Displacement structure of group inverses

Flexure hinges based micro-displacement structure has been widely used for micro-precision machinery, and the natural frequency characteristics analysis is one of the most important elements in the structure design. In this paper, natural frequency characteristics analysis of a micro-displacement structure with parallel flexible hinges is presented. The effects of each structure parameter to the natural frequency of the micro-displacement structure are simulation by dynamics modeling. The parameters can be divided into three categories, namely, parallel flexure hinges parameter, micro-displacement structure parameter and material parameter. Two micro-displacement structures using common materials are machined for frequency test. The test results of two micro-displacement structure verified the modeling analysis, and the natural frequency characteristics analysis in this paper can be referenced in micro-displacement structure design.

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Group inverses and Drazin inverses of bidiagonal and triangular Toeqlitz matrices

Journal of the Australian Mathematical Society ◽

10.1017/s1446788700020036 ◽

1977 ◽

Vol 24 (1) ◽

pp. 10-34 ◽

Cited By ~ 74

Author(s):

R. E. Hartwig ◽

J. Shoaf

Keyword(s):

Toeplitz Matrices ◽

Arbitrary Ring ◽

Group Inverses ◽

Necessary And Sufficient

AbstractNecessary and sufficient sonditions are given for the existence of the group and Drazin inverses of bidiagonal and triangular Toeplitz matrices over an arbitrary ring.

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Displacement Structure: Theory and Applications

SIAM Review ◽

10.1137/1037082 ◽

1995 ◽

Vol 37 (3) ◽

pp. 297-386 ◽

Cited By ~ 282

Author(s):

Thomas Kailath ◽

Ali H. Sayed

Keyword(s):

Structure Theory ◽

Displacement Structure

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Simulation on Trajectory Planning of 6R Manipulator Based on the Shortest Distance Criterion

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.602-605.942 ◽

2014 ◽

Vol 602-605 ◽

pp. 942-945

Author(s):

Qing Qing Huang ◽

Guang Feng Chen ◽

Jiang Hua Li ◽

Xin Wei

Keyword(s):

Trajectory Planning ◽

Inverse Kinematics ◽

Spline Interpolation ◽

Algebraic Method ◽

End Effector ◽

Cartesian Space ◽

Shortest Distance ◽

Inverse Solutions ◽

Group Inverses ◽

Forward And Inverse Kinematics

This paper concerns the trajectory planning and simulation for 6R Manipulator. First, algebraic method was used to deduce the forward and inverse kinematics of 6R manipulator. All inverse solutions were expressed in atan2 to eliminate redundant roots to get the corresponding inverse formula. For the trajectory planning of manipulator in Cartesian space, using the cubic spline interpolation to get the drive function of joint, getting a unique solution from eight group inverses by the shortest distance criterion, and then obtained the actual end-effector trajectory. Using Matlab to verify the proposed trajectory planning method, validated results show that the proposed algorithm is feasible and effective.

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