• Journal of the Korean Society for Precision Engineering
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• v.14 no.7
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• pp.154-162
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• 1997

본 논문은 구속된 기계 시스템의 운동 제어 설계를 위한 새로운 방법을 제안한다. 구속된 기계 시스템의 운동 제어에는 지금까지 주로 사용되어온 Lagrange의 운동 방정식에 의한 모델링 보다 Udwadia와 Kalaba에 의해 제안된 운동 방정식에 의한 모델링이 더욱 적합함을 보였으며 이는 Holonomic 및 Nonholonomic 구속 조건을 비롯한 대부분의 구속 조건이 포함된다. 문헌에 잘 알려진 두 시스템을 시뮬레이션을 통하여 비교 함으로써 본 논문에 제안된 방법이 보다 우수한 결과를 보여줌을 확인 할 수 있었다. 또한 지금까지 불가능 하였던 비선형 일반 속도(gereralized velocity)를 포함한 구속 조건도 용이하게 제어됨을 보임으로써 광범위한 구속된 기계 시스템의 제어 문제를 통일된 방법으로 접근 할 수 있음을 제시하였다.

• Journal of Mechanical Science and Technology
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• v.17 no.4
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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.

• Journal of Mechanical Science and Technology
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• v.16 no.8
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• pp.1072-1078
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• 2002

The constrained motion requires the determination of constraint force acting on unconstrained systems for satisfying given constraints. Most of the methods to decide the force depend on numerical approaches such that the Lagrange multiplier method, and the other methods need vector analysis or complicated intermediate process. In 1992, Udwadia and Kalaba presented the generalized inverse method to describe the constrained motion as well as to calculate the constraint force. The generalized inverse method has the advantages which do not require any linearization process for the control of nonlinear systems and can explicitly describe the motion of holonomically and/or nongolonomically constrained systems. In this paper, an explicit equation to describe the constrained motion is derived by minimizing the performance index, which is a function of constraint force vector, with respect to the constraint force. At this time, it is shown that the positive-definite weighting matrix in the performance index must be the inverse of mass matrix on the basis of the Gauss's principle and the derived differential equation coincides with the generalized inverse method. The effectiveness of this method is illustrated by means of two numerical applications.