  When a moving frame defined along a space curve is required to keep an axis
aligned with the tangent direction of motion, the use of rotation-minimizing
frames (RMF) avoids unnecessary rotations in the normal plane. The construction
of rigid body motions using a specific subset of quintic curves with rational
RMFs (RRMFs) is here considered. In particular, a novel geometric
characterization of such subset enables the design of a local algorithm to
interpolate an assigned stream of positions, together with an initial frame
orientation. To achieve this, the translational part of the motion is described
by a parametric $G^1$ spline curve whose segments are quintic RRMFs, with a
globally continuous piecewise rational rotation-minimizing frame. A selection
of numerical experiments illustrates the performances of the proposed method on
synthetic and arbitrary data streams.
