• Honam Mathematical Journal
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• v.37 no.4
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• pp.487-504
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• 2015

For a smooth plane curve, the curvature can be characterized by the rate of change of the angle between the tangent vector and a fixed vector. In this article we prove that the curvature of a space curve can also be given by the rate of change of the locally defined angle between the tangent vector at a point and the nearby point. By using height functions, we introduce turning angle of a space curve and characterize the curvature by the rate of change of the turning angle. The main advantage of the turning angle is that it can be used to characterize the curvature of discrete curves. For this purpose, we introduce a discrete turning angle and a discrete curvature called visual curvature for space curves. We can show that the visual curvature is an approximation of curvature for smooth curves.

• Journal of The Korean Society of Integrative Medicine
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• v.7 no.3
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• pp.149-157
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• 2019

Purpose : This study aims to check the relationship between the size of curvature in scoliosis patients and the reduction rate of curvature after wearing a brace and the relationships of the size of curvature and correction angle with Body Mass Index (BMI). Methods : With 30 adolescent girls who had never worn a brace, their Cobb angle and BMI were measured before manufacturing braces, and their corrected Cobb angle was measured after wearing the manufactured scoliosis braces. Results : The size of the major curvature before wearing the brace and the reduction rate of the curvature after putting it on had a negative correlation in both the major curvature (r=-.465, p<.01) and the minor curvature (r=-.516, p<.01). The size of the minor curvature and the reduction rate of the minor curvature before and after putting it on also had a negative correlation (r=-.429, p<.05). As for the relationship between the size of curvature and BMI, they had a negative correlation in both the major curvature (r=-.141) and the minor curvature (r=-.123), and as for the relationship between the reduction rate of curvature and BMI after wearing the brace, they had a positive correlation in both the major curvature (r=.251) and the minor curvature (r=.136); however, it was not statistically significant (p>.05). Conclusion : In conclusion, the larger the size of curvature, the lower the reduction rate of curvature after wearing the brace became. The larger the size of curvature, the lower the BMI became. The higher the BMI, the higher the correction ratio of the brace became. Therefore, it is judged that it is necessary to provide early treatment and manage body composition before scoliosis progresses.

• Journal of Korean Neurosurgical Society
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• v.52 no.5
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• pp.447-451
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• 2012

Objective : To characterize the importance of the vertical angle of the sacral curvature (VASC) in lumbar disc herniations. Methods : Morphological data derived from lumbar sagittal MRI imaging. The statistical significance of the findings are discussed. The angles of 60 female patients with lumbar disc herniations (LDH) were compared with the 34 female patients without LDH. Results : 128 of the 185 patients met our inclusion criteria. The vertical angle of sacral curvature is statistically significantly bigger in females with lumbar disc herniations when compared to subjects in control group, 28.32 and 25.4, respectively. (p=0.034<0.05). Same difference was not seen in males. Conclusion : The vertical angle of sagittal sacral curvature may be another risk factor in females with lumbar disc herniations.

• Restorative Dentistry and Endodontics
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• v.37 no.2
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• pp.104-109
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• 2012

Objectives: The purpose of this study was to evaluate the buccolingual curvature at the apical one third in type II mesial canals of mandibular molars using the radius and angle of curvature. Materials and Methods: Total 100 mandibular molars were selected. Following an endodontic access in the teeth, their distal roots were removed. #15 H- or K-files (Dentsply Maillefer) were inserted into the mesiobuccal and mesiolingual canals of the teeth. Radiographs of the teeth were taken for the proximal view. Among them, type II canals were selected and divided into two subgroups, IIa and IIb. In type IIa, two separate canals merged into one canal before reaching the apex and in type IIb, two separate canals merged into one canal within the apical foramen. The radius and angle of curvature of specimens were examined. Results: In type II, mean radius of curvature in mesiolingual and mesiobuccal canals were 2.82 mm and 3.58 mm, respectively. The radius of the curvature of mesiolingual canals were significantly smaller than that of mesiobuccal canals in type II, and especially in type IIa. However, there were no statistically significant differences in radius of curvature between mesiobuccal and mesiolingual canals in type IIb and there were no significant differences in angle of curvature between type IIa and IIb. Conclusion: In this study, type II mesial canals of mandibular molars showed severe curvature in the proximal view. Especially, mesiolingual canals of type IIa had more abrupt curvature than mesiobuccal canals at the apical one third.

• The Journal of Churna Manual Medicine for Spine and Nerves
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• v.5 no.1
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• pp.31-40
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• 2010

Objectives: To investigate the change of the cervical spine curvature after whiplash injury. Methods: Clinical study carried out in 46 patients who already had neck pain and took a cervical lateral X-Ray in Jaseng Oriental hospital. these patients had whiplash injury whitin one year. We followed up the cervical lateral X-Ray after that. Cervical spine curvature was measured using four measuring method. Type of cervical spine curvature was analyzed by Jochumsen method, Ishihara Index. T-test was used. Results: By Jackson's Angle and Cobb's angle, it is tend to be more Iordotic curvature after whiplash injury. In Jochumsen method, Ishihara Index the cervical spine curvature was significantly increased their Iordotic angle(P<0.05). Conclusion: The results suggest that after whiplash injury, patients cervical curvature change more Iordortic curve.

• The Journal of Churna Manual Medicine for Spine and Nerves
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• v.1 no.2
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• pp.111-123
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• 2006

Objectives: This study is performed to evaluate the clinical effect of chuna therapy on the neck pain associated with kyphotic cervical curvature. Methods: This study carried out on three patients with neck pain & kyphotic cervical curvature who have received treatment in Depar1ment of Oriental Rehabilitation Medicine, Daejon Oriental Hospital of Daejon University from 28th July 2006 to 3th November 2006. Pre and post treatment, We evaluated the cervical angle, Jackson's angle, Jochumsen method, Ishihara index, VAS and effective score of treatment. Results & Conclusions: Two patients who received Chuna treatment recovered cervical curvature and improved neck pain. But One patient who dosen't received Chuna treatment was no improvement in cervical curvature & neck pain.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2006.05a
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• pp.377-378
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• 2006

The knuckle crane mainly consists of six parts such as swing, main boom, outer boom, extension boom, hydraulic rotor and knuckle. And the hydraulic rotor is connected at the end of extension boom has rotor block, rotor body, rotor vane. In this study, we carried out kinematics analysis of the hydraulic rotor block curvature for a knuckle crane. Then, we showed the formula to establish the radius of a circumscribed circle to form the rotor block curvature. Third, we analyzed the stress at each point of the rotor block curvature according to the contact angle. From the result of this study, we designed the rotor block curvature with a proper contact angle for a knuckle crane to guarantee the stability of hydraulic rotor.

• Journal of the Korean Society for Precision Engineering
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• v.17 no.8
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• pp.113-119
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• 2000

There are two major factors which affect the cam design : the pressure angle and the radius of curvature, Cam shape will have an instantaneous radius of curvature at every point. Even though the design constraint of the pressure angle has been satisfied the follower may still not complete the desired contact motion. If the radius of the follower roller is larger than the concave(negative) radius on the cam it occurs the gap between the cam and the follower roller at the contact point. And also if the curvature of the pitch curve of the cam is too sharp the cam profile may be undercut. This paper proposes a new approach which uses the relative velocity of the follower roller parallel to the tangent line at the contact point on the cam surface for determining the pressure angle and the relative acceeration for determining the radius of curvature.

• Journal of Korean Medicine Rehabilitation
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• v.25 no.4
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• pp.83-92
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• 2015

Objectives To measure and analyze the curvature of the cervical spine for university students. Methods This study carried out on 132 students. The cervical spine curvature was measured by six measuring methods. The type and numeric value of cervical spine curvature was analyzed by Angle of cervical curve (C1~C7), Angle of cervical curve (C2~C7), Jackson's angle, Ishihara Index, Depth of cervical curve and Method of Jochumsen. Cervical spine curvatures between male and female are compared by Mann-Whitney test. Rate of type of cervical curvature between male and female are compared by linear by linear association. Results 1. The average of angle of cervical curve (C1~C7) is $33.78{\pm}9.85^{\circ}$, angle of cervical curve (C2~C7) is $10.28{\pm}8.12^{\circ}$. The average of Jackson's angle is $14.02{\pm}10.01^{\circ}$, average of Ishihara Index is $8.46{\pm}10.58%$. The average of Depth of cervical curve is $5.15{\pm}4.72mm$ and average of Method of Jochumsen is $0.94{\pm}3.83mm$. 2. More than half of student's cervical curvature showed hypolordosis except Ishihara index. 3. There was significant difference in numeric value of cervical curvature between male and female both groups in terms of Ishihara index. 4. There were insignificant differences between male and female in terms of type of cervical curvature. Conclusions According to above results, we found out average of student's cervical curve. And the results suggest that most of the student's cervical curvature decrease.

• Journal of the Korean Institute of Landscape Architecture
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• v.28 no.2
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• pp.10-16
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• 2000

The purpose of this study is to identify relationships between a central angle and a radius of curvature of divided roads in flat terrain of traditional villages, suggesting layout criteria for traditional villages: Nak-an, Sung-Eup, Ha-Whe. This study is sought to find the optimum model through the various SAS regression analyses. a regression analysis of this data was adopted to induce the relationship formula between a central angle of curve and a radius of curvature. Results of this study are as follows: 1) Most of the divided roads in traditional villages have a complex curve rather than a simple curve. 2) A central angle of curve has ranged from 11$^{\circ}$to 127$^{\circ}$, with a mean degree of 63.9. 3) In the lower level of central angle(11-40$^{\circ}$), the branch roads have distributed with a high frequency, but with a low frequency in the higher level of central angle(90-140$^{\circ}$). 4) A radius of curvature in the divided roads has ranged from 0.9m to 59.6, but half of the roads have concentrated on 1-6m of the curvature. 5) Compared to the result of hilly villages in previous study(Ahn, 1999), value of central angels in flat villages is lower than that of hilly villages, while a mean value of the curvature is higher than that of hilly villages. 6) A Non-linear regression analysis, resulting from the SAS application, was useful method to induce a relationship formula between a central angle and a radius of curvature in the branch roads. Our study's formula is as follow: R=100.3*EXP(-0.06*$\delta$)+3.91. 7) Our study model has less error than that of the Kishizuka's method, being applicable to a broader range of the branch roads. 8) A minimum radius of curvature in our study has showed 3.9m, suggesting to reconsider applications of the Kishizuka's(5.8m) in the footpass design, In the study for this presupposition model the efficiency and utility of it can be estimated to grow large according to how much and how far it includes both extremes of data. This study is for the application to a design in future through the numerical formula of divided roads of various traditional villages. The studies from now on will be about the quasi-hilly quasi-hilly village and hilly village supplementing these factors more.