• 제목/요약/키워드: equation of straight line

검색결과 70건 처리시간 0.026초

직선의 대수적 표현과 직선성(直線性)으로서의 기울기 (Revisiting Linear Equation and Slope in School Mathematics : an Algebraic Representation and an Invariant of Straight Line)

  • 도종훈
    • 한국수학교육학회지시리즈E:수학교육논문집
    • /
    • 제22권3호
    • /
    • pp.337-347
    • /
    • 2008
  • 도형으로서의 직선을 좌표평면에서 대수적으로 표현하는 과정에서 곧음이라는 직선의 고유한 성질은 삼각형의 닮음에 의해 x값의 변화량에 대한 y값의 변화량의 비가 일정하다는 성질로 구체화되고, 이로부터 기울기의 개념이 자연스럽게 등장한다. 이때 기울기는 좌표평면에서 직선의 직선다움 즉, 직선성(直線性)을 나타내주는 수학적 개념으로 서로 평행인 직선을 구분하지 않을 때 한 직선의 불변량이라 할 수 있고, 직선의 방정식은 일정한 비로서의 기울기가 지닌 성질을 대수적으로 표현한 것이라 할 수 있다. 본 논문에서는 좌표평면에서의 직선 및 직선성(直線性)으로서의 기울기 개념이 학교수학에서 어떻게 다루어지고 있는지 분석하고, 개선 방안에 대하여 논의한다.

  • PDF

회전하는 강체허브에서 전개하는 보 끝단의 직선궤적오차 저감 (Straight-line Path Error Reduction for the End of a Flexible Beam Deploying from a Rotating Rigid Hub)

  • 김병진;김형래;정진태
    • 한국소음진동공학회논문집
    • /
    • 제24권11호
    • /
    • pp.898-906
    • /
    • 2014
  • This paper presents a reduction method for a straight-line path error of a flexible beam deploying from a rotating rigid hub. Previous studies discussed about only vibration phenomena of flexible beams deploying from rotating hubs; however, this study investigates a vibration reduction of a rotating beam with variable length. The equation of motion and associated boundary conditions are derived for a flexible beam deploying from a rotating rigid hub, and then they are transformed to a variational equation. By applying the Galerkin method, the discretized equations are obtained from the variational equation. Based on the discretized equations, the dynamic responses of a rotating/deploying beam are analyzed when the beam end has a straight line motion. A reduction method for the trajectory error is proposed, using the average length of a rotating/deploying beam. It is shown that the proposed method is able to reduce the residual vibration of a rotating/deploying beam.

비대칭성이 고려된 나선형 시험 모델을 통한 손상 수상함의 직진 안정성 추정 (Estimation of Straight Line Stability of a Damaged Surface Combatant through Spiral Maneuver Test Model Considering Asymmetry)

  • 하정수;정연환
    • 시스템엔지니어링학술지
    • /
    • 제16권2호
    • /
    • pp.110-117
    • /
    • 2020
  • In this paper, we estimated the straight line stability by performing a 3 degree of freedom spiral test simulation of a intact/damaged surface combatant using the hydrodynamic coefficient obtained through the PMM(Planar motion mechanism) test based on system engineering process. A model ship was ONR Tumblehome and damaged compartment was set on the starboard bow. As a result of conducting a spiral test simulation based on the experimental results of J.Ha (2018), the asymmetric straight line stability due to the damaged compartment was confirmed. In the case of a ship in which the starboard bow was damaged, it was confirmed that it had the characteristic to deflect to the left when going straight. Also, when estimating the straight line stability of a both port and starboard asymmetric surface combatant, a separated equation of motion model that sees the port and starboard as different ships seems suitable.

격자형 용접선 추적을 위한 용접 이동로봇의 모델링 및 제어 (Modeling and Control of Welding Mobile Robot for the Tracking of Lattice Type Welding Seam)

  • 이근유;서진호;오명석;김상봉
    • 대한기계학회:학술대회논문집
    • /
    • 대한기계학회 2003년도 춘계학술대회
    • /
    • pp.923-928
    • /
    • 2003
  • This paper presents the motion control of a mobile robot with arc sensor for lattice type welding. Its dynamic equation and motion control method for welding speed and seam tracking are described. The motion control is realized in the view of keeping constant welding speed and precise target line even though the robot is driven along a straight line or comer. The mobile robot is modeled based on Lagrange equation under nonholonomic constraints and the model is represented in state space form. The motion control of the mobile robot is separated into three driving motions of straight locomotion, turning locomotion and torch slider controls. For the torch slider control, the proportional integral derivative (PID) control method is used. For the straight locomotion, a concept of decoupling method between input and output is adopted and for the turning locomotion, the turning speed is controlled according to the angular velocity value at each point of the comer with range of $90^{\circ}$ constrained to the welding speed. The proposed control methods are proved through simulation results and the results have proved that the mobile robot has enough ability to apply the lattice type welding line.

  • PDF

Modeling and Motion Control of Mobile Robot for Lattice Type Welding

  • Jeon, Yang-Bae;Kim, Sang-Bong
    • Journal of Mechanical Science and Technology
    • /
    • 제16권1호
    • /
    • pp.83-93
    • /
    • 2002
  • This paper presents a motion control method and its simulation results of a mobile robot for a lattice type welding. Its dynamic equation and motion control methods for welding speed and seam tracking are described. The motion control is realized in the view of keeping constant welding speed and precise target line even though the robot is driven for following straight line or curve. The mobile robot is modeled based on Lagrange equation under nonholonomic constraints and the model is represented in state space form. The motion control of the mobile robot is separated into three driving motions of straight locomotion, turning locomotion and torch slider control. For the torch slider control, the proportional-integral-derivative (PID) control method is used. For the straight locomotion, a concept of decoupling method between input and output is adopted and for the turning locomotion, the turning speed is controlled according to the angular velocity value at each point of the corner with range of 90$^{\circ}$ constrained to the welding speed. The proposed control methods are proved through simulation results and these results have proved that the mobile robot has enough ability to apply the lattice type welding line.

아크센서를 적용한 격자형 용접용 모빌 로봇의 제어 (Motion Control of Mobile Robot with Arc Sensor for Lattice Type Welding)

  • 전양배;한영대;김상봉
    • 대한기계학회:학술대회논문집
    • /
    • 대한기계학회 2001년도 춘계학술대회논문집B
    • /
    • pp.319-324
    • /
    • 2001
  • This paper presents the motion control of a mobile robot with arc sensor for lattice type welding. Its dynamic equation and motion control method for welding speed and seam tracking are described. The motion control is realized in the view of keeping constant welding speed and precise target line even though the robot is driven along a straight line or corner. The mobile robot is modeled based on Lagrange equation under nonholonomic constraints and the model is represented in state space form. The motion control of the mobile robot is separated into three driving motions of straight locomotion, turning locomotion and torch slider controls. For the torch slider control, the proportional integral derivative (PID) control method is used. For the straight locomotion, a concept of decoupling method between input and output is adopted and for the turning locomotion, the turning speed is controlled according to the angular velocity value at each point of the comer with range of $90^{\circ}$ constrained to the welding speed. The experiment has been done to verify the effectiveness of the proposed controllers. These results are shown to fit well by the simulation results.

  • PDF

직선의 방정식을 기반으로 한 프로젝터 영상의 기하왜곡 보정 (Geometric Distortion Compensation of Projector Image based on Equation of Straight Line)

  • 정정일;조진수
    • 인터넷정보학회논문지
    • /
    • 제11권5호
    • /
    • pp.27-35
    • /
    • 2010
  • 본 논문에서는 평면 스크린을 사용할 수 없는 휴대형 프로젝터의 사용 환경에서 평면이 아닌 임의의 영사면(혹은 벽면)의 기하학적 형태에 의해 발생되는 영상의 기하학적 왜곡을 효과적으로 보정할 수 있는 방법을 제안한다. 제안한 방법에서는 먼저 격자패턴을 임의의 영사면에 영사한 후 영사면의 형태에 따라 왜곡된 격자패턴과 원본 격자패턴 간의 기하학적 관계를 나타내는 직선의 방정식을 도출한다. 다음으로 영사면의 기하학적 형태에 따라 적절하게 적용될 수 있는 원본 격자패턴의 크기를 결정하여 도출된 직선의 방정식으로부터 왜곡된 영상을 대칭적으로 보정할 수 있는 보정패턴을 생성한다. 최종적으로 프로젝터로부터 영사될 실제 영상을 격자패턴과 동일하게 분할하여 보정패턴에 맞게 미리 워핑(warping)함으로써 영사된 영상의 기하학적 왜곡을 보정한다. 제안한 방법의 성능 평가를 위하여 평면 스크린을 사용할 수 없는 영사 환경에서 자주 접할 수 있는 영사면 형태들인 기울어진 평면, 꺾인 평면 및 곡면을 대상으로 영사 영상 보정에 대한 실험을 진행하였다. 실험결과로부터 일반적으로 발생하는 몇 가지 영사면의 형태들에 인한 기하학적 왜곡들이 적절히 보정되어 제안한 방법이 영사 영상의 기하학적 왜곡을 매우 효과적으로 보정할 수 있음을 알 수 있었다.

현장 열응답시험과 현장 대수성시험결과를 동시 분석 가능한 통합전산 Program에 관한 연구 (A Study on the Integrated Computer Program for the Multi Analysis of In-Situ Aquifer and Geothermal Response Test)

  • 한정상;한혁상;윤운상
    • 한국지열·수열에너지학회논문집
    • /
    • 제4권1호
    • /
    • pp.11-19
    • /
    • 2008
  • Groundwater flow in confined aquifer and heat transport in underground geologic media are using same governing equation(line source) like well fuction. Therefore the conventional slope method using only later data obtained from in-situ thermal response test to determine the thermal conductivity of vertical geothermal heat exchanger(GHEX) is basically identical with one of Theis straight line method of aquifer test under artesian condition. In case that the pumping rate(Q, $m^3$/d) and drawdown(s,m) which are used for input data of existing hydrogeologic computer programs for aquifer test are replaced and converted to supplying heat energy per unit length of bore hole(Q/L,w/m or Kcal/h.m) and temperatures (T,$^{\circ}C$)measured at in and out-let of GHEX as in put data respectively, thermal conductivity around geothermal heat exchanger can be easily estimated without any special modification of the existing hydrogeologic computer program. Two numbers of time series temperature variation data obtained from in situ geothermal response test are analized using Theismethods(standard curve and straight line method) by using existing aquifer test program and conventional Slope method proposed by ASHRAE. The results show that thermal conductivity values estimated by two straight methods are identical and the difference of estimated values between standard curve methods and Slope method are also within acceptable ranges. In general,the thermal conductivity estimated from Theis straight linemethod gives more accurate value than the one of Slope method due to that Slope method uses only visual matching otherwise Theis method uses automatic curve matching estimation with reducing RSS.

  • PDF

NUMERICAL MODELING OF TWO-DIMENSIONAL ADVECTION-DISPERSION IN OPEN CHANNEL

  • Lee, Myung-Eun;Kim, Young-Han;Seo, Il-Won
    • Water Engineering Research
    • /
    • 제4권1호
    • /
    • pp.45-58
    • /
    • 2003
  • Two-dimensional depth-averaged advection-dispersion equation was simulated using FEM. In the straight rectangular channel, the advection-dispersion processes are simulated so that these results can be compared with analyti-cal solutions for the transverse line injection and the point injection. In the straight domain the standard Galerkin method with the linear basis function is found to be inadequate to the advection-dispersion analysis compared to the upwind finite element scheme. The experimental data in the S-curved channel were compared with the result by the numerical model using SUPG(Streamline upwind Petrov-Galerkin) method.

  • PDF

AIGaAs/GaAs 이종접합 바이폴라 트랜지스터의 온도 변화에 따른 전기적 특성에 대한 연구 (Temperature Dependence of Electrical Characteristics of AIGaAs/GaAs Heterojunction Bipolar Transistors)

  • 박문평;이태우;김일호;박성호;편광의
    • 한국전기전자재료학회:학술대회논문집
    • /
    • 한국전기전자재료학회 1996년도 추계학술대회 논문집
    • /
    • pp.349-352
    • /
    • 1996
  • When the ideality factor of collector current of AIGaAs/GaAs Heterojunction Bipolar Transistors (HBTs) is larger than unity, conventional $I_{CO}$ / $T^2$ versus 1000/T plot used in the determination of the barrier height of base-emitter junction of HBT was deviated from the straight line. We introduced the effective temperature $T_{eff}$ as nT in the Thermionic-emission equation. The modified $I_{CO}$ /TB versus 1000/ $T_{eff}$ plot was on the straight line in the temperature range considered. The activation energy obtained from the modified plot is 1.61 eV. The conduction band discontinuity calculated using this value was 0.305 eV and this value is coincident with the generally accepted value of 0.3 eV. eV.

  • PDF