A Study on the Characteristic Equations of Positive Semidefinite Matrices and Its Application on the Design of Isotropic Manipulator
碩士 === 國立臺灣科技大學 === 機械工程系 === 89 === Efficient methods to determine the ratio of the minimum and maximum singular values of the Jacobian are developed using the theory of polynomials and the characteristics of positive semidefinite matrices. First, the methods for solving a cubic or biquadratic are...
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| Format: | Others |
| Language: | zh-TW |
| Published: |
2001
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| Online Access: | http://ndltd.ncl.edu.tw/handle/94052004087528987004 |
| Summary: | 碩士 === 國立臺灣科技大學 === 機械工程系 === 89 === Efficient methods to determine the ratio of the minimum and maximum singular values of the Jacobian are developed using the theory of polynomials and the characteristics of positive semidefinite matrices. First, the methods for solving a cubic or biquadratic are studied. These methods, along with the discriminant of polynomials, are then used to develop algorithms for computing minimum and maximum singular values of 3 x 3 and 4 x 4 matrices or solving polynomials with higher degree. The proposed methods compute the singular values of a matrix analytically (without using a numerical approach) so they can obtain the ratio (of the minimum and maximum singular values) at a much lower cost. Based on the developed methods, we propose several global measures to evaluate manipulability of manipulators. The optimal design of isotropic manipulators is also investigated.
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