Bennett 4R linkage, a classic overconstrained one, could realise complex spatial motions with the least links in 3D space, it hence has attracted lots of attentions in mechanism. To get larger and realise more complex deployable structures, lots of Bennett 4R linkages are expected to be connected as mobile assemblies with one DOF. While, all of these existed assemblies were constructed by tessellation, and they hence could not realise deployable polyhedrons.
       In order to extend the potential of deployable structures and seek more structures constructed with Bennett 4R linkages, Dr. Fufu Yang and Prof. Yan Chen from Tianjin University as well as Prof. Zhong You from the University of Oxford proposed a novel linkage by connecting two identical Bennett 4R linkage with 4 spherical joints, and this linkage could realise the transformation between cuboctahedron and octahedron with one DOF.

A mobile assembly constructed with two Bennett linkages

The linkage composed with triangular links

The transformable polyhedron

Physical model of the transformable polyhedron

        According to the symmetric feature of two identical Bennett 4R linkages, the geometric conditions to construct a one-DF assembly with four spherical joints were derived. Then, the authors realised the transformation between cuboctahedron and octahedron with one DOF. The directions of revolute joints were obtained by studying the geometric properties of the deployed and the folded configurations, i.e., cuboctahedron and octahedron. Although the symmetries of the polyhedrons are broken, it is indeed with one DOF and with no bifurcation, which were demonstrated by the kinematic analysis and the truss-transformation method. Finally, a physical model was fabricated to verify the results.
        The work was accepted by Mechanism and Machine Theory, the official research journal of the International Federation for the Promotion of Mechanism and Machine Science (IFToMM) on Nov. 5, 2019. It is available online now and provides a way to design new deployable structures with overconstrained linkages.

Fufu Yang, Zhong You, Yan Chen, 2020, Mobile Assembly of Two Bennett Linkages and Its Application to Transformation Between Cuboctahedron and Octahedron, Mechanism and Machine Theory 145, 103698.
(https://doi.org/ 10.1016/j.mechmachtheory.2019.103698)