publications

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“…The robot under study is a simplified version of the MEPaM that has been developed at the Monash University [16,19]. This architecture is derived from the 3-PPSP that was introduced earlier [20].…”

Section: Mechanism Architecturementioning

confidence: 99%

See 1 more Smart Citation

Self-motion conditions for a 3-PPPS parallel robot with delta-shaped base

Chablat

Ottaviano

Venkateswaran

2019

Mechanism and Machine Theory

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This paper presents the self-motion conditions of the 3-PPPS parallel robot with an equilateral mobile platform and an equilateral-shaped base. The study of the direct kinematic model shows that this robot admits self-motion of the Cardanic type as the 3-RPR planar parallel robot where the first revolute joint of each leg is actuated or the PamINSA parallel robot. This property explains why the direct kinematic model admits an infinite number of solutions in the center of the workspace but has never been studied until now. The condition of this singularity is described and the location of the self-motion in the workspace with respect to all the singularities is then presented. The quaternion parameters are used to represent the singularity surfaces and the self-motion conditions in the workspace.

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Section: Mechanism Architecturementioning

confidence: 99%

“…According to the leg topology of the 3-PPPS robot, there is no serial singularity because the determinant of the B matrix does not vanish. Using the same approach as in [19], we can determine the matrix A and its determinant can be factorized as follows:…”

Section: Singularity Analysis and Self-motion Locusmentioning

confidence: 99%

Self-motion conditions for a 3-PPPS parallel robot with delta-shaped base

Chablat

Ottaviano

Venkateswaran

2019

Mechanism and Machine Theory

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“…The topology of the legs of the 3-PPPS robot means that there is no serial singularity because the determinant of the matrix B does not vanish. In using the same approach that in [19], we can evaluate the matrix A and its the determinant can be factorized as…”

Section: Singularity Analysismentioning

confidence: 99%

Kinematics and Workspace Analysis of a 3PPPS Parallel Robot With U-Shaped Base

Chablat

Baron

Jha

2017

Volume 5B: 41st Mechanisms and Robotics Conference

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This paper presents the kinematic analysis of the 3-PPPS parallel robot with an equilateral mobile platform and a U-shape base. The proposed design and appropriate selection of parameters allow to formulate simpler direct and inverse kinematics for the manipulator under study. The parallel singularities associated with the manipulator depend only on the orientation of the end-effector, and thus depend only on the orientation of the end effector. The quaternion parameters are used to represent the aspects, i.e. the singularity free regions of the workspace. A cylindrical algebraic decomposition is used to characterize the workspace and joint space with a low number of cells. The discriminant variety is obtained to describe the boundaries of each cell. With these simplifications, the 3-PPPS parallel robot with proposed design can be claimed as the simplest 6 DOF robot, which further makes it useful for the industrial applications.

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“…Among these approaches Grassmann-Cayley Algebra ( ) GCA is probably one of the most efficient since it provides sufficient tools to properly analyze geometrically the singularity condition without coordinate expression. GCA approach is suitable for analyzing the rigidity of the framework of the architecture and for scene analysis [1][2][3][4][5][6][7][8].It has a powerful tools for geometric interpretation of coordinate free representation and singularity analyzing in real time computing .The solution provided in GCA language by vanishing the superbrackets decomposition is a single condition which contains all general and particular cases [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17].To prevent the clash of serial robot's actuators which are in singularity configuration, we firstly determined t J related to its twist and secondly calculate the dependency condition of the det( ) t J which rows are Plücker coordinate lines.…”

Section: Introductionmentioning

confidence: 99%