Institute of Mathematics for Industry

Seminar



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A closed linkage mechanism having a degenerate configuration space


Hold Date 2018-05-08 12:00~2018-05-08 13:00

Place Lecture Room S W1-C-503, West Zone 1, Ito campus, Kyushu University

Object person  

Speaker Shizuo KAJI (Institute of Mathematics for Industry, Kyushu University)

Abstract:
\emph{Linkage} is a mechanism consisting of rigid bars connected by revolute joints (hinges). Each hinge joins two adjacent bars and can rotate them around its axis. A linkage mechanism is said to be \emph{closed} if it has the topology of a circle. We consider a closed linkage with n-hinges (hence, n-bars). Possible states of such a linkage form \emph{the configuration space}, which can be thought of as a subspace of (S^1)^n. By dimension counting, the configuration space is generically n-6 dimensional. We discovered a closed linkage mechanism, which seems to have several interesting properties; most notably, the 1-dimensional configuration space regardless of n. Most of the results are only numerically confirmed and yet to be proved.