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Research on the kinematic singularity and the force singularity of the Stewart platform

Yuan Qiu

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Abstract

When the Stewart platform moves, the kinematic singularity and the force singularity may accur. By analyzing the Jacobian matrix of the kinematic equation and the Jacobina matrix of the force equation, this paper shows the relationship between the elements, the determinants, and the condition numbers of the two Jacobian matrixes. Meanwhile the two kinds of singularity manifolds are also compared. The analysis and an example indicate that the kinematic singularity and the force singularity occur simultaneously.

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What this paper is about

When the Stewart platform moves, the kinematic singularity and the force singularity may accur. By analyzing the Jacobian matrix of the kinematic equation and the Jacobina matrix of the force equation, this paper shows the relationship between the elements, the determinants, and the condition numbers of the two Jacobian matrixes. Meanwhile the two kinds of singularity manifolds are also compared. The analysis and an example indicate that the kinematic singularity and the force singularity occur simultaneously.

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Available abstract

When the Stewart platform moves, the kinematic singularity and the force singularity may accur. By analyzing the Jacobian matrix of the kinematic equation and the Jacobina matrix of the force equation, this paper shows the relationship between the elements, the determinants, and the condition numbers of the two Jacobian matrixes. Meanwhile the two kinds of singularity manifolds are also compared. The analysis and an example indicate that the kinematic singularity and the force singularity occur simultaneously.

Key concepts: Singularity, Jacobian matrix and determinant, Kinematics, Essential singularity, Stewart platform, Mathematics, Matrix (chemical analysis), Mathematical analysis

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