• 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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• 2001.04a
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• pp.255-258
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• 2001

This introduces a improved method of the forward kinematics analysis, which finds the 6DOF motions and velocities from the given six cylinder lengths in the Steward platform. The numerical method(Newton Raphson Mehotd)of the forward kinematics analysises has the disadvantage of the long calculated time. To overcome this, we propose the competitive method that determine a proper initial value. Through the competitive method, we can select a proper initial value so that the calculate time is reduced. therefore we can give the property of the real time process to the forward kinematics analysis. We show the result comparing between general Newton-Raphson method and proposed one. From the result we verify the performance of the proposed method.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.32 no.2
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• pp.202-208
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• 2008

A 6 DOF Multi axis simulation table (MAST) is used to perform vibration and fatigue tests for parts or assemblies of automobiles, aircraft, or other systems. It consists of a table and 6 linear actuators. For its attitude control, we have to adjust the lengths of 6 actuators properly. The system is essentially a parallel mechanism. Three actuators are connected to the table directly and other three actuators are connected indirectly. Because of these, the MAST shows also a serial mechanism#s property: the inverse kinematics is more complicated than a pure parallel mechanism and each actuator can operate independently. The authors have performed a kinematics analysis of the 6 DOF MAST. We have presented an analytical and a numerical solution for the inverse and forward kinematics, and we have verified the solutions by a 3D CAD software.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.28 no.12
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• pp.1845-1855
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• 2004

This paper presents the forward kinematics of the Casing Oscillator that is a construction machine. The Structure of the Casing Oscillator is similar to those of 4 degree-of-freedom mechanisms with a redundancy. With analytical (geometrical) methods, the solutions of the forward position kinematics problem are significantly found by both solving an 8$^{th}$ -order polynomial equation in one unknown variable and using one over-constraint geometrical equation which can be derived under the condition of a redundancy. The proposed forward kinematics has closed-form solutions and allows Auto-Balancing control of the moving platform in real time. Numerical examples are presented and the results are verified by an inverse kinematics analysis.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1997.10a
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• pp.237-240
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• 1997

The casing oscillator is a construction equipment to clamp, oscillate and push a casing for foundation work. In case that the casing oscillator is operated on the slant ground, if another construction heavy equipment is not used, it is impossible to insert the casing in ground using only casing oscillator. So in this paper, we present the new casing oscillator that need not to level the ground for work of casing insertion. This mechanism can execute 4 DOF motion by actuating 5 single - rod hydraulic cylinders. The forward kinematics analysis of the casrng oscillator by tetrahedron geometry is performed so predict workspace, direction and poison of casing oscillatoer.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.7
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• pp.1632-1642
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• 1994

The Stewart Platform is a six-degree-of-freedom in-parallel-actuated manipiulator mechanism. The kinematic behavior of parallel mechanisms shows inverse characteristics as compared that of serial mechanisms; i.e, the inverse kinematic problem of Stewart Platform is straightforward, but no closed form solution of the forward kinematic problem has been previously presented. Thus it is difficult to calculate the 6 DOF displacement of the platform from the measured lengths of the six actuators in real time. Here, a real-time estimation algorithm which solves the Stewart Platform kinematic problem is proposed and tested through computer simulations and experiments. The proposed algorithm shows stable convergence characteristics, no estimation errors in steady state and good estimation performance with higher sampling rate. In experiments it is shown that the estimation result is the same as that of simulation even in the presence of measurement noise.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2000.11a
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• pp.224-228
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• 2000

In this paper, the kinematics of the new type of parallel manipulator is studied, and neural network is applied to solve the forward kinematics problem. The parallel manipulator, called a Stewart platform, has an easy and unique solution about the inverse kinematics, however the forward kinematics is difficult to get the solution because of the lack of an efficient algorithm due to its highly nonlinearity. This paper proposes the neural network scheme as an alternative Newton-Raphson method. The neural network is found to improve its accuracy by adjusting the offset of the result obtained.

• 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.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2002.10a
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• pp.580-583
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• 2002

This paper presents a novel pose description corresponding to the structure characteristics of parallel manipulators, which is convenient and intuitionistic to us. A class of 3-RSR parallel manipulator is considered here. Through analysis on geometry theory, we obtain a new method of the closed-form solution to the forward kinematics. The closed-form solution contains two different meanings-analytical and real-time. So we reach the goal of practical application and control. A numerical example is also presented and are verified by an inverse kinematics analysis. It shows that the method has a practical value for real-time control.