• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.9 no.2
• /
• pp.99-106
• /
• 2005

We present a relation between the orthogonality of the constrained Legendre polynomials over the triangular domain and the BB ($B{\acute{e}zier}\;-Bernstein$) coefficients of the polynomials using the equivalence of orthogonal complements. Using it we also show that the best constrained degree reduction of polynomials in BB form equals the best approximation of weighted Euclidean norm of coefficients of given polynomial in BB form from the coefficients of polynomials of lower degree in BB form.

• Communications of the Korean Mathematical Society
• /
• v.23 no.2
• /
• pp.279-284
• /
• 2008

In this paper, we present the constrained Jacobi polynomial which is equal to the constrained Chebyshev polynomial up to constant multiplication. For degree n=4, 5, we find the constrained Jacobi polynomial, and for $n{\geq}6$, we present the normalized constrained Jacobi polynomial which is similar to the constrained Chebyshev polynomial.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.24 no.2 s.173
• /
• pp.535-542
• /
• 2000

This paper presents a method for the dynamic analysis of constrained multibody systems undergoing abrupt collision. The proposed method uses a longer time interval to check collision than that of c onventional method. This reduces the computational effort significantly. To calculate collision points on two colliding rigid bodies, one may introduce constraints of contact. However, this causes reduction of degree of freedom and difficulty of numerical analysis. The proposed method can calculate collision points without above mentioned problems. Three numerical examples are given to demonstrate the computational efficiency and the usefulness of the proposed method.

• Journal of the Korean Society of Manufacturing Process Engineers
• /
• v.7 no.2
• /
• pp.52-59
• /
• 2008

The objective of this study is to develop an automatic object changer unit to improve processing problems existed in the conventional horizontal machining center. To achieve this goal, this study designed a horizontal transfer as the second project continued to the first project that designed a upward and downward traverse unit. A horizontal traverse unit shows a symmetric structure and consists of frame, which consists of four unit tools, motor and reducer, which are fixed at a frame, operation unit with pinions, first traverse unit, and second traverse unit. Constraint conditions based on the operation mechanism with these elements were configured and obtained following results after modeling a model for a traverse motor. In the kinematic expression of sliding motion with one degree of freedom, the sliding motion is constrained. Also, the rack 3 installed at a frame is used to configure possible kinematic constraint conditions of the rack 2 according to the rolling motion of the pinion 2 in the first traverse unit. In addition, the moment of inertia that is a type of kinetic energy in a converted horizontal traverse unit in the side of the reducer can be applied to introduce the moment of inertia of a converted horizontal traverse unit in the side of the reducer by using the sum of kinetic energy in the rack and pinion, which is a part of the horizontal traverse unit. Also, the equation of motion of the converted upward and downward traverse unit in the side of the motor using the equation of motion of the motor. Furthermore, the horizontal traverse unit predetermines the mass of the first and second traverse unit and applied load including the radius and reduction ratio of the pitch circle in the pinion 1 and applied load to the rack 2. Then, a proper motor can be determined using several parameters in the upward and downward traverse unit in order to verify such predetermined specifications. In future studies later this study, a simulation that verifies the results of the previous two stages of studies using a finite element method.