• Title/Summary/Keyword: Direct kinematics solution

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New Closed-Form Direct Kinematic Solution of the 3-6 Stewart-Gough Platform Using the Tetrahedron Approach

  • Song, Se-Kyong;Kwon, Dong-Soo
    • 제어로봇시스템학회:학술대회논문집
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    • 2001.10a
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    • pp.83.4-83
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    • 2001
  • The paper presents a new closed-form, not a polynomial-form, solution of the direct kinematics of the 3-6 (Stewart-Gough) Platform. Many research works have presented a single high-order polynomial equation of the direct kinematics. However the polynomial equation causes potential problems such as complicated formulation procedures and discrimination of the actual solution from all roots, which results in time-consuming task and heavy computational burden. Thus, to overcome these problems, we use a new formulation approach, based on the Tetrahedron Approach, to derive easily a closed-form nonlinear equation of the direct kinematics and use not the Newton-Raphson method, but the Secant method to obtain quickly the solution from ...

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New Direct Kinematic Formulation of 6 D.O.F Stewart-Cough Platforms Using the Tetrahedron Approach

  • Song, Se-Kyong;Kwon, Dong-Soo
    • Transactions on Control, Automation and Systems Engineering
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    • v.4 no.3
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    • pp.217-223
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    • 2002
  • The paper presents a single constraint equation of the direct kinematic solution of 6-dof (Stewart-Gough) platforms. Many research works have presented a single polynomial of the direct kinematics for several 6-dof platforms. However, the formulation of the polynomial has potential problems such as complicated formulation procedures and discrimination of the actual solution from all roots. This results in heavy computational burden and time-consuming task. Thus, to overcome these problems, we use a new formulation approach, called the Tetrahedron Approach, to easily derive a single constraint equation, not a polynomial one, of the direct kinematics and use two well-known numerical iterative methods to find the solution of the single constraint equation. Their performance and characteristics are investigated through a series of simulation.

Direct Position Kinematics Solution For Casing Oscillator Using the Kinematic Inversion (기구학적 전이를 이용한 케이싱 오실레이터의 순기구학 해석)

  • 백재호;배형섭;이은준;박명관
    • 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.

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Inverse Kinematics for Five-axis Machines Using Orthogonal Kinematics Chain (5축 밀링가공기의 직교 특성을 이용한 역기구학 방정식의 유도)

  • So, Bum-Sik;Jung, Yoong-Ho
    • Korean Journal of Computational Design and Engineering
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    • v.13 no.2
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    • pp.153-161
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    • 2008
  • This paper proposes an efficient algorithm for deriving inverse kinematics equation of 5-axis machine. Because the joint order and direction of 5-axis machine are different for each type of machine, each type of machine needs its own inverse kinematics equation for post-processing of NC data. Also derived inverse kinematics equation may cause problems of indeterminate and inconsistent solution. In order to resolve these problems, we have developed a generic method to derive direct kinematics equation by considering orthogonal joints of 5-axis machines. Using this method, we also have proposed a general algorithm for deriving inverse kinematics equation for various types of 5-axis machines.

Calculating the Feedrate of 5-Axis NC Machining Data for the Constant Cutting Speed at a CL-point (공구 끝의 일정한 절삭속도를 위한 5축 NC 가공 데이터의 이송속도 산출)

  • 이철수;이제필
    • Korean Journal of Computational Design and Engineering
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    • v.6 no.2
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    • pp.69-77
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    • 2001
  • This paper describes a method of calculating the feedrate for the constant cutting speed at a CL-point in 5-axis machining. Unlike 3-axis machining, 5-axis machining has the flexibility of the tool motions due to two rotation axes. But the feedrate at joint space differs from the feedrate at a tool tip(the CL-point) of the 3D Euclidean space for the tool motions. The proposed algorithm adjusts the feedrate based on 5-axis NC data, the kinematics of a machine, and the tool length. The following calculations is processed for each NC block to generate the new feedrate; 1) calculating the moving distance at the CL-point, 2) calculating the moving time by the given feedrate, 3) calculating the feedrate of each axis, 4) getting the new feedrate. The proposed algorithm was applied to a 5-axis machine which had a tilting spindle and a rotary table. Totally, the result of the algorithm reduced the machining time and smoothed the cutting-load by the constant cutting speed at the CL-point.

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Stochastic hygrothermoelectromechanical loaded post buckling analysis of piezoelectric laminated cylindrical shell panel

  • Lal, Achchhe;Saidane, Nitesh;Singh, B.N.
    • Smart Structures and Systems
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    • v.9 no.6
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    • pp.505-534
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    • 2012
  • The present work deals with second order statistics of post buckling response of piezoelectric laminated composite cylindrical shell panel subjected to hygro-thermo-electro-mechanical loading with random system properties. System parameters such as the material properties, thermal expansion coefficients and lamina plate thickness are assumed to be independent of the temperature and electric field and modeled as random variables. The piezoelectric material is used in the forms of layers surface bonded on the layers of laminated composite shell panel. The mathematical formulation is based on higher order shear deformation shell theory (HSDT) with von-Karman nonlinear kinematics. A efficient $C^0$ nonlinear finite element method based on direct iterative procedure in conjunction with a first order perturbation approach (FOPT) is developed for the implementation of the proposed problems in random environment and is employed to evaluate the second order statistics (mean and variance) of the post buckling load of piezoelectric laminated cylindrical shell panel. Typical numerical results are presented to examine the effect of various environmental conditions, amplitude ratios, electrical voltages, panel side to thickness ratios, aspect ratios, boundary conditions, curvature to side ratios, lamination schemes and types of loadings with random system properties. It is observed that the piezoelectric effect has a significant influence on the stochastic post buckling response of composite shell panel under various loading conditions and some new results are presented to demonstrate the applications of present work. The results obtained using the present solution approach is validated with those results available in the literature and also with independent Monte Carlo Simulation (MCS).