This paper presents a new synthesis approach for expandable polyhedral linkages, which are synthesized by inserting appropriate link groups into the faces of polyhedron and interconnecting them by a special composite hinges (called gusset by K. Wohlhart). The overconstrained expandable polyhedral linkages are movable with one degree of freedom (DOF).The link groups are single DOF scaling planar linkages. The gussets are multiple rotary joints whose axes converge at the corresponding vertices of the polyhedron and the number of the rotary joints equals the one of the faces which meet at the vertices. This new approach is suitable for any polyhedron whatever is regular or irregular polyhedron. To verify this new approach, the expandable regular hexahedral linkage is modeled in the SolidWorks and its mobility are studied based on screw theory and topology graph.

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