Browsing by Author "Yan, CD"

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A constrained multibody system dynamics avoiding kinematic singularities
(2002-03-01)
Huang, CF
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Yan, CD
;
Jeng, SL
;
Cheing, WH
;
機械工程學系
In the analysis of constrained multibody systems, the constraint reaction forces are normally expressed in terms of the constraint equations and a vector of Lagrange multipliers. Because it fails to incorporate conservation of momentum, the Lagrange multiplier method is deficient when the constraint Jacobian matrix is singular. This paper presents an improved dynamic formulation for the constrained multibody system. In our formulation, the kinematic constraints are still formulated in terms of the joint constraint reaction forces and moments; however, the formulations are based on a second-order Taylor expansion so as to incorporate the rigid body velocities. Conservation of momentum is included explicitly in this method; hence the problems caused by kinematic singularities can be avoided. In addition, the dynamic formulation is general and applicable to most dynamic analyses. Finally the 3-leg Stewart platform is used for the example of analysis.
Method for finding multiple roots of polynomials
(2006-02-01)
Yan, CD
;
Chieng, WH
;
機械工程學系
;
Department of Mechanical Engineering
Conventional numerical methods for finding multiple roots of polynomials are inaccurate. The accuracy is unsatisfactory because the derivatives of the polynomial in the intermediate steps of the associated root-finding procedures are eliminated. Engineering applications require that this problem be solved. This work presents an easy-to-implement method that theoretically completely resolves the multiple-root issue. The proposed method adopts the Euclidean algorithm to obtain the greatest common divisor (GCD) of a polynomial and its first derivative. The GCD may be approximate because of computational inaccuracy. The multiple roots are then deflated into simple ones and then determined by conventional root-finding methods. The multiplicities of the roots are accordingly calculated. A detailed derivation and test examples are provided to demonstrate the efficiency of this method. (c) 2006 Elsevier Ltd. All rights reserved.