Hitoshi Tokunaga

Constraint reduction based on a Lie algebra for kinematic analysis of assembly

In assembly modeling, it is necessary to capture the relative positions of components in the assembly. Many problems are related to constraint representation and its manipulation, such as constraint reduction. This paper formulates the constraints as groups of rigid body transformations and proposes a constraint reduction procedure based on the Lie algebra. This approach is then applied to the constraint representation and reduction in an assembly model. The reduced kinematic model of assembly can be derived by the proposed method for kinematic analysis.

Constraint Representation and Reduction based on Lie Algebra in Assembly Model

In assembly modelling, it is necessary to capture the relative positions of components in the assembly. Many such problems concern constraint representation and its manipulation such as constraint reduction. This paper formulates the constraints as groups of rigid body transformations and proposes a constraint reduction procedure, based on Lie algebra. Then, this approach is applied to the constraint representation and reduction in an assembly model.

A Kinematic Model of Assembly using Contact Constraint Representation in Configuration Space.

部品の幾何要素間の接合関係に基づいて, 組立品の運動可能領域を導出することが可能な組立品の機構モデルを提案することを目的として, 以下のことを行った.(1) 位置と姿勢の範囲を考慮した幾何要素間の接触拘束の配位空間における表現方法を示した.(2) それら接触拘束の表現を多部品の組立品に対して拡張した.(3) 組立晶の運動可能領域を導出するために拘束問関係の表現方法を提案した.(4) 提案した組立品の機構モデルを機構解析に対して適用し, 本手法の有効性を確認した.今後は, 導出された運動可能領域から機構の自由度をチェックする手法の提案, より効率的な計算のための拘束数削減法の提案, 形状誤差を伴う機構への拡張等が, 課題として考えられる.

Method of offset surface generation based on configuration space

Some offset surface generation methods for multi-axis machine tools use heuristic methods to consider the various orientations of cutting tools and thereby achieve cutting tool collision avoidance. In this paper in order to realize analytical cutting tool collision avoidance for multi-axis machine tools, the authors propose the application of configuration space, which can represent both the position and orientation of cutting tools simultaneously to offset surface generation.