• Journal of Mechanical Science and Technology
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• v.19 no.spc1
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• pp.364-370
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• 2005

A stable walking pattern generation method for a biped robot is presented in this paper. In general, the ZMP (zero moment point) equations, which are expressed as differential equations, are solved to obtain a stable walking pattern. However, the number of differential equations is less than that of unknown coordinates in the ZMP equations. It is impossible to integrate the ZMP equations directly since one or more constraint equations are involved in the ZMP equations. To overcome this difficulty, DAE (differential and algebraic equation) solution method is employed. The proposed method has enough flexibility for various kinematic structures. Walking simulation for a virtual biped robot is performed to demonstrate the effectiveness and validity of the proposed method. The method can be applied to the biped robot for stable walking pattern generation.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.9
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• pp.2339-2348
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• 1994

The objective of this paper is to develop a solution method for the differential-algebraic equation(DAE) derived from constrained muti-body dynamic systems. Mechanical systems are often modeled as bodies and joints. Differential equations of motion are formulated for bodies. Since the bodies are connected by joint, the differential variables must satisfy the kinematic constraint equations that come from the joints. Difficulties are arised due to drift of the differential variables off the constraint equations. An optimization method is adopted to correct the drift of the differential variables. To demonstrate the efficiency of the proposed method a slider-crank mechanism is analyzed dynamically. Identical results are obtained as these from the commercial program DADS. Dynamic analysis of a High Mobility Multi-purpose Wheeled. Vehicle(HMMWV) is carried out to show the practicalism of the proposed method.

• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.215-229
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• 2005

In this paper, constraint aggregation is combined with the adjoint and multiple shooting strategies for optimal control of differential algebraic equations (DAE) systems. The approach retains the inherent parallelism of the conventional multiple shooting method, while also being much more efficient for large scale problems. Constraint aggregation is employed to reduce the number of nonlinear continuity constraints in each multiple shooting interval, and its derivatives are computed by the adjoint DAE solver DASPKADJOINT together with ADIFOR and TAMC, the automatic differentiation software for forward and reverse mode, respectively. Numerical experiments demonstrate the effectiveness of the approach.

• Journal of Mechanical Science and Technology
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• v.19 no.spc1
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• pp.461-472
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• 2005

A formulation for flexible multibody systems (MBS) is investigated, where rigid MBS substructures are coupled with flexible bodies described by a nonlinear finite element (FE) approach. Several aspects that turned out to be crucial for the presented approach are discussed. The system describing equations are given in differential algebraic form (DAE), where many sophisticated solvers exist. In this paper the performance of several solvers is investigated regarding their suitability for the application to the usually highly stiff DAE. The substructures are connected with each other by nonlinear algebraic constraint equations. Further, partial derivatives of the constraints are required, which often leads to extensive algebraic trans-formations. Handcoding of analytically determined derivatives is compared to an approach utilizing algorithmic differentiation.

• Coupled systems mechanics
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• v.3 no.3
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• pp.291-304
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• 2014

Paper discusess a dynamic engineering problem of a mass attached to a pendulum sliding along a cable. In this problem the pendulum mass and the cable are coupled together in a model described by a system of differential algebraic equations (DAE). In the paper we have presented formulation of the system of differential equations that models the problem and determination of the initial conditions. The developed model is general in a sense of free choice of support location, elastic cable properties, pendulum length and inclusion of braking forces. Examples illustrate and validate the model.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.30 no.3
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• pp.8-16
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• 2002

The implicit formulation of rotor dynamics for helicopter flight simulation has been derived and and presented. The generalized vector kinematics regarding the relative motion between coordinates were expressed as a unified matrix operation and applied to get the inertial velocities and accelerations at arbitaty rotor blade span position. Based on these results the rotor aeromechanic equations for flapping dynamics, lead-lag dynamics and torque dynamics were formulated as an implicit form. Spatial integration methods of rotor dynamic equations along blade span and the expanded applicability of the present implicit formulations for arbitrary hings geometry and hinge sequences have been investigated. Time integration methods for present DAE(Differential Algebraic Equation) to calculate dynamic response calculation are recommenaded as future works.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.56 no.6
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• pp.1000-1006
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• 2007

This paper presents a methodology to calculate an optimal solution of equilibrium to differential algebraic equations for power systems. It employs a nonlinear interior point method to solve the optimization formulation which includes dynamic equations representing the two-axis synchronous generator model with AVR and speed governing controls, algebraic equations, and steady-state nonlinear loads. This paper also adopts two algorithms for the improvement of solution convergence. In power system analysis and control, equilibrium optimization (EOPT) is applicable for diverse purposes that need the consideration of dynamic model characteristics at a steady-state condition.

• Journal of the Korean Society for Railway
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• v.5 no.3
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• pp.174-180
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• 2002

In multibody dynamics, DAE(Differential Algebraic Equations) that combine differential equations of motion and kinematic constraint equations should be solved. To solve these equations, either coordinate partitioning method or constraint stabilization method is commonly used. The most typical coordinate partitioning methods are LU decomposition, QR decomposition, and SVD(singular value decomposition). The objective of this research is to suggest a hybrid coordinate partitioning method in the dynamic analysis of multibody systems containing singular configurations. Two coordinate partitioning methods, i.e. LU decomposition and QR decomposition for constrained multibody systems, are combined for a new hybrid coordinate partitioning method. The proposed hybrid method reduces the simulation time while keeping accuracy of the solution.

• Journal of Mechanical Science and Technology
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• v.19 no.spc1
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• pp.377-387
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• 2005

The equations of motion of two-wheeled vehicles, e.g. bicycles or motorcycles, are developed by using Lagrange's equations for quasi-coordinates. The pure rolling constraints between the ground and the two wheels are considered in the dynamical equations of the system. For each wheel, two nonholonomic and two holonomic constraints are introduced in a set of differential-algebraic equations (DAE). The constraint Jacobian matrix is obtained by collecting all the constraint equations and converting them into the velocity form. Equilibrium, an algorithm for searching for equilibrium points of two-wheeled vehicles and the associated problems are discussed. Formulae for calculating the radii of curvatures of ground-wheel contact paths and the reference point are also given.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.25 no.2
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• pp.109-118
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• 2013

The absence of a simple and general analytical model has been a problem in the design and analysis of desiccant-assisted air-conditioning systems. In this study, such an analytical model has been developed based on the approximate integral solution of the coupled transient ordinary differential equations for the heat and mass transfer processes in a desiccant wheel. It turned out that the initial conditions should be determined by the solution of four linear algebraic equations including the heat and mass transfer equations for the air flow as well as the energy and mass conservation equations for the desiccant bed. It is also shown that time-averaged exit air temperature and humidity relations could be given in terms of the heat and mass transfer effectiveness.