Transactions of the Korean Society of Mechanical Engineers A (대한기계학회논문집A)

The Korean Society of Mechanical Engineers (대한기계학회)
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Use of Parametric Generalized Coordinates for Kinematic Constraint Formulation of Low Degree-of-Freedom Joints

저자유도 조인트의 구속조건 생성을 위한 파라메트릭 일반좌표 이용

  • Lee, Jung Keun (Dept. of Mechanical Engineering, Hankyong Nat'l Univ.) ;
  • Lee, Chul Ho (Dept. of Mechanical Engineering, Hanyang Univ.) ;
  • Bae, Dae Sung (Dept. of Mechanical Engineering, Hanyang Univ.)
  • Received : 2013.04.26
  • Accepted : 2013.08.14
  • Published : 2013.10.01
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Abstract

In multibody mechanical systems, low-degree-of-freedom (DOF) joints such as revolute and translational joints are much more frequently used than high-DOF joints. In order to formulate kinematic constraint equations, especially for low-DOF joints, in an efficient and systematic manner, this paper presents a parametric generalized coordinate formulation as a new approach for describing constraint equations. In the proposed approach, joint constraint equations are formulated in terms of a mixed set of Cartesian and parametric generalized coordinates, which drastically reduces the complexity and computational cost of the partial derivatives of the constraints such as the constraint Jacobian. The proposed formulation is validated using a simple cylinder-crank system with an implicit integrator.

다물체 기계시스템에서 핀조인트나 병진조인트 같은 저자유도 조인트는 고자유도 조인트보다 훨씬 빈번하게 사용된다. 저자유도 조인트에 대한 기구학적 구속조건식을 효율적이고 체계적으로 공식화하기 위해, 본 논문은 구속조건식을 표현하는 새로운 접근방법으로 파라메트릭 일반좌표를 이용한다. 제안된 방법에서는 직교좌표와 파라메트릭 일반좌표를 혼합하여 조인트 구속조건을 생성하는데, 이는 구속조건에 대한 자코비안과 같은 구속조건 편미분행렬을 매우 간단하게 표현되도록 하므로써 공식의 복잡성과 계산시간을 단축시킨다. 제안된 방법은 암시적 적분기를 바탕으로 실린더-크랭크시스템에서 검증되었다.

Keywords

References

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