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Algebraic Manipulations (algebraic + manipulation)

Distribution by Scientific Domains

Engineering	50%

Selected Abstracts

A tetrahedron approach for a unique closed-form solution of the forward kinematics of six-dof parallel mechanisms with multiconnected joints

JOURNAL OF FIELD ROBOTICS (FORMERLY JOURNAL OF ROBOTIC SYSTEMS), Issue 6 2002
Se-Kyong Song
This article presents a new formulation approach that uses tetrahedral geometry to determine a unique closed-form solution of the forward kinematics of six-dof parallel mechanisms with multiconnected joints. For six-dof parallel mechanisms that have been known to have eight solutions, the proposed formulation, called the Tetrahedron Approach, can find a unique closed-form solution of the forward kinematics using the three proposed Tetrahedron properties. While previous methods to solve the forward kinematics involve complicated algebraic manipulation of the matrix elements of the orientation of the moving platform, or closed-loop constraint equations between the moving and the base platforms, the Tetrahedron Approach piles up tetrahedrons sequentially to directly solve the forward kinematics. Hence, it allows significant abbreviation in the formulation and provides an easier systematic way of obtaining a unique closed-form solution. © 2002 Wiley Periodicals, Inc. [source]

Guaranteed H, robustness bounds for Wiener filtering and prediction

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 1 2002
P. Bolzern
Abstract The paper deals with special classes of H, estimation problems, where the signal to be estimated coincides with the uncorrupted measured output. Explicit bounds on the difference between nominal and actual H, performance are obtained by means of elementary algebraic manipulations. These bounds are new in continuous-time filtering and discrete-time one-step ahead prediction. As for discrete-time filtering, the paper provides new proofs that are alternative to existing derivations based on the Krein spaces formalism. In particular, some remarkable H, robustness properties of Kalman filters and predictors are highlighted. The usefulness of these results for improving the estimator design under a mixed H2/H, viewpoint is also discussed. The dualization of the analysis allows one to evaluate guaranteed H, robustness bounds for state-feedback regulators of systems affected by actuator disturbances. Copyright © 2001 John Wiley & Sons, Ltd. [source]

Notes on quantitative structure-properties relationships (QSPR) (1): A discussion on a QSPR dimensionality paradox (QSPR DP) and its quantum resolution

JOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 7 2009
Ramon Carbó-Dorca
Abstract Classical quantitative structure-properties relationship (QSPR) statistical techniques unavoidably present an inherent paradoxical computational context. They rely on the definition of a Gram matrix in descriptor spaces, which is used afterwards to reduce the original dimension via several possible kinds of algebraic manipulations. From there, effective models for the computation of unknown properties of known molecular structures are obtained. However, the reduced descriptor dimension causes linear dependence within the set of discrete vector molecular representations, leading to positive semi-definite Gram matrices in molecular spaces. To resolve this QSPR dimensionality paradox (QSPR DP) here is proposed to adopt as starting point the quantum QSPR (QQSPR) computational framework perspective, where density functions act as infinite dimensional descriptors. The fundamental QQSPR equation, deduced from employing quantum expectation value numerical evaluation, can be approximately solved in order to obtain models exempt of the QSPR DP. The substitution of the quantum similarity matrix by an empirical Gram matrix in molecular spaces, build up with the original non manipulated discrete molecular descriptor vectors, permits to obtain classical QSPR models with the same characteristics as in QQSPR, that is: possessing a certain degree of causality and explicitly independent of the descriptor dimension. © 2008 Wiley Periodicals, Inc. J Comput Chem, 2009 [source]

Exact integration of the stiffness matrix of an 8-node plane elastic finite element by symbolic computation

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 1 2008
L. Videla
Abstract Computer algebra systems (CAS) are powerful tools for obtaining analytical expressions for many engineering applications in both academic and industrial environments. CAS have been used in this paper to generate exact expressions for the stiffness matrix of an 8-node plane elastic finite element. The Maple software system was used to identify six basic formulas from which all the terms of the stiffness matrix could be obtained. The formulas are functions of the Cartesian coordinates of the corner nodes of the element, and elastic parameters Young's modulus and Poisson's ratio. Many algebraic manipulations were performed on the formulas to optimize their efficiency. The redaction in CPU time using the exact expressions as opposed to the classical Gauss,Legendre numerical integration approach was over 50%. In an additional study of accuracy, it was shown that the numerical approach could lead to quite significant errors as compared with the exact approach, especially as element distortion was increased.© 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2007 [source]