• Journal for History of Mathematics
• /
• v.34 no.4
• /
• pp.137-149
• /
• 2021

The center of gravity of a triangle is the center of a physical shape. This is the content in the second grade of middle school, 'The Use of Similarity'. Unlike the cases of circumcenter and incenter, which are easily recognized visually, it is not easy for teachers to guide students with the visual meaning of center of gravity. According to the survey results, students, regardless of academic achievement, grade, and major, perceived the center of gravity of various plane figure as the center of their shape within a limited area through visual judgment. With reference to the results and contents of this process, it is hoped that the point of the three medians is meaningful not only in argumentative definition that the intersection of the triple line is the center of gravity of the triangle, but also in the center of a figure.

• Transactions of the Korean Society of Automotive Engineers
• /
• v.18 no.5
• /
• pp.91-99
• /
• 2010

The center of gravity on vehicle is a fundamentally important point for assessing and measuring the characteristics of vehicle dynamics. Especially, the center of gravity height on vehicles is the closest factor with respect to rollover accidents in a social issue nowadays. In this paper, the center of gravity height in conjunction with vehicle parameters of vehicle weight, driving axle and roof height after measured by vehicle weight and loading location by means of VCGM developed by KATRI with good performance that the accuracy was less than 0.6% and repeatability 0.3% for vehicles being used in the whole world was observed. As a result of study, the location of center of gravity height on vehicle was able to be estimated with only roof height on vehicle.

• The Transactions of the Korean Institute of Electrical Engineers D
• /
• v.49 no.5
• /
• pp.257-263
• /
• 2000

One of the basic assumptions in the static gait design for a walking robot is that the weight of leg should be negligible compared to that of body, so that the total gravity center is not affected by swing of a leg. Based on the ideal assumption of zero leg-weight, conventional static gait has been simply designed for the gravity center of body to be inside the support polygon, consisting of each support leg's tip position. In case that the weight of leg is relatively heavy, however, while the gravity center of body is kept inside the support polygon, the total gravity center of walking robot can be out of the polygon due to weight of a swinging leg, which causes instability in walking. Thus, it is necessary in the static gait design of a real robot a compensation scheme for the fluctuation in the gravity center. In this paper, a body impedance control is proposed to obtain the total gravity center based on foot forces measured from load cells of a real walking robot and to adjust its position to track the pre-designed trajectory of the corresponding ideal robot's body center. Therefore, the walking stability is secured even in case that the weight of leg has serious influence on the total gravity center of robot.

• Journal of Korean Society of Occupational and Environmental Hygiene
• /
• v.22 no.3
• /
• pp.257-264
• /
• 2012

Objectives: This study's aims were to evaluate the effects of load center of gravity within an object lifted and feet placements on peak EMG amplitude acting on bilateral low back muscle groups, and to suggest adequate foot strategies with an aim to reducing low back pain incidence while lifting asymmetric load. Methods: The hypotheses that asymmetric load imposes more peak EMG amplitude on low back muscles contralateral to load center of gravity than symmetric load and maximum peak EMG amplitude out of bilateral ones can be relieved by locating one foot close to load center of gravity in front of the other were established based on biomechanics including safety margin model and previous researches. 11 male subjects were required to lift symmetrically a 15.8kg object during 2sec according to each conditions; symmetric load-parallel feet (SP), asymmetric load-parallel feet (AP), asymmetric load-one foot contralateral to load center of gravity in front of the other (AL), and asymmetric load-one foot ipsilateral to load center of gravity in front of the other (AR). Bilateral longissimus, iliocostalis, and multifidus on right and left low back area were selected as target muscles, and asymmetric load had load center of gravity 10cm deviated to the right from the center in the frontal plane. Results: Greater peak EMG amplitude in left muscle group than in right one was observed due to the effect of load center of gravity, and mean peak EMG amplitudes on both sides was not affected by load center of gravity because of EMG balancing effect. However, the difference of peak EMG amplitudes between both sides was significantly affected by it. Maximum peak EMG amplitude out of both sides and the difference of peak EMG amplitude between both sides could be reduced with keeping one foot ipsilateral to load center of gravity in front of the other while lifting asymmetric load. Conclusions: It was likely that asymmetric load lead to the elevated incidence of low back pain in comparison with symmetric load based on maximum peak EMG amplitude occurrence and greater imbalanced peak EMG amplitude between both sides. Changing feet positions according to the location of load center of gravity was suggested as one intervention able to reduce the low back pain incidence.

• Journal of the Korea Society of Computer and Information
• /
• v.29 no.1
• /
• pp.263-271
• /
• 2024

This paper analysis of spatial differences in the efficiency of regional industrial enterprises in China from 2011 to 2021. The efficiency analysis uses the DEA-CCR model. The input variables for efficiency analysis are total assets and annual average employees, and the output variables are revenue from principal business and total profits. Using trend surface analysis and gravity center model, to analysis the spatial differences of efficiency in different regions. From the results of the gravity center model, the coordinates of the gravity center of China's regional industrial enterprise efficiency in 2011 are 112.303°E & 34.239°N, and 2021 are 111.753°E & 33.791°N, which indicates that the gravity center of the efficiency of China's regional industrial enterprises in the 2011-2021 period generally moves to the southwest. From the results of the trend surface analysis, the efficiency of industrial enterprises in China's regional industrial enterprises appears to show spatial differences in both the eastwest and the northsouth directions.

• Journal of Biosystems Engineering
• /
• v.41 no.3
• /
• pp.170-176
• /
• 2016

Purpose: This study aimed to improve the method for determining the position of the center of gravity for agricultural tractors. Methods: The proposed method uses trigonometric functions and coordinate transformation. Data were measured according to the ISO 789-6 test procedures for the center of gravity of agricultural tractors. The height calculated using the proposed method was compared with that determined from an AutoCAD drawing. To find the center of gravity of the tractor, the algorithm for finding the intersection of the two lines was used. Results: The vertical height from the ground to the center of gravity is 682.06 mm. The vertical coordinates obtained from the calculation and the drawing were the same. Conclusions: The developed method uses trigonometric and polar coordinate transformation. The method was compared and verified with the AutoCAD drawing results. The results indicate that users can apply this developed method instead of the plotting method which is an inconvenient and time-consuming. Further, users can program Microsoft Excel to easily determine the vertical coordinate. In addition, researchers will propose this method to the ISO as a standard method for determining the center of gravity in accordance with ISO 789-6.

• Journal for History of Mathematics
• /
• v.26 no.5_6
• /
• pp.371-388
• /
• 2013

In ${\ll}$The Method${\gg}$, Archimedes presented the famous heuristic technique for calculating areas, volumes and centers of gravity of various plane and solid figures, utilizing the law of the lever. In that treatise, Archimedes used the fact that the center of gravity of a cone lies one-quarter of the way from the center of the base to the vertex, but the proof of this is not extant in his works. This study analyzes the propositions and their relations of ${\ll}$The Method${\gg}$ focusing on the procedural characteristics of the 'method' of Archimedes. According to the result of that analysis, this study discusses the likely approach which was taken for Archimedes to find out the center of gravity of a cone.

• Kyungpook Mathematical Journal
• /
• v.55 no.2
• /
• pp.473-484
• /
• 2015

Archimedes determined the center of gravity of a parabolic section as follows. For a parabolic section between a parabola and any chord AB on the parabola, let us denote by P the point on the parabola where the tangent is parallel to AB and by V the point where the line through P parallel to the axis of the parabola meets the chord AB. Then the center G of gravity of the section lies on PV called the axis of the parabolic section with $PG=\frac{3}{5}PV$. In this paper, we study strictly locally convex plane curves satisfying the above center of gravity properties. As a result, we prove that among strictly locally convex plane curves, those properties characterize parabolas.

• Korean Journal of Applied Biomechanics
• /
• v.13 no.3
• /
• pp.199-215
• /
• 2003

The purpose of this study was to attempt new starting motion and supply present starting motion in the 500M short track speed skating according to the center of gravity position. The center of gravity position ratio was divided starting motion into five(type A : front 80%-back 20%, type B front 70%-back 30%, type C : front 50%-back 50%, type D : front 30%-back 70%, type E : front 20%-back 80%). The three dimension motion analysis with DLT(direct linear transformation) method was executed using two video cameras. The following conclusion was that It was appear that reaction and execution time in starting motion was the most short in type B. It was characteristic that step of skaters was shorten and center of gravity position ratio was not effect to change of the step in each event. It was appear that the displacement of type D and type E were longer than that type A and type B during the starting motion. It was appear that skill types of center of gravity position ratio to the front were lower than that to the back and contract a posture. Observing the above, it was conclusion that skill type B of center of gravity position ratio to the tent was more effect than that to the back. But it is important that these skill type was most used to the competition and estimate the result.

• Korean Journal of Applied Biomechanics
• /
• v.14 no.3
• /
• pp.285-299
• /
• 2004

The purpose of this study is to identify female 500m sprint start motion by the center of gravity position in short track speed skating. The center of gravity position ratio was divided into three type(type A front : 80%-back : 20%, type B front : 70%-back 30%, type C front: 50%-back : 50%). Three video cameras were used for 3D motion analysis with DLT method and the results were as follows: The elapsed time in starting motion was appeared that type B was the shortest and type A was the longest. It was appear that the stroke length of type A was longer than that type B and C during starting phase. This result was similar to displacement of center of gravity. It was appeared that skill type of center of gravity position ratio type B' ankle and knee joint angle were lower than that of type A and C. Observing these results it was conclusion that skill type B of center of gravity position ratio was more faster than that of type A and C. But it is important that these skill type needed to verifying more subjects.