• Transactions of the Korean Society of Automotive Engineers
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• v.9 no.1
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• pp.156-162
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• 2001

An effective and practical method is presented for solving the forward kinematics of a 6-DOF Stewart Platform, using neural network algorithm together with Newton-Raphson method. An approximated solution is obtained from trained neural network, then it is used as an initial estimate for Newton-Raphson method. A series of accurate solutions are calculated with reasonable speed for the entire workspace of the platform. The solution procedure can be used for driving a real-time simulation platform.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2004.10a
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• pp.525-529
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• 2004

A novel translational 3-dof parallel mechanism is proposed and analyzed. The mechanism consists of three RRPS serial subchains and an additional passive 3-dof type serial subchain. Three RRPS serial subchains alone may form a structure of the 6-DOF Stewart Platform mechanism. However, in the proposed mechanism, an additional passive serial subchain acts as constraints to restrict the output motion of the mechanism in 3-DOF translational space. The closed form position solutions of the proposed mechanism and its first-order kinematic model are derived. Then its workspace size and kinematic characteristics are examined via kinematic isotropic index.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2004.10a
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• pp.520-524
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• 2004

In this work, a novel spherical 3-dof parallel mechanism is proposed and analyzed. The mechanism consists of three RRPS serial subchains and an additional passive 3-dof type serial subchain. Three RRPS serial subchains alone may form a structure of 6-DOF Stewart Platform mechanism. However, in the proposed mechanism, an additional passive serial subchain acts as constraints to restrict the output motion of the mechanism within 3-DOF spherical space. The closed form solutions of position analysis of the proposed mechanism and its first-order kinematic model are derived. Then its workspace size and kinematic characteristics are examined via kinematic isotropic index.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.25 no.8
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• pp.1206-1212
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• 2001

The kinematic analysis of Stewart platform manipulator(SPM) is carried out in order to reduce the calculation time for its forward kinematic solution when the iterative numerical method is employed. The kinematic equations for three substructures of the 6-3 SPM are newly derived by introducing Denavit-Hartenberg link parameters and using kinematic constraints associated with the SPM and substructure kinematics. It is shown that the forward kinematics can be easily solved from three nonlinear equations with three unknown variables only, leading to a great reduction in calculation time.

• 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 A
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• v.25 no.3
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• pp.339-352
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• 2001

The inverse kinematics problem of Stewart platform is straightforward, but no closed form solution of the forward kinematic problem has been presented. Since we need the real-time forward kinematic solution in MIMO control and the motion monitoring of the platform, it is important to acquire the 6 DOF displacements of the platform from measured lengths of six cylinders in small sampling period. Newton-Raphson method a simple algorithm and good convergence, but it takes too long calculation time. So we reduce 6 nonlinear kinematic equations to 3 polynomials using Nairs method and 3 polynomials to 2 polynomials. Then Newton-Raphson method is used to solve 3 polynomials and 2 polynomials respectively. We investigate operation counts and performance of three methods which come from the equation reduction and Newton-Raphson method, and choose the best method.

• Proceedings of the KSME Conference
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• 2000.11a
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• pp.541-547
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• 2000

This paper presents the closed-form forward kinematics of the 6-6 Stewart platform of planar base and moving platform. Based on algebraic elimination method and with one extra linear sensor, it first derives an 8th-degree univariate equation and then finds tentative solution sets out of which the actual solution is to be selected. In order to provide more exact solution despite the error between measured sensor value and the theoretical one, a correction method is also used. The overall procedure requires so little computation time that it can be efficiently used for realtime applications. In addition, unlike the iterative schemes e.g. Newton-Raphson, the algorithm does not require initial estimates of solution and is free of the problems that it does not converge to actual solution within limited time. The presented method has been implemented in C language and a numerical example is given to confirm the effectiveness and accuracy of the developed algorithm.

• Journal of the Korean Society for Precision Engineering
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• v.16 no.8
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• pp.186-192
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• 1999

This paper introduces a study of a method for the forward kinematic analysis, which finds the 6 DOF motions and velocities from the given six cylinder lengths in the Stewart platform. From the viewpoints of kinematics, the solution for the inverse kinematic is easily found by using the vectors of the links which are composed of the joint coordinates in base and plate frames, to act contrary to the serial manipulator, but forward kinematic is difficult because of the nonlinearity and complexity of the Stewart platform dynamic equation with the multi-solutions. Hence we, first in this study, introduce the linear estimator using the Luenberger's observer, and the estimator using the nonlinear measured model for the forward kinematic solutions. But it is difficult to find the parameter of the design for the estimation gain or to select the estimation gain and the constant steady state error exists. So this study suggests the estimator with the estimation gain to be learned by the neural network with the structure of multi-perceptron and the learning method using back propagation and shows the estimation performance using the simulation.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.14 no.12
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• pp.6090-6097
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• 2013

A pneumatically-driven driving simulator that provides a realistic representation of the driving environment was developed. The motion platform for the driving simulator is a mechatronic device that gives a driver the realistic feeling of an actual vehicle. The cost of the motion platform comprises the largest part of the expenses in developing a driving simulator. In this project, to develop a low-cost motion platform, the self-built motion platform based on the Stewart platform configuration that is constructed by six pneumatic cylinders was used as its actuator. The Stewart platform that moves in response to the operating signals of the joystick showed satisfactory tracking performance. We confirmed the possibility of the driving simulator using rFactor that is a commercially available racing game software.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10b
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• pp.28-31
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• 1996

We propose an estimator design method of Stewart platform, which gives the 6DOF, positions and velcities of Stewart platform from the measured cylinder length. The solution of forward kinematics is not solved yet as a useful realtime application tool because of the complexity of the equation with multiple solutions. Hence we suggest an nonlinear estimator for the forward kinematics solution using Luenberger observer with nonlinear error correction term. But the way of residual gain selection of the estimator is not clear, so we suggest an algebraic Riccati equation for gain matrix using Lyapunov method. This algorithm gives the sufficient condition of the stability of error dynamics and can be extended to general nonlinear system.