Geometric analysis of Bennett's spherical 8-bar linkage and its spatial counterpart

TL;DR

This paper presents a geometric analysis of Bennett's spherical 8-bar linkage and its spatial counterpart, revealing symmetries and structural properties through line reflection methods.

Contribution

It introduces a geometric approach to analyze two symmetric overconstrained linkages, highlighting their symmetries and relation to classical Bennett and Bricard linkages.

Findings

Identification of symmetries in spatial poses

Connection between spherical and spatial linkages

Geometric dissection via line reflections

Abstract

We provide a geometric approach to two combinatorically symmmetric overconstrained spatial linkages. Both contain eight bodies and twelve revolute joints and collapse in aligned poses. The first one is spherical and the union of six spherical isograms. It is the spherical image of a Bricard octahedron of type~3 and was already analysed 1912 by Bennett. The second linkage is the dualized version and composed from six Bennett isograms. Our approach via line reflections discloses some symmetries at spatial poses.