• Journal of Institute of Control, Robotics and Systems
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• v.18 no.5
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• pp.496-501
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• 2012

An equilibrium point of a WIP (Wheeled Inverted Pendulum) with changing its center of gravity is derived and validated by various numerical simulations. Generally, the WIP has two equilibrium points which are unstable and stable one. The unstable one is interested in this study. To keep the WIP over the unstable equilibrium point, the WIP is consistently being adjusted. A state feedback controller for the WIP needs a control reference for the equilibrium point. The control reference can be obtained by studying an equilibrium point of the WIP based on statics. By using Lagrange method, this study is deriving dynamic equations of the WIP both with and without changing its center of gravity. Various numerical simulations are carried out to show the validation of the equilibrium point.

• Journal of Ocean Engineering and Technology
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• v.34 no.5
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• pp.334-341
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• 2020

Most towfish systems do not have propulsive devices and cannot compensate for perturbation motion, which can affect the observation data. This paper discusses attitude control of a towfish with elevators on the left and right tail wings to improve the quality of the observational data. Specifically, we investigate the relationships between the towing point, the center of gravity, and the drag forces produced by the elevators to clarify whether the elevators can control the attitude of the towfish sufficiently for various positions of the towing point and center of gravity. The feasible positions of the towing point and center of gravity are defined by mechanical analyses, and simulations are conducted to verify that the elevators can provide attitude control in these positions. The simulation results show that at some positions, the elevators can control the attitude quickly and sufficiently even if disturbances exist.

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

• Journal for History of Mathematics
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• v.34 no.4
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• pp.137-149
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• 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
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• v.18 no.5
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• pp.91-99
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• 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.

• Journal of the Korean Society for Precision Engineering
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• v.27 no.12
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• pp.41-47
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• 2010

There are many unbalanced models such as helicopter's rotor blades, small-sized precision motor in industrial applications. In the real products, their gravity center usually does not accord with the desired gravity center. If the deviation is large between them, it can be a major cause of vibration and noise as the part of model rotate. Therefore the gravity center in the rotational parts should be controlled properly because of static and dynamic balancing of the parts. In the research, the rotor blade of unmanned helicopter has been selected to obtain the high quality of balancing. In order to achieve the purpose, measuring system has been developed. In the system applied principle is three point weighting method, which is one of the Multiple-point Weighting Method. It has circle fitting for compensation of machining error, after measuring the values. From this study, the results showed that the proposed measurement procedure gives reliable and precise gravity center.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2009.06a
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• pp.541-542
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• 2009

• Journal of Educational Research in Mathematics
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• v.15 no.3
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• pp.335-352
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• 2005

In this paper, we consider a center of gravity of convex polygon which could be an enriched topic for the gifted in mathematics(7th grades) and suggested a case that the gifted experienced a center of gravity. Based on properties of Archimedes' center of mass, we define it as a point which make a polygon be in counterpoised with its area and explain how to find that point through using integral calculus or internal division. Then we consider that the gifted would experience various kinds of mathematical thinking and apply diverse ways of problem solving 3s searching for this topic. As this research, the teacher would be able to conduct the gifted with penetration into center of gravity and to let them participate in advanced learning courses which value ma-thematical thinking while they undergo similar experiences such as mathematicians.

• Journal of Korean Physical Therapy Science
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• v.8 no.2
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• pp.1059-1064
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• 2001

This study is aimed at diagnosing transmutation aspect with the respective of hemiplegia patient's static adaptation of posture which is influenced by anti-gravity excercise, center of gravity shifting movement and segmental movement adaption of the legs and arms by key-point control in the process of Bobatli's treatment approach. The patients for the investigation of this study were selected as a total 17 patients who were doing the physical-therapy in Tae-gu Rehabilitation Center, and diagnosed as hemiplegia patients by Rehabilitation Medicine department in Kyung-buk University hospital. And also, there investigated into temporal transition that keep the attitude with one-leg standing on the ground concerning static attitude adaption on the basis of the before of anti-gravity movement and the after of 4-weeks movement. The findings of this study were as follows: With the respective the time to keep standing pose by one-leg at static attitude transmutation, affected side showed meaningful differences as a l.86/sec, 2.62/sec at 4 weeks later considering the before and after of this experiment.(p<0.01), non-affected side at the aspect of attitude keeping time, but there didn't showed meaningful differences statistically.

• The Journal of Korea Robotics Society
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• v.6 no.4
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• pp.317-322
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• 2011

An augmented state feedback controller for a Wheeled Inverted Pendulum (WIP) is proposed in this research. The augmented state feedback controller is able to keep the WIP returning to the origin. Generally, the WIP has both stable and unstable equilibrium points. To keep the WIP over the unstable equilibrium point, the WIP consistently is being controlled. A simple state feedback controller is letting the WIP out of the origin when the center of gravity of the WIP locates out of the schematic center line. In some case of applications, it may not be desirable that the WIP is drifting out of the initial location. The proposed augmented state feedback controller is able to keep the WIP at the initial location whether its center of gravity lies out of the center line or not. Numerical simulations are carried out to show the validation of the augmented sated feedback controller.