Preliminary results on twisting and folding mechanisms of supercoiled filaments are presented. We examine competing kinematic models for single and multiple coil formation, starting from a plane circle and we evaluate the effects of curvature on writhing and packing rates. The analysis is performed by using a simple thin filament model under conservation of linking number. Time-dependent evolutions of epicycloid curves are used to perform transition from twist to writhe. These results may find useful applications in modelling natural phenomena, from magnetic field dynamos in astrophysical flows to compaction mechanisms of DNA in cell biology.