We describe the principles of building a moving vision platform (a Rig) that once calibrated can thereon self-adjust to changes in its internal configuration and maintain an Euclidean representation of the 3D world using only projective measurements. We term this calibration paradigm "OmniRig". We assume that after calibration the cameras may change critical elements of their configuration, including internal parameters and centers of projection. Theoretically we show that knowing only the rotations between a set of cameras is sufficient for Euclidean calibration even with varying internal parameters and unknown translations. No other information of the world is required.