Analysis of the Bennett linkage in the geometry of tori

Spatial link mechanisms with revolute pairs (7R) can be analyzed only on the basis of a three-bar mechanism with a higher pair in the form of two general tori. These mechanisms have special positions, where mobility is changeable. These special positions include bifurcation points, dead points or extreme positions. A situation when two tori overlap distinguishes one type of these positions. A kinematic system with a higher pair becomes an invariable immobile system. In an equivalent structure of a 7R mechanism, three links form an invariable immobile system, and the remaining four may have one or two degrees of additional freedom. Two spatial dyads of the 7R mechanism may form (e.g. in a synthesis process) a 4R system of the Bennett linkage, which is equivalent to two identical and overlapping tori. This paper focuses on presenting such a special case.