The design theory of a spatial 4C linkage to move a rigid body through four specified spatial positions determines a congruence of lines that may be used as fixed axes of the linkage, called the central axis congruence. In this paper, we locate a central axis congruence in space by identifying six arbitrary lines that it is to contain; we do not specify the positions of a rigid body or the associated relative displacement screws. We find that this yields 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 then show how to determine sets of four spatial positions that generate the given central axis congruence.

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