Square deployable frames for space applications. Part 1: theory

The Bennett linkage is a three-dimensional 4R overconstrained mechanism consisting of four rigid links connected by revolute hinges whose axes of rotation are neither parallel nor concurrent. In general, it cannot be folded up compactly. This paper investigates the existence of alternative forms of the linkage in order to achieve the most compact folding and maximum expansion so that the linkage can be used as basic building blocks of large deployable structures for aerospace applications. This study has resulted in the creation of an effective deployable element based on the Bennett linkage. A simple method to build the Bennett linkage in its alternative form has been introduced and verified. The corresponding networks have been obtained following a layout similar to that the original Bennett linkage, which the authors discovered previously. This approach can also be extended to other types of overconstrained linkages so that they can be used for building large deployable assemblies as well.