Planar two-legged parallel robots with three degrees of freedom have been suggested in the literature as a solution to reduce the leg interference problem of their conventional three-legged counterparts, and since then have attracted considerable attention. This paper presents a singularity analysis of these robots. Three alternatives, namely the robots with 2-RRR, 2-RPR, and 2-PRR structures are considered. Type I, II, and III singularity conditions are obtained taking into account all possible actuation schemes. Several singularity-free actuation schemes are enumerated and discussed. The performed analysis also shows that adjustable designs are possible for manipulators with 2-PRR structures to have singularity-free operation. The proposed design concept and its effectiveness are illustrated through numerical examples.