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.

翻译：本文利用离散空间曲线理论对一类称为万花环的封闭运动链进行建模。通过利用离散曲线变形与半离散可积系统之间的联系，我们使用椭圆theta函数描述了万花环的运动。本研究展示了一个有趣实例，其中可积系统在由几何约束定义的多项式方程实解空间中生成了一条轨道。