Bennettʹs linkage and the cylindroid

Bennettʹs linkage is a spatial 4R closed chain that can move with one degree of freedom. The set of relative displacement screws that form the one-dimensional workspace of this device defines a ruled surface known as a cylindroid. The cylindroid is generally obtained as a result of a real linear combination of two screws. Thus, the workspace of Bennettʹs linkage is directly related to a one-dimensional linear subspace of screws. In this paper, we examine in detail Bennettʹs linkage and its associated cylindroid, and introduce a reference pyramid which provides a convenient way to relate the two. These results are fundamental to efficient techniques for solving the synthesis equations for spatial RR chains.