In this paper, we introduce linkages as new drawing tools and show that this tool is complete, i.e., all diagrams that can be described constructively can be drawn with linkages. This class includes the constraint problems with distance constraints only. As an application, we show that the simplest constrained graph which is beyond the scope of Owen and Hoffmann's popular triangle decomposition me thods can be transformed to pure geometric constructive form. To solve the equations raised from linkage constructions, we propose a geometric method which is based on dynamic locus generation.