Construction of an Anosov Spatial Linkage

The triple linkage of Thurston and Weeks exhibits Anosov behavior for certain parameter values, which can be shown by examining the Gauss curvature of the configuration space equipped with the metric induced by kinetic energy. In this paper, we consider a spatial linkage that can be viewed as a conversion of the triple linkage. We show that the configuration space asymptotically becomes a Riemannian submanifold of the four-dimensional torus $$\mathbb{T}^{4}$$ taking the limit of the parameters. Through verified numerical computation, we demonstrate that the asymptotic configuration space has negative curvature, and hence that for parameters close to the limit the linkage is Anosov by structural stability of an Anosov flow.