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

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.