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This paper analyzes tendon-driven mechanisms (TDMs) with active and passive tendons and proposes a method for designing TDMs. First, we group TDMs into six classes according to their controllability and the number of driving degrees of freedom. In this classification system, the conventional underactuated mechanisms are grouped into three classes, two of which have often previously been grouped together although they have different manipulation abilities. Next, we analyze bias forces to separate and decouple a given TDM into several smaller TDMs. Finally, we propose a design method for combining smaller TDMs into an appropriate TDM. Using this method, we can easily determine an appropriate tendon transmission that meets the requirements for the number of tendons, the hardware of the tendon routing, and arbitrary joint constraint that has useful applications in prosthetic and biomimetic hands. Numerical examples show that the proposed method guarantees a nonsingular series actuation transmission and that the designed underactuated TDMs could achieve arbitrary stiffness independent of the actuation effort compared with the conventional underactuated TDM with torsion springs.