A proposed general method for constructing compatibility linkages for the dimensional synthesis of planar mechanism components is presented. These components include a single link, a dyad, a triad, and a quadriad for up to the maximum number of precision positions and are derived here for components having one of its links with unknown angular displacements. Also included are derived formulas for calculating number of degrees of freedom and number of links of the respective compatibility linkages. Bernshtein formula is introduced for the computation of number of possible solutions. The concept of solution structure and the solution procedure are also introduced to assist the application of compatibility linkages in solving dimensional synthesis problems and an example is given to demonstrate different solution positions of a compatibility linkage.