• Journal of the Chungcheong Mathematical Society
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• v.24 no.3
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• pp.437-447
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• 2011

In this paper we present a new variant of the Euler-Chebyshev method for solving nonlinear equations. Analysis of convergence is given to show that the presented methods are at least fifth-order convergent. Several numerical examples are given to illustrate that newly presented methods can be competitive to other known fifth-order methods and the Newton method in the efficiency and performance.

• Transactions of the Korean Society of Automotive Engineers
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• v.4 no.4
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• pp.9-17
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• 1996

This paper develops a sequential updating method of the Euler parameter generalized coordinates for the machine kinematics and dynamics, The Newton's method is slightly modified so as to utilize the Jacobian matrix with respect to the virtual rotation instead of this with repect to the Euler parameters. An intermediate variable is introduced and the modified Newton's method solves for the variable first. Relational equation of the intermediate variable is then solved for the Euler parameters. The solution process is carried out efficiently by symoblic inversion of the relational equation of the intermediate variable and the iteration equation of the Euler parameter normalization constraint. The proposed method is applied to a kinematic and dynamic analysis with the Generalized Coordinate Partitioning method. Covergence analysis is performed to guarantee the local convergence of the proposed method. To demonstrate the validity and practicalism of the proposed method, kinematic analysis of a motion base system and dynamic analysis of a vehicle are carried out.

• Journal for History of Mathematics
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• v.27 no.2
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• pp.127-138
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• 2014

In this paper we investigate how Newton discovered the generalized binomial theorem. Newton's binomial theorem, or binomial series can be found in Calculus text books as a special case of Taylor series. It can also be understood as a formal power series which was first conceived by Euler if convergence does not matter much. Discovered before Taylor or Euler, Newton's binomial theorem must have a good explanation of its birth and validity. Newton learned the interpolation method from Wallis' famous book ${\ll}$Arithmetica Infinitorum${\gg}$ and employed it to get the theorem. The interpolation method, which Wallis devised to find the areas under a family of curves, was by nature arithmetrical but not geometrical. Newton himself used the method as a way of finding areas under curves. He noticed certain patterns hidden in the integer binomial sequence appeared in relation with curves and then applied them to rationals, finally obtained the generalized binomial sequence and the generalized binomial theorem.

• Proceedings of the KIEE Conference
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• 2005.10b
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• pp.591-593
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• 2005

This paper presents the dynamic analysis of a humanoid robot using Nastran that is one of FEM analysis program. Generally, computer program based on the Lagrange-Euler method or Newton-Euler method was used for dynamic analysis of a robot. The Lagrange-Euler method requires much calculation performance and it is also hard to apply to complex structure, and the Newton-Euler method limits accurate modeling and calculation for closed structure like a humanoid robot. In this paper, mechanical and structural data are obtained from the Nastran. It is possible for Nastran to make model similar to real system and can apply a physical properties and laws to model. So, accurate simulation is possible. From this result, accurate data is gained by Nastran. Furthermore, this method is shown to be a useful method that guarantees accuracy for trajectory planning.

• 제어로봇시스템학회:학술대회논문집
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• 2005.06a
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• pp.296-301
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• 2005

This paper describes the kinematics, dynamics and control of a 6-DOF shaking table with a bell crank structure, which converts the direction of reciprocating movements. In this shaking table, the bell crank mechanism is used to reduce the amount of space needed to install the shaking table and create horizontal displacement of the platform. In kinematics, joint design is performed using $Gr{\ddot{u}}bler's$ formula. The inverse kinematics of the shaking table is discussed. The derivation of the Jacobian matrix is presented to evaluate singularity conditions. Considering the maximum stroke of the hydraulic actuator, collision between links and singularity, workspace is computed. In dynamics, computations are based on the Newton-Euler formulation. To derive parallel algorithms, each of the contact forces is decomposed into one acting in the direction of the leg and the other acting in the plane orthogonal to the direction of the leg. Applying the Newton-Euler approach, the solution of inverse dynamics is almost completely parallel. Only one of the steps-the application of the Newton-Euler equations to the platform-must be performed on one single processor. Finally, the efficient control scheme is proposed for the tracking control of the motion platform.

• Nuclear Engineering and Technology
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• v.52 no.11
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• pp.2630-2637
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• 2020

The structure design of divertor Multi-Functional Maintenance Platform (MFMP) actuated by hydraulic system for China Fusion Engineering Test Reactor (CFETR) was introduced in this paper. The model of MFMP was established according to maintenance requirements. In this paper, Newton-Euler method and the improved virtual work principle were used, the equivalent driving force of each actuator was obtained through the equivalent Jacobian inverse matrix derived from velocity relationship among the components. The accuracy of the model was verified by ADAMS simulation. The stability control of the heavy-duty components driven by hydraulic cylinders based on Newton-Euler method and improved virtual work principle was established.

• 한국전산유체공학회:학술대회논문집
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• 1998.11a
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• pp.153-159
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• 1998

The Newton-Krylov method on the unstructured grid flow solver using the cell-centered spatial discretization oi compressible Euler equations is presented. This flow solver uses the reconstructed primitive variables to get the higher order solutions. To get the quadratic convergence of Newton method with this solver, the careful linearization of face flux is performed with the reconstructed flow variables. The GMRES method is used to solve large sparse matrix and to improve the performance ILU preconditioner is adopted and vectorized with level scheduling algorithm. To get the quadratic convergence with the higher order schemes and to reduce the memory storage. the matrix-free implementation and Barth's matrix-vector method are implemented and compared with the traditional matrix-vector method. The convergence and computing times are compared with each other.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.25 no.11
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• pp.1820-1828
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• 2001

The dynamics of the 6-3 Stewart platform manipulator (SPM) is newly derived based on the kinematic relations particularly developed fur the SPM. The essence of the analysis is to deal with three subsystems of the SPM, each consisting of the command and feedback line links associated with two joined neighboring actuators. The dynamics of the command and feedback line links are first formulated using Lagrange and Newton-Euler method and then combined to derive the dynamic equations of motion fur the SPM. The derived nonlinear equations of motion are so computationally effective that it can be easily applied to real-time high-speed tracking control of 6-3 SPM.

• Transactions of the Korean Society of Mechanical Engineers
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• v.8 no.6
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• pp.584-590
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• 1984

This study is to develop a program, with which the motion of the system can be simulated in view of kinematics and dynamics, and then evaluate functional capabilities of many robots in order to select the most suitable one for any given working conditions. According to the theory of Denavit & Hartenberg, rectangular coordinate is set at each joint in the robot of six joints, as this one is the major concern, and transformation matrices are derived between any two coordinates. The necessary displacement of each joint for executing a given a work is obtained from the position and posture transformation and the in-stantaneous velocity of the joint is got from given velocity distribution of the path. The necessary torque of each joint is finally calculated by Newton-Euler Method. This simulation program is applied to a robot with six rotational joints, Rotational angle and torque to time which has a given motion trajectory are figured and also torque to r.p.m.

• Journal of Mechanical Science and Technology
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• v.16 no.1
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• pp.13-23
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• 2002

This paper presents inverse kinematic and dynamic analyses of HexaSlide type six degree-of-freedom parallel manipulators. The HexaSlide type parallel manipulators (HSM) can be characterized as an architecture with constant link lengths that are attached to moving sliders on the ground and to a mobile platform. In the inverse kinematic analyses, the slider and link motion (position, velocity, and acceleration) is computed given the desired mobile platform motion. Based on the inverse kinematic analysis, in order to compute the required actuator forces given the desired platform motion, inverse dynamic equations of motion of a parallel manipulator is derived by the Newton-Euler approach. In this derivation, the joint friction as well as all link inertia are included. Relative importance of the link inertia and joint frictions on the computed torque is investigated by computer simulations. It is expected that the inverse kinematic and dynamic equations can be used in the computed torque control and model-based adaptive control strategies.