グラスマン・ケイリー代数を用いた低自由度パラレルマニピュレータの特異点解析
Singularity Analysis of Lower-Mobility Parallel Manipulators Using Grassmann-Cayley Algebra
脚が駆動力と拘束モーメントの両方を加えるパラレルマニピュレータについて、逆ヤコビ行列の行を構成する直線のプラッカー座標の従属性をグラスマン・ケイリー代数で定式化し、特異点条件をベクトル形式で導出した研究。
著者: Daniel Kanaan, Philippe Wenger, Stéphane Caro, Damien Chablat
分類: cs.RO
原文アブストラクト
This paper introduces a methodology to analyze geometrically the singularities of manipulators, of which legs apply both actuation forces and constraint moments to their moving platform. Lower-mobility parallel manipulators and parallel manipulators, of which some legs do not have any spherical joint, are such manipulators. The geometric conditions associated with the dependency of six Pl\"ucker vectors of finite lines or lines at infinity constituting the rows of the inverse Jacobian matrix are formulated using Grassmann-Cayley Algebra. Accordingly, the singularity conditions are obtained in vector form. This study is illustrated with the singularity analysis of four manipulators.
