An automated polishing process of free-form surfaces requires a tool path that covers the entire surface equally and forms an overlapping pattern without visible artifacts. The recently presented double-spiral tool paths assure a coverage of the entire surface with a continuous, non-overlapping path and low variation in distance between adjacent traces of the path. We build upon this approach by constructing cycloids of flexible radii that fill the space between adjacent traces. The use of cycloids mimics the cyclic movement when polishing by hand. The approach operates in a precomputed configuration space (c-space) given in form of an adaptive quadrilateral heightfield mesh. Operating in c-space avoids having to deal with the issues of patch-boundary oscillations or long, stretched triangles in non-uniform rational b-spline surface or triangular mesh representations, respectively. Our algorithm computes appropriate spheroids that are intersected with the c-space to compute the cycloids. We derive a smooth representation of the cycloids using arcs in a rational Bézier formulation. We apply our approach to real-world examples to demonstrate its effectiveness in covering the entire surface with the desired polishing movements.