PASSING A CENTRAL AXIS CONGRUENCE THROUGH 6 ARBITRARY LINES IN-SPACE

The design theory of a spatial 4C linkage to move a rigid body through four specified spatial positions determines a congruence of lines tha t may be used as fixed axes of the linkage, called the central axis co ngruence. In this paper, we locate a central axis congruence in space by identifying six arbitrary lines that it is to contain; we do not sp ecify the positions of a rigid body or the associated relative displac ement screws. We find that this yield at least one and as many as five different central axis congruences through a given set of six lines. Having defined the congruence without identifying any positions, we th en show how to determine sets of four spatial positions that generate the given central axis congruence.