Assembling complete pole configurations for (over)constrained planar mechanisms

The complete pole configuration of a planar n-link mechanism having one instantaneous degree of mobility, possesses (3n-4)/2 independent poles determining (n-2)2/2 remaining poles of the configuration. The dependency is demonstrated through Desargues' Theorem and her generalizations. Simultaneously, pole configurations have been "elated" into three-dimensional point-lattices intersected by a plane. The insight obtained in these configurations allows the designer to find clues in building overconstrained linkage mechanisms meeting certain geometrical properties