• International Journal of CAD/CAM
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• v.8 no.1
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• pp.11-20
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• 2009

The conventional methods of boundary-conformed 2D surfaces generation usually yield some problems. This paper deals with two boundary-conformed 2D surface generation methods, one conventional approach, the linear Coons method, and a new method, boundary-conformed interpolation. In this new method, unidirectional 2D surface has been generated using some of the geometric properties of the given boundary curves. A method of simultaneous displacement of the interpolated curves from the opposite boundaries has been adopted. The geometric properties considered for displacements include weighted combination of angle bisector and linear displacement vectors at all the data-points of the two opposite generating curves. The algorithm has one adjustable parameter that controls the characteristics of transformation of one set of curves from its parents. This unidirectional process has been extended to bi-directional parameterization by superimposing two sets of unidirectional curves generated from both boundary pairs. Case studies show that this algorithm gives reasonably smooth transformation of the boundaries. This algorithm is more robust than the linear Coons method and capable of resolving the 2D boundary-conformed parameterization problems.

• School Mathematics
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• v.18 no.3
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• pp.589-609
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• 2016

In this study, researchers have modernly reinterpreted geometric solving of cubic equations presented by an arabic mathematician, Omar Khayyam in medieval age, and have considered the pedagogical significance of geometric solving of the cubic equations using two conic sections in terms of analytic geometry. These efforts allow to analyze educational application of mathematics instruction and provide useful pedagogical implications in school mathematics such as 'connecting algebra-geometry', 'induction-generalization' and 'connecting analogous problems via analogy' for the geometric approaches of cubic equations: $x^3+4x=32$, $x^3+ax=b$, $x^3=4x+32$ and $x^3=ax+b$. It could be possible to reciprocally convert between algebraic representations of cubic equations and geometric representations of conic sections, while geometrically approaching the cubic equations from a perspective of connecting algebra and geometry. Also, it could be treated how to generalize solution of cubic equation containing variables from geometric solution in which coefficients and constant terms are given under a perspective of induction-generalization. Finally, it could enable to provide students with some opportunities to adapt similar solving procedures or methods into the newly-given cubic equation with a perspective of connecting analogous problems via analogy.

• Journal of the Korean School Mathematics Society
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• v.18 no.4
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• pp.411-429
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• 2015

In this study we investigated the effects of using GSP in solving geometric problems. Especially we focused the effects of GSP in leveled students' connection of geometry and algebra. High leveled students prefer to use algebraic formula to solve geometric problems. But when they did not know the geometric meaning of their algebraic formula, they could recognize the meaning after using GSP. Middle and low leveled students usually used GSP to obtain hints to solve the problems. For the low leveled students GSP was usually used to understand the meaning of the problem, but it did not make them solve the problem.

• Journal of Educational Research in Mathematics
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• v.19 no.1
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• pp.143-161
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• 2009

This study was designed to gain insights into students' visualization process in geometric problem solving. The visualization model for analysing visual process for geometric problem solving was developed on the base of Duval's study. The subjects of this research are two Grade 9 students and six Grade 10 students. They were given 2D-geometric problems. Their written solutions were analyzed problem is research depicted characteristics of process of visualization of individually. The findings on the students' geometric problem solving process are as follows: In geometric problem solving, visualization provided a significant insight by improving the students' figural apprehension. In particular, the discoursive apprehension and the operative apprehension contributed to recognize relation between the constituent of figures and grasp structure of figure.

• Journal of Korean Institute of Industrial Engineers
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• v.21 no.3
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• pp.329-343
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• 1995

Traditionally, machining process sequence was influenced and constrained by the design information obtained from CAD data base, i.e., class of operations, geometric shape, tooling, geometric tolerance, etc. However, even though all the constraints from design information are considered, there may exist more than one way to feasibly machine parts. This research is focused on the integrated problem of operations sequencing and machine tools selection in the presence of the product mix and their production volumes. With the transitional costs among machining operations, the operation sequencing problem can be formulated as a well-known Traveling Salesman Problem (TSP). The transitional cost between two operations is expressed as the sum of total machining time of the parts on a machine for the first operation and transportation time of the parts from the first machine to a machine for the second operation. Therefore, the operation sequencing problem formulated as TSP cannot be solved without transitional costs for all operation pairs. When solved separately or serially, their mutual optima cannot be guaranteed. Machining operations sequencing and machine tool selection problems are two core problems in process planning for discretely machined parts. In this paper, the interrelated two problems are integrated and analyzed, zero-one integer programming model for the integrated problem is formulated, and the solution methods are developed using a Tabu Search technique.

• Journal of Educational Research in Mathematics
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• v.19 no.4
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• pp.531-543
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• 2009

This study identified what cognitive attributes are required of eighth graders to solve geometrical problems such as 'Recall,' 'Analyze,' 'Justify,' 'Synthesize/Integrate,' and 'Solve Non-routine Problems' by using the cognitive diagnostic theory. The five attributes are proved as the skills for solving the geometric problems. Many students have not fully mastered the attributes of 'Justify' and 'Synthesize/Integrate'. There was high correlation between these attributes. 'Analyze' best predicted the changes in the geometric achievement. And while students with high levels of geometrical achievement have mastered all the five attributes, those in the mid- and low-level range of performance have mastered fewer attributes.

• Journal of Korean Society for Quality Management
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• v.5 no.1
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• pp.23-29
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• 1977

Geometric programming is very useful for the solution of certain nonlinear programming problems in which the objective function and the constraints are posynomial expressions. By solving the dual program, it can be obtained that the solution of the primal program of Geometric programming. And, more efficient solution is to form an Augmented program possessing degree of difficult zero. A regional water-quality management problem may involve a multistage constrained optimization with many decision variables. In this problem, especially, appling that solution to it is also useful. This paper is described that : 1) the efficient solution of a water-quality management model formed by Geometric programming and 2) the algorithm developed to apply easily a real system by modifing and simplifing the solution.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2000.11a
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• pp.670-673
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• 2000

This paper attempt analysis and computer simulation of dynamics of a set of dual multi-joint fingers with soft-deformable tips which are grasping. Firstly, a set of differential equation describing dynamics of the fingers and object together with geometric constraint of tight area-contacts is formulated by Euler-Lagrange's formalism. Secondly, problems of controlling both the internal force and the rotation angle of the grasped object under the constraints of area-contacts of tight area-contacts are discussed. The effect of geometric constraints of area-contacts on motion of the overall system is analyzed and a method of computer simulation for overall system of differential-algebraic equations is presented. Finally, simulation results are shown and the effects of geometric constraints of area-contact is discussed.

• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.132.6-132
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• 2001

This paper aims to derive a mathematical model of the dynamics of handling tasks in field robot which stable grasping and manipulates a rigid object with some dexterity. Firstly, a set of differential equation describing dynamics of the manipulators and object together with geometric constraint of tight area-contacts is formulated by Lagrange equation. Secondly, problems of controlling both the internal force and the rotation angle of the grasped object under the constraints of area-contacts of tight area-contacts are discussed. The effect of geometric constraints of area-contacts on motion of the overall system is analyzed and a method of computer simulation for overall system of differential-algebraic equations is presented. Thirdly, simulation results are shown and the effects of geometric constraints of area-contact is discussed.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.9
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• pp.2284-2296
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• 1994

Force control of robotic mechanisms continues to be a challenging area. Previous implementation have seldom produced satisfactory results, and researchers in the past have experienced significant instability problems associated with their force controllers. In this study, a new stability factor in force control will be pointed out. When a manipulator is constrained to an environment(force-controlled), geometric instability due to the relationship between the manipulator configuration and the force-controlled direction is shown to be a significant factor in overall system stability. This exploratory study points out a rather intuitive, geometrically based stability factor in terms of an effective system stiffness and analyzes the phenomenon both analytically and graphically. Also, a stiffness control algorithm using the kinematic redundancy of a kinematically redundant manipulator is proposed to improve the overall stability in force control.