高次柔軟性と剛性の再定義に向けた大域的アプローチ
A global approach for the redefinition of higher-order flexibility and rigidity
二重ワット機構などのカスプ機構が示す高次剛性の矛盾を解決するため、多面体の可撓性判定に用いられるSabitovの有限アルゴリズムに着想を得た大域的アプローチを提案し、高次柔軟性と剛性を再定義する。
著者: Georg Nawratil
分類: math.AG, cs.RO
原文アブストラクト
The famous example of the double-Watt mechanism given by Connelly and Servatius raises some problems concerning the classical definitions of higher-order flexibility and rigidity, respectively, as they attest the cusp configuration of the mechanism a third-order rigidity, which conflicts with its continuous flexion. Some attempts were done to resolve the dilemma but they could not settle the problem. As cusp mechanisms demonstrate the basic shortcoming of any local mobility analysis using higher-order constraints, we present a global approach inspired by Sabitov's finite algorithm for testing the bendability of a polyhedron, which allows us (a) to compute iteratively configurations with a higher-order flexion and (b) to come up with a proper redefinition of higher-order flexibility and rigidity. The presented approach is demonstrated on several examples (double-Watt mechanisms and Tarnai's Leonardo structure). Moreover, we determine all configurations of a given 3-RPR manipulator with a third-order flexion and present a corresponding joint-bar framework of flexion order 23.
