One of the primary objectives of the GRIEG research project SCREAM: Symmetry, Curvature Reduction, and EquivAlence Methods was to investigate interesting geometric structures (Cartan, contact, (para-)CR, etc.) originating from simple mechanical systems. The simplest of these are the so-called "planar robots." Around a decade ago, Paweł Nurowski and Gil Bor established some general results and formulated the key questions related to these systems. In this talk, I will provide an overview of their geometry and will discuss in further detail one of the more interesting examples: the three-edge snake robot. This talk is based on an ongoing joint work with Paweł Nurowski.