A plane symmetric 6R foldable ring

The design of a deployable structure which deploys from a compact bundle of six parallel bars to a rectangular ring is considered. The structure is a plane symmetric Bricard linkage. The internal mechanism is described in terms of its Denavit–Hartenberg parameters; the nature of its single degree of freedom is examined in detail by determining the exact structure of the system of equations governing its movement; a range of design parameters for building feasible mechanisms is determined numerically; and polynomial continuation is used to design rings with certain specified desirable properties.