This chapter presents a methodology for the systematic reconstruction of design concepts of lost machines. Design specifications of the target subject are addressed. Various atlases of generalized kinematic chains are introduced and provided as the inclusive data banks for the generation of feasible specialized chains. The concept of specialization is further presented for identifying all possible reconstruction designs. An example regarding the conceptual design of planetary gear trains for infinitely various transmissions [1, 2] is adopted simply for the purpose of illustrating each step of the design methodology in detail.