ABSTRACT In this paper, we present a kinematic theory for Hoberman and other similar foldable linkages. By recognizing that the building blocks of such linkages can be modeled as planar linkages, different classes of possible solutions are systematically obtained including some novel arrangements. Criteria for foldability are arrived by analyzing the algebraic locus of the coupler curve of a PRRP linkage. They help explain generalized Hoberman and other mechanisms reported in the literature. New properties of such mechanisms including the extent of foldability, shape-preservation of the inner and outer profiles, multi-segmented assemblies and heterogeneous circumferential arrangements are derived. The design equations derived here make the conception of even complex planar radially foldable mechanisms systematic and easy. Representative examples are presented to illustrate the usage of the design equations and the kinematic theory. INTRODUCTION This paper is concerned with foldable linkages. The applications of such linkages range from consumer products and toys to architectural applications and massive deployable space structures. They belong to the class of over-constrained linkages. It is their particular arrangement of specially designed, suitably-proportioned rigid links that renders them mobile often with a single degree of freedom. Therefore we see such mechanisms as inventions rather than results of systematic design. Two such examples are shown i
