Model of 5R spatial linkage in the geometry of tori

The present study covers the problem of a kinematic analysis of a spatial 5R single DOF linkage. This mechanism was constructed by combining two 4R universal mechanisms presented in tori geometry (Bil, 2012). The problem can be presented as the effect of an intersection of two tori in such a manner that the circles that form these tori do not coincide (Bil, 2010; 2011; 2012; 2012). As a result of this, a 5R model was obtained of a five-bar mechanism. It was demonstrated that there are 16 cases of the intersection of two universal tori with constant linear dimensions and that they differ with the angles of the mutual positions of rotation axes. A particular case of the five-bar mechanism presented herein is the well-known Goldberg mechanism (Goldberg, 1943), which was initially formed out of a particular case combination of two Bennett mechanisms (Bennett, 1903; Baker, 1979).