Abstract
Equilibrium shapes of a planar polygonal linkage are cyclic configurations. We describe all possible sets of cyclic configurations for pentagonal linkages.
Highlights
We study polygonal linkages L with two xed vertices and their exes on a plane with allowed self-intersections
In this framework, we give a list of all possible sets of cyclic congurations a typical pentagonal linkage
Summary
Íà êîíôèãóðàöèîííîì ïðîñòðàíñòâå øàðíèðíîãî ìíîãîóãîëüíèêà ìîæåò áûëü íå ìåíåå 2g + 2, ãäå g ðîä êîíôèãóðàöèîííîãî ïðîñòðàíñòâà, è íå áîëåå ÷åòûðíàäöàòè êðèòè÷åñêèõ òî÷åê. Îñíîâíàÿ òðóäíîñòü äîêàçàòåëüñòâà èõ ñóùåñòâîâàíèÿ ñîñòîèò â òîì, ÷òî, êàê îòìå÷åíî åùå â ñòàòüå Â.Âàðôîëîìååâà [7], êîëè÷åñòâî êðèòè÷åñêèõ òî÷åê íà êîíôèãóðàöèîííîì ïðîñòðàíñòâå î÷åíü ÷óâñòâèòåëüíî ê èçìåíåíèþ äëèí øàðíèðíîãî ìíîãîóãîëüíèêà. 5: Âïèñàííûå êîíôèãóðàöèè øàðíèðíîãî ïÿòèóãîëüíèêà (1;0.98; 0.98;0.499; 0.499) (êîíôèãóðàöèîííîå ïðîñòðàíñòâî ïîâåðõíîñòü ðîäà äâà). 8: Âïèñàííûå êîíôèãóðàöèè øàðíèðíîãî ïÿòèóãîëüíèêà (1;0.98;0.97;0.5;0.5) (êîíôèãóðàöèîííîå ïðîñòðàíñòâî ïîâåðõíîñòü ðîäà òðè). 10: Âïèñàííûå êîíôèãóðàöèè øàðíèðíîãî ïÿòèóãîëüíèêà (1;0.9;0.8;0.8;0.7) (êîíôèãóðàöèîííîå ïðîñòðàíñòâî ïîâåðõíîñòü ðîäà ÷åòûðå). Öïåîíëòîðâèîíïàèñóàãíëíàîìéåîæêäîëóî−O−P→pi îèêð−Oó−pæ−i+→í1î.ñÓòèã.îë âñåãäà îïðåäåëÿöåíòðàëüíîé åòñÿ êàê ïîëîæèòåëüíûé, íå ó÷èòûâàÿ îðèåíòàöèè
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