This paper aims at providing a method to synthesize mechanical architectures of self-adaptive robotic fingers driven by linkages. Self-adaptive mechanisms are used in robotic fingers to provide the latter with the ability to adjust themselves to the shape of the object seized without any dedicated electronics, sensor, or control. This type of mechanisms has been known for centuries but the increased capabilities of digital systems have kept them in the shadows. Recently, because of the lack of commercial and industrial success of complex robotic hands, self-adaptive mechanisms have attracted much more interest from the research community and several prototypes have been built. Nevertheless, only a handful of prototypes are currently known. It is the aim of this paper to present a methodology that is able to generate thousands of self-adaptive robotic fingers driven by linkages with two and three phalanges. First, potential kinematic architectures are synthesized using a well-known technique. Second, the issue of proper actuation and passive element(s) selection and location is addressed.