The geometric aspects of Burmester theory, as used in planar four-bar linkage synthesis, are examined to define a general procedure which is applied to the generation of the joint loci of spatial dyads with axis joints. The joints are geometrically related to the screw axes of the prescribed motion, by means of a screw triangle. The geometric relationships are typically separated into several geometric constraints. Each geometric constraint is considered separately to generate the loci of lines representing joint axes which satisfy, the constraint. Combining the loci from each constraint produces a single loci of all the possible fixed or moving joints. The geometric approach is shown to have several benefits not obtained in numerical and pure analytical techniques, especially in relating the characteristics of the loci to the physical linkage and its required motion.