scholarly journals A Task-Driven Approach to Unified Synthesis of Planar Four-Bar Linkages Using Algebraic Fitting of a Pencil of G-Manifolds

2017 ◽  
Vol 17 (3) ◽  
Author(s):  
Q. J. Ge ◽  
Anurag Purwar ◽  
Ping Zhao ◽  
Shrinath Deshpande
Keyword(s):  
Least Squares ◽  
Singular Values ◽  
Singular Value ◽  
Geometric Constraints ◽  
Motion Generation ◽  
Value Decomposition ◽  
Four Bar Linkage ◽  
The Given ◽  
Best Fit ◽  
Additional Constraints

This paper studies the problem of planar four-bar motion generation from the viewpoint of extraction of geometric constraints from a given set of planar displacements. Using the image space of planar displacements, we obtain a class of quadrics, called generalized- or G-manifolds, with eight linear and homogeneous coefficients as a unified representation for constraint manifolds of all four types of planar dyads, RR, PR, and PR, and PP. Given a set of image points that represent planar displacements, the problem of synthesizing a planar four-bar linkage is reduced to finding a pencil of G-manifolds that best fit the image points in the least squares sense. This least squares problem is solved using singular value decomposition (SVD). The linear coefficients associated with the smallest singular values are used to define a pencil of quadrics. Additional constraints on the linear coefficients are then imposed to obtain a planar four-bar linkage that best guides the coupler through the given displacements. The result is an efficient and linear algorithm that naturally extracts the geometric constraints of a motion and leads directly to the type and dimensions of a mechanism for motion generation.

A Task Driven Approach to Unified Synthesis of Planar Four-Bar Linkages Using Algebraic Fitting of a Pencil of G-Manifolds

2013 ◽  
Author(s):  
Q. J. Ge ◽  
Ping Zhao ◽  
Anurag Purwar
Keyword(s):  
Least Squares ◽  
Singular Values ◽  
Geometric Constraints ◽  
Motion Generation ◽  
Motion Approximation ◽  
Value Decomposition ◽  
Four Bar Linkage ◽  
The Given ◽  
Best Fit ◽  
Additional Constraints

This paper studies the problem of planar four-bar motion approximation from the viewpoint of extraction of geometric constraints from a given set of planar displacements. Using the Image Space of planar displacements, we obtain a class of quadrics, called Generalized- or G-manifolds, with eight linear and homogeneous coefficients as a unified representation for constraint manifolds of all four types of planar dyads, RR, PR, and PR, and PP. Given a set of image points that represent planar displacements, the problem of synthesizing a planar four-bar linkage is reduced to finding a pencil of G-manifolds that best fit the image points in the least squares sense. This least squares problem is solved using Singular Value Decomposition. The linear coefficients associated with the smallest singular values are used to define a pencil of quadrics. Additional constraints on the linear coefficients are then imposed to obtain a planar four-bar linkage that best guides the coupler through the given displacements. The result is an efficient and linear algorithm that naturally extracts the geometric constraints of a motion and leads directly to the type and dimensions of a mechanism for motion generation.

A Task Driven Approach to the Synthesis of Spherical 4R Linkages Using Algebraic Fitting Method

2013 ◽  
Author(s):  
Ping Zhao ◽  
Xiangyun Li ◽  
Anurag Purwar ◽  
Kartik Thakkar ◽  
Q. J. Ge
Keyword(s):  
Linear Method ◽  
Geometric Constraints ◽  
Motion Generation ◽  
Constraint Manifold ◽  
Fitting Method ◽  
Kinematic Mapping ◽  
Motion Approximation ◽  
The Given ◽  
Best Fit ◽  
Additional Constraints

This paper studies the problem of spherical 4R motion approximation from the viewpoint of extraction of circular geometric constraints from a given set of spherical displacements. This paper extends our planar 4R linkage synthesis work to the spherical case. By utilizing kinematic mapping and quaternions, we map spherical displacements into points and the workspace constraints of the coupler into intersection of algebraic quadrics (called constraint manifold), respectively, in the image space of displacements. The problem of synthesizing a spherical 4R linkage is reduced to finding a pencil of quadrics that best fit the given image points in the least squares sense. Additional constraints on the pencil identify the quadrics that represent a spherical circular constraint. The geometric parameters of the quadrics encode information about the linkage parameters which are readily computed to obtain a spherical 4R linkage that best navigates through the given displacements. The result is an efficient and largely linear method for spherical four-bar motion generation problem.

Polytopic Decomposition of the Linear Parameter-Varying Model Based on HOSVD

2012 ◽  
Vol 203 ◽  
pp. 142-147 ◽  
Author(s):  
Ming Hao Wang ◽  
Gang Liu ◽  
Hong Qing Hou
Keyword(s):  
Singular Values ◽  
Singular Value ◽  
Linear Parameter ◽  
Linear Parameter Varying ◽  
Reduced Rank ◽  
System A ◽  
Rank Tensor ◽  
Lpv System ◽  
Value Decomposition ◽  
The Given

For the solution of an infinite number of LMI in the parameters trajectory of LPV system, a method based on the tensor product transformation is proposed to tranform the LPV system into the convex polytopic structure. Firstly, discretizing the given LPV system within the interzone of the changing parameters and storing it into a tensor, and then using higher order singular value decomposition (HOSVD), discarding smaller and non-zero singular values and their corresponding singular vectors, reconstructing the reduced-rank tensor to obtain a finite number of LTI vertex systems. The final example shows that the convex polytopic system obtained by this method can substitute the original LPV system within the allowed error.

scholarly journals Methods for Updating the Singular Value Decomposition

1974 ◽  
Vol 3 (26) ◽  
Author(s):  
Linda Kaufman
Keyword(s):  
Singular Value Decomposition ◽  
Least Squares ◽  
Singular Values ◽  
Singular Value ◽  
Linear Least Squares ◽  
Least Squares Problem ◽  
Linear Least Squares Problem ◽  
Value Decomposition ◽  
Made In

The linear least squares problem of minimizing ||Ax~ - b~||_(2) where A is an m X n matrix, m >= n, may be solved using the singular value decomposition in approximately 2mn^(3) + 4n^(3) multiplications. In this paper the problem of solving ||A'x~ - b~||_(2) is considered where A' results from deleting or adding a column to A. This might occur when a change is made in the model of a process. Instead of computing the singular value decomposition of A' from scratch, the singular value decomposition of A is updated. Since the updating require about 6n^(3) multiplications the algorithms are useful when m >> n. The problem of recalculation some or all of the singular values of a matrix A', which is obtained by deleting or adding a row or a column from a matrix A, whose singular value decomposition is known, is also studied.

scholarly journals Through-Wall Image Enhancement Based on Singular Value Decomposition

2012 ◽  
Vol 2012 ◽  
pp. 1-20 ◽  
Author(s):  
Muhammad Mohsin Riaz ◽  
Abdul Ghafoor
Keyword(s):  
Singular Value Decomposition ◽  
Image Enhancement ◽  
Visual Inspection ◽  
Signal To Noise Ratio ◽  
Singular Values ◽  
Singular Value ◽  
Information Theoretic ◽  
Value Decomposition ◽  
Suppress Noise ◽  
Wall Imaging

Singular value decomposition and information theoretic criterion-based image enhancement is proposed for through-wall imaging. The scheme is capable of discriminating target, clutter, and noise subspaces. Information theoretic criterion is used with conventional singular value decomposition to find number of target singular values. Furthermore, wavelet transform-based denoising is performed (to further suppress noise signals) by estimating noise variance. Proposed scheme works also for extracting multiple targets in heavy cluttered through-wall images. Simulation results are compared on the basis of mean square error, peak signal to noise ratio, and visual inspection.

Lyapunov and marginal instability in Hamiltonian systems

1999 ◽  
Vol 77 (8) ◽  
pp. 603-633 ◽  
Author(s):  
J Grindlay
Keyword(s):  
Lyapunov Exponents ◽  
Nonlinear Oscillator ◽  
Linear Chain ◽  
Mathieu Equation ◽  
Singular Values ◽  
Space Velocity ◽  
Singular Value ◽  
The Stability ◽  
Value Decomposition ◽  
Simple Systems

The variational equations and the evolution matrix are introduced and used to discuss the stability of a bound Hamiltonian trajectory. Singular-value decomposition is applied to the evolution matrix. Singular values and Lyapunov exponents are defined and their properties described. The singular-value expansion of the phase-space velocity is derived. Singular values and Lyapunov exponents are used to characterize the stability behaviour of five simple systems, namely, the nonlinear oscillator with cubic anharmonicity, the quasi-periodic Mathieu equation, the Hénon-Heilesmodel, the 4+2 linear chain with cubic anharmonicity, and an integrable system of arbitrary order.PACS Nos.: 03.20, 05.20

scholarly journals Identification Method for Voltage Sags Based on K-means-Singular Value Decomposition and Least Squares Support Vector Machine

Energies ◽  
2019 ◽  
Vol 12 (6) ◽  
pp. 1137 ◽  
Author(s):  
Haoyuan Sha ◽  
Fei Mei ◽  
Chenyu Zhang ◽  
Yi Pan ◽  
Jianyong Zheng
Keyword(s):  
Support Vector Machine ◽  
Singular Value Decomposition ◽  
Least Squares ◽  
Short Circuit ◽  
Singular Value ◽  
Support Vector ◽  
Voltage Sag ◽  
Svm Classifier ◽  
Identification Algorithm ◽  
Value Decomposition

Voltage sag is one of the most serious problems in power quality. The occurrence of voltage sag will lead to a huge loss in the social economy and have a serious effect on people’s daily life. The identification of sag types is the basis for solving the problem and ensuring the safe grid operation. Therefore, with the measured data uploaded by the sag monitoring system, this paper proposes a sag type identification algorithm based on K-means-Singular Value Decomposition (K-SVD) and Least Squares Support Vector Machine (LS-SVM). Firstly; each phase of the sag sample RMS data is sparsely coded by the K-SVD algorithm and the sparse coding information of each phase data is used as the feature matrix of the sag sample. Then the LS-SVM classifier is used to identify the sag type. This method not only works without any dependence on the sag data feature extraction by artificial ways, but can also judge the short-circuit fault phase, providing more effective information for the repair of grid faults. Finally, based on a comparison with existing methods, the accuracy advantages of the proposed algorithm with be presented.

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