• Title/Summary/Keyword: Lagrange's Method

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Spacecraft Rendezvous Considering Orbital Energy and Wait Time (에너지와 대기시간을 고려한 우주비행체 랑데부)

  • Oghim, Snyoll;Leeghim, Henzeh
    • Journal of the Korean Society for Aeronautical & Space Sciences
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    • v.45 no.9
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    • pp.775-783
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    • 2017
  • In this paper, an impulsive rendezvous problem by using minimum energy of spacecraft in different orbits is addressed. In particular, the orbits considered in this paper are the general orbits including the elliptic orbit, while most of the orbits considered in the literature have been restricted within co-planar or circular orbits. The constraints for solving this optimization problem are the Kepler's equation formulated with the universal variable, and the final position and velocity of two spacecraft. Also, the Lagrange coefficients, sometimes called as f and g solution, are used to describe the orbit transfer. The proposed method technique is demonstrated through numerical simulation by considering the minimum energy, and both the minimum energy and the wait time, respectively. Finally, it is also verified by comparing with the Hohmann transfer known as the minimum energy trajectory. Although a closed-form solution cannot be obtained, it shows that the suggested technique can provide a new insight to solve various orbital transfer problems.

Kinematic and Dynamic Analyses of Human Arm Motion

  • Kim, Junghee;Cho, Sungho;Lee, Choongho;Han, Jaewoong;Hwang, Heon
    • Journal of Biosystems Engineering
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    • v.38 no.2
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    • pp.138-148
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    • 2013
  • Purpose: Determining an appropriate path is a top priority in order for a robot to maneuver in a dynamically efficient way especially in a pick-and-place task. In a non-standardized work environment, current robot arm executes its motion based on the kinematic displacements of joint variables, though resulting motion is not dynamically optimal. In this research we suggest analyzing and applying motion patterns of the human arm as an alternative to perform near optimum motion trajectory for arbitrary pick-and-place tasks. Methods: Since the motion of a human arm is very complicated and diverse, it was simplified into two links: one from the shoulder to the elbow, and the other from the elbow to the hand. Motion patterns were then divided into horizontal and vertical components and further analyzed using kinematic and dynamic methods. The kinematic analysis was performed based on the D-H parameters and the dynamic analysis was carried out to calculate various parameters such as velocity, acceleration, torque, and energy using the Newton-Euler equation of motion and Lagrange's equation. In an attempt to assess the efficacy of the analyzed human motion pattern it was compared to the virtual motion pattern created by the joint interpolation method. Results: To demonstrate the efficacy of the human arm motion mechanical and dynamical analyses were performed, followed by the comparison with the virtual robot motion path that was created by the joint interpolation method. Consequently, the human arm was observed to be in motion while the elbow was bent. In return this contributed to the increase of the manipulability and decrease of gravity and torque being exerted on the elbow. In addition, the energy required for the motion decreased. Such phenomenon was more apparent under vertical motion than horizontal motion patterns, and in shorter paths than in longer ones. Thus, one can minimize the abrasion of joints by lowering the stress applied to the bones, muscles, and joints. From the perspectives of energy and durability, the robot arm will be able to utilize its motor most effectively by adopting the motion pattern of human arm. Conclusions: By applying the motion pattern of human arm to the robot arm motion, increase in efficiency and durability is expected, which will eventually produce robots capable of moving in an energy-efficient manner.

A Study on the Impact Fracture of Fragile Materials (취성재료의 충격파괴에 관한 연구 II)

  • 양인영;김택현;정낙규;이상호;김선규
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.14 no.6
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    • pp.1417-1425
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    • 1990
  • In this paper, when the glass plate of fragile material is subjected to impact load, the fracture pattern and the generation phenomenon of cone crack were theoretically clarified by using the analysis method of impulsive stress in the first paper. The numerical analysis results of strain distribution at a distance of 0.1cm, from the impact loading point to 5cm, were compared with experimental results. The main conclusions obtained are as follows; (1) The generation phenomenon of cone crack at the impact fracture of the glass plate can be analytically confirmed by using the three dimensional dynamic theory of elasticity. And the numerical analysis results of strain distribution using this theory are relatively in close agreement with the crack size obtained from the impact fracture experiment. (2) After the stress wave generated at the impact point propagated to the spherical compressive wave, this stress wave reflected from the back surface and reached again at the surface of the plate to the spherical stress wave. Then the generation of cone crack can be confirmed along the stress wave surface. (3) The plate is the thicker, the more is the generation phenomenon of cone crack at the lower impact velocity range (20m/s-35m/s). Because the fracture generate before the maximum tensile stress acting to the glass plate, cone crack was rarely ever generated.

A Study on the Feedforward Control Algorithm for Dynamic Positioning System Using Ship Motion Prediction (선체운동 예측을 이용한 Dynamic Positioning System의 피드포워드 제어 알고리즘에 관한 연구)

  • Song, Soon-Seok;Kim, Sang-Hyun;Kim, Hee-Su;Jeon, Ma-Ro
    • Journal of the Korean Society of Marine Environment & Safety
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    • v.22 no.1
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    • pp.129-137
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    • 2016
  • In the present study we verified performance of feed-forward control algorithm using short term prediction of ship motion information by taking advantage of developed numerical simulation model of FPSO motion. Up until now, various studies have been conducted about thrust control and allocation for dynamic positioning systems maintaining positions of ships or marine structures in diverse sea environmental conditions. In the existing studies, however, the dynamic positioning systems consist of only feedback control gains using a motion of vessel derived from environmental loads such as current, wind and wave. This study addresses dynamic positioning systems which have feedforward control gain derived from forecasted value of a motion of vessel occurred by current, wind and wave force. In this study, the future motion of vessel is forecasted via Brown's Exponential Smoothing after calculating the vessel motion via a selected mathematical model, and the control force for maintaining the position and heading angle of a vessel is decided by the feedback controller and the feedforward controller using PID theory and forecasted vessel motion respectively. For the allocation of thrusts, the Lagrange Multiplier Method is exploited. By constructing a simulation code for a dynamic positioning system of FPSO, the performance of feedforward control system which has feedback controller and feedforward controller was assessed. According to the result of this study, in case of using feedforward control system, it shows smaller maximum thrust power than using conventional feedback control system.

The Cross-sectional Mass Flux Observation at Yeomha Channel, Gyeonggi Bay at Spring Tide During Dry and Flood Season (단면 관측을 통한 경기만 염하수로의 대조기 평수시와 홍수시 유출입량 변화특성 조사)

  • Lee, Dong-Hwan;Yoon, Byung-Il;Kim, Jong-Wook;Gu, Bon-Ho;Woo, Seung-Buhm
    • Journal of Korean Society of Coastal and Ocean Engineers
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    • v.24 no.1
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    • pp.16-25
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    • 2012
  • To calculate the total mass flux that change in dry and flood season in the Yeomha Channel of Gyeonggi Bay, the 13 hour bottom tracking observation was performed from the southern extremity. The value of the total mass flux(Lagrange flux) was calculated as the sum of the Eulerian flux value and stroke drift value and the tidal residual flow was harmonically analyzed through the least-squares method. Moreover, the average during the tidal cycle is essential to calculate the mass flux and the tidal residual flow and there is the need to equate the grid of repeatedly observed data. Nevertheless, due to the great differences in the studied region, the number of vertical grid tends to change according to time and since the horizontal grid differs according to the transport speed of the ship as a characteristic of the bottom tracking observation, differences occur in the horizontal and vertical grid for each hour. Hence, the present study has vertically and horizontally normalized(sigma coordinate) to equate the grid per each hour. When compared to the z-level coordinate system, the Sigma coordinate system was evaluated to have no irrationalities in data analysis with 5% of error. As a result of the analysis, the tidal residual flow displayed the flow pattern of sagging in the both ends in the main waterway direction of dry season. During flood season, it was confirmed that the tidal residual flow was vertical 2-layer flow. As a result of the total mass flux, the ebb properties of 359 cm/s and 261 cm/s were observed during dry and flood season, respectively. The total mass flux was moving the intertidal region between Youngjong-do and Ganghwa-do.