• Title/Summary/Keyword: recursive equations

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A recursive approach for mechanical system design sensitivity analysis

  • Daesung Bae
    • Transactions of the Korean Society of Machine Tool Engineers
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    • v.10 no.1
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    • pp.101-111
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    • 2001
  • Recursive formulas have been effective in solving the equations of motion for large scale constratined mechanical sys-tems. However, derivation of the formulas has been limited to individual terms in the equations of motion, such as veloci-ty, acceleration. and generalized forces. The recursive formulas are generalized in this paper. The velocity transformation method is employed to transform the equations of motion from Cartesian to the joint spaces. Computational structure of the equations of motion in the joint space is carefully examined to classify all necessary computational operations into sev-eral categories. The generalized recursive formula for each category is then developed and applied whenever such a cate-gory of computation is encountered. Since the velocity transformation method yields the equations of motion in a compact form and computational efficiency is achieved by generalized recursive formulas, the proposed method is not only easy to implement but is also efficient. A library of generalized recursive formulas is developed to implement a dynamic analysis algorithm using backward difference.

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ELASTOKINEMATIC ANALYSIS OF A SUSPENSION SYSTEM WITH LINEAR RECURSIVE FORMULA

  • KANG J. S.
    • International Journal of Automotive Technology
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    • v.6 no.4
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    • pp.375-381
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    • 2005
  • This paper presents linear algebraic equations in the form of recursive formula to compute elastokinematic characteristics of a suspension system. Conventional methods of elastokinematic analysis are based on nonlinear kinematic constrant equations and force equilibrium equations for constrained mechanical systems, which require complicated and time-consuming implicit computing methods to obtain the solution. The proposed linearized elastokinematic equations in the form of recursive formula are derived based on the assumption that the displacements of elastokinematic behavior of a constrained mechanical system under external forces are very small. The equations can be easily computerized in codes, and have the advantage of sharing the input data of existing general multi body dynamic analysis codes. The equations can be applied to any form of suspension once the type of kinematic joints and elastic components are identified. The validity of the method has been proved through the comparison of the results from established elastokinematic analysis software. Error estimation and analysis due to piecewise linear assumption are also discussed.

Real-time Projectile Motion Trajectory Estimation Considering Air Resistance of Obliquely Thrown Object Using Recursive Least Squares Estimation (비스듬히 던진 물체의 공기저항을 고려한 재귀 최소 자승법 기반 실시간 포물선 운동 궤적 추정)

  • Jeong, Sangyoon;Chwa, Dongkyoung
    • The Transactions of The Korean Institute of Electrical Engineers
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    • v.67 no.3
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    • pp.427-432
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    • 2018
  • This paper uses a recursive least squares method to estimate the projectile motion trajectory of an object in real time. The equations of motion of the object are obtained considering the air resistance which occurs in the actual experiment environment. Because these equations consider air resistance, parameter estimation of nonlinear terms is required. However, nonlinear recursive least squares estimation is not suitable for estimating trajectory of projectile in that it requires a lot of computation time. Therefore, parameter estimation for real-time trajectory prediction is performed by recursive least square estimation after using Taylor series expansion to approximate nonlinear terms to polynomials. The proposed method is verified through experiments by using VICON Bonita motion capture system which can get three dimensional coordinates of projectile. The results indicate that proposed method is more accurate than linear Kalman filter method based on the equations of motion of projectile that does not consider air resistance.

Dynamic Analysis of a Chain of Rigid Rods

  • Attia, Hazem Ali
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.8 no.2
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    • pp.75-86
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    • 2004
  • In this study, a recursive algorithm for generating the equations of motion of a chain of rigid rods is presented. The methods rests upon the idea of replacing the rigid body by a dynamically equivalent constrained system of particles. The concepts of linear and angular momentums are used to generate the rigid body equations of motion without either introducing any rotational coordinates or the corresponding transformation matrices. For open-chain, the equations of motion are generated recursively along the serial chains. For closed-chain, the system is transformed to open-chain by cutting suitable kinematic joints with the addition of cut-joints kinematic constraints. An example of a closed-chain of rigid rods is chosen to demonstrate the generality and simplicity of the proposed method.

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RECURSIVE TWO-LEVEL ILU PRECONDITIONER FOR NONSYMMETRIC M-MATRICES

  • Guessous, N.;Souhar, O.
    • Journal of applied mathematics & informatics
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    • v.16 no.1_2
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    • pp.19-35
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    • 2004
  • We develop in this paper some preconditioners for sparse non-symmetric M-matrices, which combine a recursive two-level block I LU factorization with multigrid method, we compare these preconditioners on matrices arising from discretized convection-diffusion equations using up-wind finite difference schemes and multigrid orderings, some comparison theorems and experiment results are demonstrated.

A Recursive Algorithm for Generating the Equations of Motion of Spatial Mechanical Systems with Application to the Five-Point Suspension

  • Attia, Hazem-Ali
    • Journal of Mechanical Science and Technology
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    • v.18 no.4
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    • pp.550-559
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    • 2004
  • In this paper, a recursive formulation for generating the equations of motion of spatial mechanical systems is presented. The rigid bodies are replaced by a dynamically equivalent constrained system of particles which avoids introducing any rotational coordinates. For the open-chain system, the equations of motion are generated recursively along the serial chains using the concepts of linear and angular momenta Closed-chain systems are transformed to open-chain systems by cutting suitable kinematic joints and introducing cut-joint constraints. The formulation is used to carry out the dynamic analysis of multi-link five-point suspension. The results of the simulation demonstrate the generality and simplicity of the proposed dynamic formulation.

ENHANCED SEMI-ANALYTIC METHOD FOR SOLVING NONLINEAR DIFFERENTIAL EQUATIONS OF FRACTIONAL ORDER

  • JANG, BONGSOO;KIM, HYUNJU
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.23 no.4
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    • pp.283-300
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    • 2019
  • In this paper, we propose a new semi-analytic approach based on the generalized Taylor series for solving nonlinear differential equations of fractional order. Assuming the solution is expanded as the generalized Taylor series, the coefficients of the series can be computed by solving the corresponding recursive relation of the coefficients which is generated by the given problem. This method is called the generalized differential transform method(GDTM). In several literatures the standard GDTM was applied in each sub-domain to obtain an accurate approximation. As noticed in [19], however, a direct application of the GDTM in each sub-domain loses a term of memory which causes an inaccurate approximation. In this work, we derive a new recursive relation of the coefficients that reflects an effect of memory. Several illustrative examples are demonstrated to show the effectiveness of the proposed method. It is shown that the proposed method is robust and accurate for solving nonlinear differential equations of fractional order.

A Non-recursive Formulation of Dynamic Force Analysis in Recursive Multibody Dynamics (순환 다물체동역학에서의 비순환적인 동하중해석 공식)

  • Kim, Seong-Su
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.21 no.5
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    • pp.809-818
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    • 1997
  • An efficient non-recursive formulation of dynamic force analysis has been developed for serially connected multibody systems. Although derivation of equations of motion is based on a recursive dynamic formulation with joint relative coordinates, in the proposed formulation, dynamic forces such as joint reaction forces and driving force are computed non-recursively for specified joints. The efficiency of the proposed formulation has been proved by the operational count and the CPU time measure, comparing with that of the conventional recursive Newton-Euler formulation. A simulation of 7-DOF RRC robot arm has been carried out to validate solutions of reaction forces by comparing with those from a commercial dynamic analysis program DADS.

A study on dynamic motion equations for a robot manipulator (로보트 팔의 제어를 위한 Dynamics 방정식들에 관한 연구)

  • 김승배;오세정;박인갑;김형래
    • 제어로봇시스템학회:학술대회논문집
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    • 1987.10b
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    • pp.52-57
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    • 1987
  • In this paper, it is dealt with the dynamic motion equations for a robot arm. Four kinds of the dynamic equations which are the Lagrange-Euler equations, the Recursive L-E equations, the Newton-Euler equations and the improved N-E equation are derived on robot PUMA 600. Finally the algorithms on these equations are programmed using PASCAL. and are compared with each other. As the results, it is found that the improved N-E equations has the most fastest execution time among the equations and can be used in real time processing.

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IMPLICIT-EXPLICIT SECOND DERIVATIVE LMM FOR STIFF ORDINARY DIFFERENTIAL EQUATIONS

  • OGUNFEYITIMI, S.E.;IKHILE, M.N.O.
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.25 no.4
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    • pp.224-261
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    • 2021
  • The interest in implicit-explicit (IMEX) integration methods has emerged as an alternative for dealing in a computationally cost-effective way with stiff ordinary differential equations arising from practical modeling problems. In this paper, we introduce implicit-explicit second derivative linear multi-step methods (IMEX SDLMM) with error control. The proposed IMEX SDLMM is based on second derivative backward differentiation formulas (SDBDF) and recursive SDBDF. The IMEX second derivative schemes are constructed with order p ranging from p = 1 to 8. The methods are numerically validated on well-known stiff equations.