• Proceedings of the Korean Society of Precision Engineering Conference
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• 2008.11a
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• pp.9-10
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• 2008

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2010.11a
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• pp.331-332
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• 2010

• Journal of the Korean Society for Precision Engineering
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• v.30 no.6
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• pp.607-614
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• 2013

In this study, effect of the sensor gain error is theoretically analyzed and simulated when mixed sequential two-prove method(MTPM) is applied for the precision measurement of straightness error of a linear motion table. According to the theoretical analysis, difference of the gain errors between two displacement sensors increases measurement error dramatically and alignment error of the straightedge is also amplified by the sensor gain difference. On the other hand, if the gain errors of the two sensors are identical, most of error terms are cancelled out and the alignment error doesn't give any influence on the measurement error. Also the measurement error of the straightness error is minimized compared with that of the straightedge's form error owing to close relationship between straightness error and angular motion error of the table in the error terms.

• Proceedings of the Korea Society of Mathematical Education Conference
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• 2010.04a
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• pp.151-163
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• 2010

This study is to provide improved teaching methods on classical geometric construction education by a straightedge and compass in school mathematics. In this paper, justifications of construction methods of Korean textbooks, for perpendicular bisector of an segment and angle bisector are discussed, which can be directly applicable to teaching geometric construction meaningfully. Based on these considerations, several implications for desirable teaching methods concerning geometric construction were suggested.

• East Asian mathematical journal
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• v.26 no.2
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• pp.151-164
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• 2010

This study is to provide improved teaching methods on classical geometric construction education by a straightedge and compass in school mathematics. In this paper, justifications of construction methods of Korean textbooks, for perpendicular bisector of an segment and angle bisector are discussed, which can be directly applicable to teaching geometric construction meaningfully. Based on these considerations, several implications for desirable teaching methods concerning geometric construction were suggested.

• The Pure and Applied Mathematics
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• v.19 no.4
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• pp.315-325
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• 2012

Let A and B denote a point, a line or a circle, respectively. For a positive constant $a$, we examine the locus $C_{AB}$($a$) of points P whose distances from A and B are, respectively, in a constant ratio $a$. As a result, we establish some equivalent conditions for conic sections. As a byproduct, we give an easy way to plot points of conic sections exactly by a compass and a straightedge.

• Transactions of the Korean Society of Mechanical Engineers
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• v.12 no.1
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• pp.163-172
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• 1988

An off-line Geometric Adaptive Control Scheme is applied to the milling machine to identify its guideway errors. In the milling process, the workpiece fixed on the bed travels along the guideway while the tool and spindle system is fixed onto the machine. The scheme is based on the exponential smoothing of post-process measurements of relative machining errors due to the tool, workpiece and bed deflections. The guideway error identification system consists of a gap sensor, a, not necessarily accurate, straightedge, and the numerical control unit. Without a priori knowledge of the variations of the cutting parameters, the time-varying parameters are also estimated by an exponentially weighted recursive least squares method. Experimental results show that the guideway error is well identified within the range of RMS values of geometric error changes between machining passes disregarding the machining conditions.

• Journal of the Korean Society for Precision Engineering
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• v.24 no.3 s.192
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• pp.117-123
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• 2007

This paper describes a three-probe system that can be used to measure the parallelism and straightness of a pair of rails simultaneously. The parallelism is measured using a modified reversal method, while the straightness is measured using a sequential two-point method. The measurement algorithms were analyzed numerically using a pair of functionally defined rails to validate the three-probe system. Tests were also performed on a pair of straightedge rails with a length of 250 mm and a maximum straightness deviation of $0.05{\mu}m$, as certified by the supplier. The experimental results demonstrated that the parallelism-measurement algorithm had a cancellation effect on the probe stage motion error. They also confirmed that the proposed system could measure the slope of a pair of rails about $0.06{\mu}rad$. Therefore, by combining this technique with a sequential differential method to measure the straightness of the rails simultaneously, the surface profiles could be determined accurately and eliminate the stage error. The measured straightness deviation of each straight edge was less than $0.05{\mu}m$, consistent with the certified value.