• Title/Summary/Keyword: Equations of motion

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Modeling and Motion-control for a Light-weight Delta Robot (경량 델타로봇의 모델링 및 모션 제어)

  • Kim, Seong-Il;Hong, Jun-Ho;Shin, Dongwon
    • Journal of the Korean Society of Manufacturing Process Engineers
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    • v.17 no.3
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    • pp.155-162
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    • 2018
  • Delta robots are usually used for industrial manufacturing, but heavy weight and expensive price have been obstacles to rapid propagation of robots in the field. The goal of this research is to make light-weight and price-competitive delta robots. To reduce the weight, we used plastic material for the arm link, and to reduce the price, we used a step-motor as the main actuator. First we formulated the equations of inverse kinematics for the designed delta robot and then verified these equations by using multibody-dynamics simulation. An algorithm of motion control was developed and applied to the motion-processing unit using a timer-interrupt of 8 milliseconds. Finally, we tested the performance of the new delta robot by checking its control of motion along line segments.

Investigation on the Generalized Hydrodynamic Force and Response of a Flexible Body at Different Reference Coordinate System (기준 좌표계에 따른 탄성체의 일반화 파랑 하중 및 응답에 대한 연구)

  • Heo, Kyeonguk;Choi, Yoon-Rak
    • Journal of the Society of Naval Architects of Korea
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    • v.58 no.6
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    • pp.348-357
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    • 2021
  • In this paper, the generalized hydrodynamic force and response of a flexible body are calculated at different reference coordinate systems. We generalize the equation of motion for a flexible body by using the conservation of momentum (Mei et al., 2005). To obtain the equations in the generalized mode, two different reference coordinates are adopted. The first is the body-fixed coordinate system by a rigid body motion. The other is the inertial coordinate system which has been adopted for the analysis. Using the perturbation scheme in the weakly-nonlinear assumption, the equations of motion are expanded up to second-order quantities and several second-order forces are obtained. Numerical tests are conducted for the flexible barge model in head waves and the vertical bending is only considered in the hydroelastic responses. The results show that the linear response does not have the difference between the two formulations. On the other hand, second-order quantities have different values for which the rigid body motion is relatively large. However, the total summation of second-order quantities has not shown a large difference at each reference coordinate system.

Analysis of flow in a square cavity with an oscillating top wall (진동하는 윗벽면을 가진 정방형 웅덩이 안에서의 흐름)

  • Min, Byeong-Gwang;Jang, Geun-Sik
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.21 no.3
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    • pp.392-404
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    • 1997
  • The flow induced by the oscillatory motion of a solid body is important in a number of practical problems. As the solid boundary oscillates harmonically, there is steady streaming motion invoked by the Reynolds stresses, which could cause extensive migration of the fluid during a period of fluid motion. We here analyzed the flow in a square cavity with an oscillating top wall for the parameters which make the time derivatives and the convective terms equally important in the entire cavity flow. The full Navier-Stokes equations are solved by the second-order time accurate Momentum Coupling Method which is devised by the authors. The particular numerical scheme does not need subiteration at each time step which is usually a required process to calculate the incompressible Navier-Stokes equations. The effect of two parameters, the Reynolds number and the frequency parameter, on the oscillatory flow has been investigated.

Stability analysis of the rotating and stationary grooved journal bearings (정지홈과 회전홈을 갖는 저널베어링의 안정성 평가)

  • Lee, M.H.;Lee, J.H.;Jang, G.H.
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2013.04a
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    • pp.141-146
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    • 2013
  • This research investigates the stability analysis for the rotating and the stationary grooved journal bearing. The dynamic coefficients of the journal bearing are calculated by using FEM and the perturbation method. When journal bearing is in whirling motion, the dynamic coefficients have time-varying components as a sine wave due to the reaction force of oil film toward the center of journal even in the steady state. The solutions for the equations of motion can be assumed as the Fourier series expansion. The equations of motion can be rewritten as the linear algebraic equations with respect to the Fourier coefficients. Then, stability of the grooved journal bearing can be calculated by Hill's infinite determinant. The periodic function of dynamic coefficients is derived using Fourier Fast Transform(FFT).The stability of journal bearing is determined as rotating speed increases and the stability of rotating grooved journal bearing is compared and discussed with the stability of stationary grooved journal bearing.

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Motion Parameter Estimation Using Hough Space Transform (Hough 영역 변환을 이용한 운동 변화량 추정)

  • Chien, Sung-Il;Kim, Jong-Woo
    • Journal of the Korean Institute of Telematics and Electronics
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    • v.27 no.11
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    • pp.92-102
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    • 1990
  • A new method for determining the motion parameters (scale, rotation, translation) of 2-D image is introduced. It employs Hough transform that maps the straight lines in the input image to the points in the Hough space (HS). This method makes use of the relations between the motion of an object in input image and the translations of peak points in the HS and thus derives relating equations about motion parameters especially when scale changes are involved. The derived equations make is efficient and simple to estimate motion parameters of input image, even if the scale parameter of input image is varied. Performance of this approach on an aircraft image is provided in detail in the presence of noise.

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The effect of finite strain on the nonlinear free vibration of a unidirectional composite Timoshenko beam using GDQM

  • Ghasemi, Ahmad Reza;Mohandes, Masood
    • Advances in aircraft and spacecraft science
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    • v.3 no.4
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    • pp.379-397
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    • 2016
  • In this manuscript, free vibrations of a unidirectional composite orthotropic Timoshenko beam based on finite strain have been studied. Using Green-Lagrange strain tensor and comprising all of the nonlinear terms of the tensor and also applying Hamilton's principle, equations of motion and boundary conditions of the beam are obtained. Using separation method in single-harmonic state, time and locative variables are separated from each other and finally, the equations of motion and boundary conditions are gained according to locative variable. To solve the equations, generalized differential quadrature method (GDQM) is applied and then, deflection and cross-section rotation of the beam in linear and nonlinear states are drawn and compared with each other. Also, frequencies of carbon/epoxy and glass/epoxy composite beams for different boundary conditions on the basis of the finite strain are calculated. The calculated frequencies of the nonlinear free vibration of the beam utilizing finite strain assumption for various geometries have been compared to von Karman one.

Analysis of the Static and Dynamic Stability Properties of the Unmaned Airship

  • Lee, Hae Chang
    • International Journal of Aeronautical and Space Sciences
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    • v.2 no.2
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    • pp.82-94
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    • 2001
  • The purpose of this paper is to analyze the static and dynamic stability-of the unmanned airship under development ; the target airship's over-all length of hull is 50m and the maximum diameter is 12.5m. For the analysis, the dynamic model of an airship was defined and both the nonlinear and linear dynamic equations of motion were derived. Two different configuration models (KA002Y and KA003Y) of the airship were used for the target model of the static stability analysis and the dynamic stability analysis. From the result of analyses, though the airship is unstable in static stability, dynamic characteristics of the airship can provide the stable dynamic stability. All of the results, airship models and dynamic flight equations will be an important basement and basic information for the next step of developing the automatic flight control system(AFCS) and the stability augmentation system(SAS) for the unmanned airship as well as for the stratospheric airship in the future.

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THE SIMPLICATION OF DYNAMICS FOR THE FLEXIBLE BODY (유연성을 갖는 매니퓰레이터 역학방정식의 간략화)

  • Park, Hwa-Sea;Bae, Jun-Kyung;Nam, Ho-Pub;Park, Chong-Kuk
    • Proceedings of the KIEE Conference
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    • 1988.07a
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    • pp.950-953
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    • 1988
  • The equations of motion for linearly elastic bodies undergoing large displacement motion are derived. This produces a set of equations which are efficient to numerically integrate. The equations for the elastic bodies are formulated and simplified to provide as much efficiency as possible in their numerical solution. A futher efficiency is obtained through the use of floating reference frame. The equation are presented in two forms for numerical integration. 1) Explicit numerical integration 2) Implicit numerical integration. In this paper, there was used the numerical integration. The implicit numerical integration is extended to solved second order equation, futher reducing the numerical effort required. The formulation given is seen to be occulate and is expected to be efficient for many types of problems.

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Non-linear Vibration Analysis for the In-plane Motion of a Semi-circular Pipe Conveying Fluid (유체를 수송하는 반원형 곡선관의 면내운동에 대한 비선형 진동 해석)

  • 정두한;정진태
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2003.05a
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    • pp.677-682
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    • 2003
  • The non-linear dynamic characteristics of a semi-circular pipe conveying fluid are investigated when the pipe is clamped at both ends. To consider the geometric non-linearity for the radial and circumferential displacements, this study adopts the Lagrange strain theory for large deformation and the extensible dynamics based on the Euler-Bernoulli beam theory for slenderness assumption. By using the Hamilton principle, the non-linear partial differential equations are derived for the in-plane motions of the pipe, considering the fluid inertia forces as a kind of non-conservative forces. The linear and non-linear terms in the governing equations are compared with those in the previous study, and some significant differences are discussed. To investigate the dynamic characteristics of the system, the discretized equations of motion are derived form the Galerkin method. The natural frequencies varying with the flow velocity are computed fen the two cases, which one is the linear problem and the other is the linearized problem in the neighborhood of the equilibrium position. Finally, the time responses at various flow velocities are directly computed by using the generalized- method. From these results, we should to describe the non-linear behavior to analyze dynamics of a semi-circular pipe conveying fluid more precisely.

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Construction of System Jacobian in the Equations of Motion Using Velocity Transformation Technique (속도변환법을 이용한 운동방정식의 시스템자코비안 구성)

  • Lee, Jae-Uk;Son, Jeong-Hyeon;Kim, Gwang-Seok;Yu, Wan-Seok
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.25 no.12
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    • pp.1966-1973
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    • 2001
  • The Jacobian matrix of the equations of motion of a system using velocity transformation technique is derived via variation methods to apply the implicit integration algorithm, DASSL. The concept of generalized coordinate partitioning is used to parameterize the constraint set with independent generalized coordinates. DASSL is applied to determine independent generalized coordinates and velocities. Dependent generalized coordinates, velocities, accelerations and Lagrange multipliers are explicitly retained in the formulation to satisfy all of the governing kinematic and dynamic equations. The derived Jacobian matrix of a system is proved to be valid and accurate both analytically and through solution of numerical examples.