• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.25 no.3
• /
• pp.339-352
• /
• 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.

• 제어로봇시스템학회:학술대회논문집
• /
• 1992.10a
• /
• pp.736-741
• /
• 1992

The Stewart platform is one example of a motion simulator which generates 6 DOF motion in space by 6 actuators connected in parallel. The present SISO controllers are designed to track displacement command of each actuator computed from reference 6 DOF motion of platform by Stewart platform inverse kinematics. But this type of control can't cope with external load variation, geometric configuration of motion simulator, and different dynamic behavior of 6 DOF motion. In this paper, a multivariable controller using H- optimal control theory is designed for linerized simulator model with each actuator driving force as control input and platform 6 DOF motion as measured output. Nonlinear simulation result of the H$_{\infty}$ MIMO controller is not satisfied in steady-state characteristics. But the proposed H$_{\infty}$ + PI control scheme shows acceptable performance.e.e.

• Proceedings of the KSME Conference
• /
• 2008.11a
• /
• pp.1944-1946
• /
• 2008

This paper analyzed orientation simulation of Stewart platform which is a parallel manipulator of 6-DOF. When platform shape had been given, inverse kinematics as the problem about length of actuator could get an answer using a vector function simply, and forward kinematics as the problem solving shape of platform through the length of actuator could get answer using repetitive and manual explaining Newton-Raphson method because it is expressed a high nonlinear polynomial expression. In addition, for control the Stewart platform it could drive simply and it could confirm the state of orientation in real-time.

• Journal of the Korean Society of Manufacturing Technology Engineers
• /
• v.24 no.6
• /
• pp.660-666
• /
• 2015

To avoid radiation exposure from repeated x-rays taken during orthopedic surgery, an x-ray permeable teleoperated Stewart platform for orthopedic fracture surgery was developed. This system is composed of a user interface device and a teleoperated operational robot, both of which use a Stewart platform mechanism. The links of the operational robot are made from an x-ray permeable material, polycarbonate, to minimize the interference. The forward and inverse kinematics algorithm applied and the structural reliability were both verified through an analysis using commercial engineering software. To monitor the operating status in real time and stop the device during an emergency, a monitoring software was developed. The performance of the x-ray permeable teleoperated Steward platform was validated experimentally.

• 제어로봇시스템학회:학술대회논문집
• /
• 1996.10b
• /
• pp.213-216
• /
• 1996

This paper studies a class of in-parallel manipulators with special geometry where the forward displacement analysis problem can be solved easier than the fully parallel manipulators. Three horizontal links of this mechanism provide 3DOFs(Degrees of Freedom), which are one degree of orientational freedom and two degrees of translatory freedom. Three vertical links of this mechanism provide 3DOFs, which are two degrees of orientational freedom and one degree of translatory freedom. The main advantages of this manipulator, compared with the Stewart platform type, are the capability to produce pure rotation and to predict the motion of the moving platform easily. Since this manipulator has simple kinematic characteristics compared with the Stewart platform, controlling in real-time is possible due to less computational burden. The purpose of this investigation is to develope an analytical method and systematic method to analyze the basic kinematics of the manipulator. The basic kinematic equations of the manipulator are derived and simulation is carried out to show the performance of the mechanism.

• Proceedings of the KSME Conference
• /
• 2000.11a
• /
• pp.541-547
• /
• 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 Institute of Control, Robotics and Systems
• /
• v.8 no.8
• /
• pp.639-648
• /
• 2002

The stewart platform manipulator is a manipulator that has the closed-loop structure with an upper plate end-effector and a base frame. The stewart platform manipulator has the merit of high working accuracy and high stiffness compared with a serial manipulator. However, this is a complex structure, so controllability of the system is not so good. In this paper, we introduce a new robust motion control algorithm using partial state feedback for a class of nonlinear systems in the presence of modelling uncertainties and external disturbances. The major contribution of this work introduces the development and design of robust observer for the state and the perturbation, which is integrated into a variable structure controller(VSC) structure. The combination of controller/observer improves the control performance, because of the robust routine called sliding mode control with sliding perturbation observer(SMCSPO). Simulation and experiment are performed to apply to the manipulator. And their results show a high accuracy and a good performance.

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

• Proceedings of the Korean Society of Precision Engineering Conference
• /
• 2004.10a
• /
• pp.525-529
• /
• 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
• /
• 2004.10a
• /
• pp.520-524
• /
• 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.