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Mounting Bennett's double helix on his skew 12-bar linkage

The many facets of Bennett's investigation into his skew four-bar linkage and its several extensions have given rise to an abundance of studies by other workers. Among his imaginative endeavours was the deployment of a double helix to convert his planar 12-bar network into a spatial counterpart. A geometrically attractive idea, its algebraic equivalent had been difficult to realize because of a lack of underlying analytical relationships. As well, recent papers have revealed apparent shortcomings in Bennett's representation. The present work is an attempt to provide a complete algebraic treatment of Bennett's novel device.