In this paper, a one-to-one correspondence is given between the tangent bundle of unit 2-sphere, TS2, and the unit dual sphere, S-D(2). According to Study's map, to each curve on S-D(2) corresponds a ruled surface in Euclidean 3-space, R-3. Through this correspondence, we have corresponded to each curve on TS2 a unique ruled surface in R-3. Moreover, the relationships between the developability conditions of these ruled surfaces and their striction curves are analyzed. It is shown that the ruled surfaces corresponding to the involute-evolute curve couples on TS2 are developable.