• 제목/요약/키워드: Constrained Mechanical Systems

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A New Approach for Motion Control of Constrained Mechanical Systems: Using Udwadia-Kalaba′s Equations of Motion

  • Joongseon Joh
    • International Journal of Precision Engineering and Manufacturing
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    • 제2권4호
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    • pp.61-68
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    • 2001
  • A new approach for motion control of constrained mechanical systems is proposed in this paper. The approach uses a new equations of motion which is proposed by Udwadia and Kalaba and named Udwadia-Kalaba's equations of motion in this paper. This paper reveals that the Udwadia-Kalaba's equations of motion is more adequate to model constrained mechanical systems rather than the famous Lagrange's equations of motion at least for control purpose. The proposed approach coverts most of constraints including holonomic and nonholonomic constraints. Comparison of simulation results of two systems which are well-known in the literature show the superiority of the proposed approach. Furthermore, a special constrained mechanical system which includes nonlinear generalized velocities in its constraint equations, which has been considered to be difficult to control, can be controlled easily. It shows the possibility of the proposed approach to being a general framework for motion control of constrained mechanical systems with various kinds of constraints.

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강성 구속기계계의 해법에 관한 연구 (A Study on Numerical Solution Methods in Stiff Constrained Mechanical Systems)

  • 한형석;박태원
    • 대한기계학회논문집
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    • 제19권2호
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    • pp.374-381
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    • 1995
  • In this paper, integration methods for stiff constrained mechanical systems are studied to analyze dynamic response of the stiff mechanical system efficiently. The stiff, non-stiff systems are identified by using eigenvalues of the Jacobian of the systems. To integrate both stiff system and non-stiff system efficiently a new switching method between the non-stiff differential equation solver and the stiff differential equation solver is presented.

Analytical Method for Constrained Mechanical and Structural Systems

  • Eun, Hee-Chang;Park, Sang-Yeol;Lee, Eun-Taik;Chung, Heon-Soo
    • Journal of Mechanical Science and Technology
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    • 제18권10호
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    • pp.1691-1699
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    • 2004
  • The objective of this study is to present an accurate and simple method to describe the motion of constrained mechanical or structural systems. The proposed method is an elimination method to require less effort in computing Moore-Penrose inverse matrix than the generalized inverse method provided by Udwadia and Kalaba. Considering that the results by numerical integration of the derived second-order differential equation to describe constrained motion veer away the constrained trajectories, this study presents a numerical integration scheme to obtain more accurate results. Applications of holonomically or nonholonomically constrained systems illustrate the validity and effectiveness of the proposed method.

Modal Analysis of Constrained Multibody Systems Undergoing Constant Accelerated Motions

  • Park, Dong-Hwan;Yoo, Hong-Hee
    • Journal of Mechanical Science and Technology
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    • 제18권7호
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    • pp.1086-1093
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    • 2004
  • The modal characteristics of constrained multibody systems undergoing constant accelerated motions are investigated in this paper. Relative coordinates are employed to derive the equations of motion, which are generally nonlinear in terms of the coordinates. The dynamic equilibrium position of a constrained multibody system needs to be obtained from the nonlinear equations of motion, which are then linearized at the dynamic equilibrium position. The mass and the stiffness matrices for the modal analysis can be obtained from the linearized equations of motion. To verify the effectiveness and the accuracy of the proposed method, two numerical examples are solved and the results obtained by using the proposed method are compared with those obtained by analytical and other numerical methods. The proposed method is found to be accurate as well as effective in predicting the modal characteristics of constrained multibody systems undergoing constant accelerated motions.

Structural and Mechanical Systems Subjected to Constraints

  • Lee, Eun-Taik;Chung, Heon-Soo;Park, Sang-Yeol
    • Journal of Mechanical Science and Technology
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    • 제18권11호
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    • pp.1891-1899
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    • 2004
  • The characteristics of dynamic systems subjected to multiple linear constraints are determined by considering the constrained effects. Although there have been many researches to investigate the dynamic characteristics of constrained systems, most of them depend on numerical analysis like Lagrange multipliers method. In 1992, Udwadia and Kalaba presented an explicit form to describe the motion for constrained discrete systems. Starting from the method, this study determines the dynamic characteristics of the systems to have positive semidefinite mass matrix and the continuous systems. And this study presents a closed form to calculate frequency response matrix for constrained systems subjected to harmonic forces. The proposed methods that do not depend on any numerical schemes take more generalized forms than other research results.

Explicit Motion of Dynamic Systems with Position Constraints

  • Eun, Hee-Chang;Yang, Keun-Hyuk;Chung, Heon-Soo
    • Journal of Mechanical Science and Technology
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    • 제17권4호
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    • pp.538-544
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    • 2003
  • Although many methodologies exist for determining the constrained equations of motion, most of these methods depend on numerical approaches such as the Lagrange multiplier's method expressed in differential/algebraic systems. In 1992, Udwadia and Kalaba proposed explicit equations of motion for constrained systems based on Gauss's principle and elementary linear algebra without any multipliers or complicated intermediate processes. The generalized inverse method was the first work to present explicit equations of motion for constrained systems. However, numerical integration results of the equation of motion gradually veer away from the constraint equations with time. Thus, an objective of this study is to provide a numerical integration scheme, which modifies the generalized inverse method to reduce the errors. The modified equations of motion for constrained systems include the position constraints of index 3 systems and their first derivatives with respect to time in addition to their second derivatives with respect to time. The effectiveness of the proposed method is illustrated by numerical examples.

Computational Method for Dynamic Analysis of Constrained Mechanical Systems Using Partial Velocity Matrix Transformation

  • Park, Jung-Hun;Yoo, Hong-Hee;Hwang, Yo-Ha
    • Journal of Mechanical Science and Technology
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    • 제14권2호
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    • pp.159-167
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    • 2000
  • A computational method for the dynamic analysis of a constrained mechanical system is presented in this paper. The partial velocity matrix, which is the null space of the Jacobian of the constraint equations, is used as the key ingredient for the derivation of reduced equations of motion. The acceleration constraint equations are solved simultaneously with the equations of motion. Thus, the total number of equations to be integrated is equivalent to that of the pseudo generalized coordinates, which denote all the variables employed to describe the configuration of the system of concern. Two well-known conventional methods are briefly introduced and compared with the present method. Three numerical examples are solved to demonstrate the solution accuracy, the computational efficiency, and the numerical stability of the present method.

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기구학적 조인트에서 마찰력을 고려한 구속 다물체계의 역동역학 해석 (Inverse Dynamic Analysis of Constrained Multibody Systems Considering Friction Forces on Kinematic Joints)

  • 박정훈;유홍희;황요하;배대성
    • 대한기계학회논문집A
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    • 제24권8호
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    • pp.2050-2058
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    • 2000
  • A method for the inverse dynamic analysis of constrained multibody systems considering friction forces acting on kinematic joints is presented in this paper. The stiction and the sliding which represent zero and non-zero relative motions are considered during the inverse dynamic analysis. Actuating forces to control the position or the orientation of constrained multibody systems are usually calculated in the inverse dynamic analysis. An iterative procedure need to be employed to calculate the actuating forces when the friction is considered. Furthermore, the actuating forces are not uniquely determined during the stiction. These difficulties are resolved by the method presented in this paper.

Nonlinear Optimal Control of an Input-Constrained and Enclosed Thermal Processing System

  • Gwak, Kwan-Woong;Masada, Glenn Y.
    • International Journal of Control, Automation, and Systems
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    • 제6권2호
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    • pp.160-170
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    • 2008
  • Temperature control of an enclosed thermal system which has many applications including Rapid Thermal Processing (RTP) of semiconductor wafers showed an input-constraint violation for nonlinear controllers due to inherent strong coupling between the elements [1]. In this paper, a constrained nonlinear optimal control design is developed, which accommodates input constraints using the linear algebraic equivalence of the nonlinear controllers, for the temperature control of an enclosed thermal process. First, it will be shown that design of nonlinear controllers is equivalent to solving a set of linear algebraic equations-the linear algebraic equivalence of nonlinear controllers (LAENC). Then an input-constrained nonlinear optimal controller is designed based on that LAENC using the constrained linear least squares method. Through numerical simulations, it is demonstrated that the proposed controller achieves the equivalent performances to the classical nonlinear controllers with less total energy consumption. Moreover, it generates the practical control solution, in other words, control solutions do not violate the input-constraints.

케인방법을 이용한 구속 다물체계의 동역학 해석 (Dynamic analysis of constrained multibody systems using Kane's method)

  • 박정훈;유홍희;황요하;배대성
    • 대한기계학회논문집A
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    • 제21권12호
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    • pp.2156-2164
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    • 1997
  • A new formulation for the dynamic analysis of constrained multibody systems is presented in this paper. The formulation employs Kane's method along with the null space method. Kane's method reduces the dimension of equations of motion by using partial velocity matrix introduced in this study : it can improve the efficiency of the formulation. Three numerical examples are given to demonstrate the accuracy and efficiency of the formulation.