In this chapter, structural analysis is applied to kinematic chains to ensure the viability of mechanism configurations before engaging in detailed design. Key structural parameters such as variety, connectivity, and redundancy are introduced, providing insight into how these factors influence control and actuation points. The concept of variety, defined as the difference between global and minimal loop mobilities, is emphasized as a criterion for actuator selection. Matrix representations—degree of control, connectivity, and redundancy matrices—are explained and applied to various planar mechanisms. Isomorphism between graphs is discussed to identify structurally equivalent mechanisms and eliminate redundant solutions in mechanism enumeration. Numerous example figures illustrate complex kinematic chains and their structural decomposition. By performing structural analysis early in the design process, engineers can eliminate infeasible or inefficient mechanisms, streamlining the path to optimal solutions. This chapter forms a crucial link between conceptual design and functional mechanism synthesis.