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Direct Kinematic Singularities of 3-3 Stewart-Gough Platforms
Copyright policy )SAGE PublicationsDirect Kinematic Singularities of 3-3 Stewart-Gough Platforms
In this article, a method to locate direct kinematic singularities of a 3-3 Stewart-Gough parallel manipulator (called a Stewart manipulator henceforth) is proposed. The Stewart manipulator is first replaced by an analogous manipulator, the 3PRPS parallel manipulator, and as the first three active joints of this manipulator remain fixed, this manipulator reduces to an asymmetric 3RPS parallel manipulator. With all moving platform's degrees of freedom, except its height, properly specified, there exists at least one height that gives rise to direct kinematic singularity of the asymmetric 3RPS manipulator and this height is a root of a cubic polynomial equation. The procedure to locate direct kinematic singularities thus reduces to solving cubic polynomial equations. Numerical results show that every singular configuration of the asymmetric 3RPS manipulator thus-determined is also a singular configuration of the 3-3 Stewart-Gough platform.
- Tamkang University Taiwan
Microsoft Academic Graph classification: Parallel manipulator Singularity Mathematics Degrees of freedom Mathematical analysis Cubic function Root (chord) Singular configuration Kinematics Kinematic singularities
arXiv: Computer Science::Robotics
Mechanical Engineering, Condensed Matter Physics
Mechanical Engineering, Condensed Matter Physics
Microsoft Academic Graph classification: Parallel manipulator Singularity Mathematics Degrees of freedom Mathematical analysis Cubic function Root (chord) Singular configuration Kinematics Kinematic singularities
arXiv: Computer Science::Robotics
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- Tamkang University Taiwan
In this article, a method to locate direct kinematic singularities of a 3-3 Stewart-Gough parallel manipulator (called a Stewart manipulator henceforth) is proposed. The Stewart manipulator is first replaced by an analogous manipulator, the 3PRPS parallel manipulator, and as the first three active joints of this manipulator remain fixed, this manipulator reduces to an asymmetric 3RPS parallel manipulator. With all moving platform's degrees of freedom, except its height, properly specified, there exists at least one height that gives rise to direct kinematic singularity of the asymmetric 3RPS manipulator and this height is a root of a cubic polynomial equation. The procedure to locate direct kinematic singularities thus reduces to solving cubic polynomial equations. Numerical results show that every singular configuration of the asymmetric 3RPS manipulator thus-determined is also a singular configuration of the 3-3 Stewart-Gough platform.