An explicit construction of Kaleidocycles

Author:

Shizuo Kaji, Kenji Kajiwara, Shota Shigetomi

Keyword:

Nonlinear Sciences, Exactly Solvable and Integrable Systems, Exactly Solvable and Integrable Systems (nlin.SI), Robotics (cs.RO), Differential Geometry (math.DG)

journal:

date:

2023-08-08 16:00:00

Abstract

We model a family of closed kinematic chains, known as Kaleidocycles, with the theory of discrete spatial curves. By leveraging the connection between the deformation of discrete curves and the semi-discrete integrable systems, we describe the motion of a Kaleidocycle by elliptic theta functions. This study showcases an interesting example in which an integrable system generates an orbit in the space of the real solutions of polynomial equations defined by geometric constraints.

PDF: An explicit construction of Kaleidocycles.pdf