• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제20권2호
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• pp.151-161
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• 2016

In this paper, we present a $C^3$ quartic B-spline approximation of circular arcs. The Hausdorff distance between the $C^3$ quartic B-spline curve and the circular arc is obtained in closed form. Using this error analysis, we show that the approximation order of our approximation method is six. For a given circular arc and error tolerance we find the $C^3$ quartic B-spline curve having the minimum number of control points within the tolerance. The algorithm yielding the $C^3$ quartic B-spline approximation of a circular arc is also presented.

• 한국기계가공학회지
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• 제10권3호
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• pp.33-38
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• 2011

A cubic spline trajectory planner with arc-length parameter is formulated with estimation by summing up to the 3rd order in Taylor's expansion. The PVAJT motion planning is presented to reduce trajectory calculation time at every cycle time of servo control loop so that it is able to generate cubic spline trajectory in real time. This method can be used to more complex spline trajectory. Several case studies are executed with different values of cycle time and sampling time, and showed the advantages of the PVAJT motion planner. A DSP-based motion controller is designed to implement the PVAJT motion planning.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제17권3호
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• pp.171-179
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• 2013

In this paper we present a method of circular arc approximation by quartic B$\acute{e}$zier curve. Our quartic approximation method has a smaller error than previous quartic approximation methods due to the alternation of the error function of our quartic approximation. Our method yields a closed form of error so that subdivision algorithm is available, and curvature-continuous quartic spline under the subdivision of circular arc with equal-length until error is less than tolerance. We illustrate our method by some numerical examples.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 2001년도 춘계학술대회 논문집
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• pp.492-495
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• 2001

In order to utilize a parallel machine tool for CAM system, the development of adequate interpolator is necessary. This paper presents a quintic B-spline interpolator with algorithm of limiting maximum interpolation error. The favored property of near arc-length parametrization in the curve representation is used in the implementation of the reference command generation. Then, this interpolator is applied to cubic parallel manipulator to show its validity.

• 한국공작기계학회논문집
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• 제13권3호
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• pp.113-118
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• 2004

In this paper, we propose a new weaving trajectory algorithm for the arc welding of a articulated manipulator. The algorithm uses the theory of Bezier spline. We make a comparison between the conventional algorithms using Catmull-Rom curve and the new algorithms using Bezier spline. The proposed algorithm has been evaluated based on the MATLAB environment in order to illustrate its good performance. Through simulations, the proposed algorithm can result in high-speed and flexible weaving trajectory planning so that it's trajectory cannot penetrate into a base metal compared to the conventional algorithm using Catmull-Rom curve.

• Journal of Welding and Joining
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• 제34권1호
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• pp.54-58
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• 2016

In this research paper, suggest method of generate same bead as an actual measurement data in virtual welding conditions, exploit morphology information of the bead that acquired through robot welding. It has many multiple risk factors to Beginners welding training, by we make possible to train welding in virtual reality, we can reduce welding training risk and welding material to exploit bead visualization algorithm that we suggest so it will be expected to achieve educational, environmental and economical effect. The proposed method is acquire data to each case performing robot welding by set the voltage, current, working angle, process angle, speed and arc length of welding condition value. As Welding condition value is most important thing in decide bead form, we would selected one of baseline each item and then acquired metal followed another factors change. Welding type is FCAW, SMAW and TIG. When welding trainee perform the training, it's difficult to save all of changed information into database likewise working angle, process angle, speed and arc length. So not saving data into database are applying the method to infer the form of bead using a neural network algorithm. The way of bead's visualization is applying the spline algorithm. To accurately represent Morphological information of the bead, requires much of morphological information, so it can occur problem to save into database that is why we using the spline algorithm. By applying the spline algorithm, it can make simplified data and generate accurate bead shape. Through the research paper, the shape of bead generated by the virtual reality was able to improve the accuracy when compared using the form of bead generated by the robot welding to using the morphological information of the bead generated through the robot welding. By express the accurate shape of bead and so can reduce the difference of the actual welding training and virtual welding, it was confirmed that it can be performed safety and high effective virtual welding education.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2003년도 ICCAS
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• pp.2743-2746
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• 2003

In this paper, we propose a new weaving trajectory algorithm for the arc welding of a articulated manipulator. The algorithm uses the theory of Bezier spline. We make a comparison between the conventional algorithms using Catmull-Rom curve and the new algorithms using Bezier spline. The proposed algorithm has been evaluated based on the MATLAB environment in order to illustrate its good performance. The algorithm has been implemented on to the industrial manipulator of DR6 so as to show its real possibility. Through simulations and real implementations, the proposed algorithm can result in high-speed and flexible weaving trajectory planning and can reduce the processing time because it needs one-half calculation compared to the conventional algorithm using Catmull-Rom curve.

• 아태비즈니스연구
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• 제9권2호
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• pp.1-13
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• 2018

Physics simulation is an important part of many interactive 2D applications and collision detection and response is key component of this simulation. While methods for reducing the number of collision tests that need to be performed has been well researched, methods for performing the final checks with collision primitives have seen little recent development. This paper presents a new collision primitive, the n-arc, constructed from piecewise circular curves or biarcs. An algorithm for performing a collision check between these primitives is presented and compared to a convex polygon primitive. The n-arc is shown to exhibit similar, though slightly slower, performance to a polygon when no collision occurs, but is considerably faster when a collision does occur. The goodness of fit of the new primitive is also compared to a polygon. While the n-arc often gives a looser fit in terms of area, the continuous tangents of the n-arcs makes them a good choice for organic, soft or curved surfaces.

• 한국정밀공학회지
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• 제14권2호
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• pp.102-112
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• 1997

This paper describes the method that can construct kinematically admissible velocity fields for forging of gear-like components which have tooth shape around the cylinder. The kinematically admissible velo- city fields for the various gear-like components, involute spur gear, trapezoidal spline, square spline, ser- ration and trochoidal gear, were constructed by pilling up the velocity components according to the shape of tooth and billet. The billets, of hollow and solid, were Al 2218 and 2024. To verify the method, the analyses and experiments were carried out and compared with each other. For analyses, the half pitches of com- ponents were divided into several deformation regions based on their tooth profile. A neutral surface was used to represent the inner flow of material during forging. Its location varied with the energy optimazation and its contour varied with the number of teeth. In experiment, the contour of material filling up the tooth zone is hyperbolic curve caused by the frictional drag on the interface of die-wall/workpiece but, in the analysis, it is an arc which retains the same contour during all forging operation.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2007년도 정기 학술대회 논문집
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• pp.577-582
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• 2007

A variational formulation for plane elasticity problems is derived based on an isogeometric approach. The isogeometric analysis is an emerging methodology such that the basis functions in analysis domain arc generated directly from NURBS (Non-Uniform Rational B-Splines) geometry. Thus. the solution space can be represented in terms of the same functions to represent the geometry. The coefficients of basis functions or the control variables play the role of degrees-of-freedom. Furthermore, due to h-. p-, and k-refinement schemes, the high order geometric features can be described exactly and easily without tedious re-meshing process. The isogeometric sensitivity analysis method enables us to analyze arbitrarily shaped structures without re-meshing. Also, it provides a precise construction method of finite element model to exactly represent geometry using B-spline base functions in CAD geometric modeling. To obtain precise shape sensitivity, the normal and curvature of boundary should be taken into account in the shape sensitivity expressions. However, in conventional finite element methods, the normal information is inaccurate and the curvature is generally missing due to the use of linear interpolation functions. A continuum-based adjoint sensitivity analysis method using the isogeometric approach is derived for the plane elasticity problems. The conventional shape optimization using the finite element method has some difficulties in the parameterization of boundary. In isogeometric analysis, however, the geometric properties arc already embedded in the B-spline shape functions and control points. The perturbation of control points in isogeometric analysis automatically results in shape changes. Using the conventional finite clement method, the inter-element continuity of the design space is not guaranteed so that the normal vector and curvature arc not accurate enough. On tile other hand, in isogeometric analysis, these values arc continuous over the whole design space so that accurate shape sensitivity can be obtained. Through numerical examples, the developed isogeometric sensitivity analysis method is verified to show excellent agreement with finite difference sensitivity.