Flexible arrangement of two Bennett tubes

TL;DR

This paper explores the design and properties of flexible structures formed by coupling two Bennett mechanisms, resulting in novel flexible tubes with quadrilateral cross-sections and skew faces, expanding the understanding of flexible polyhedral arrangements.

Contribution

It introduces three new 4-dimensional families of flexible Bennett tube structures, linking them to flexible bipyramids and biprisms, and discusses their properties.

Findings

Three new families of flexible Bennett tubes identified

Flexible tubes can have quadrilateral cross-sections with skew faces

Connections established between Bennett tubes, bipyramids, and biprisms

Abstract

In analogy to flexible bipyramids, also known as Bricard octahedra, we study flexible couplings of two Bennett mechanisms. The resulting flexible bi-Bennett structures can be used as building blocks of flexible tubes with quadrilateral cross-section that possess skew faces. We present three 4-dimensional families of flexible arranged Bennett tubes and discuss some of their properties as well as their relation to flexible bipyramids and biprisms, respectively.