It has been previously shown that non-architecturally singular parallel manipulators of Stewart–Gough type, where the planar platform and the planar base are related by a projectivity, have either so-called elliptic self-motions or pure translational self-motions. As the geometry of all manipulators with translational self-motions is already known, we focus on elliptic self-motions. We show that these necessarily one-parameter self-motions have a second, instantaneously local, degree of freedom in each pose of the self-motion. More-over, we introduce a geometrically motivated classification of elliptic self-motions and study the so-called orthogonal ones in detail.