Embedding rotations in translational configuration space

This paper presents the graphical embedding of the rotational degree of freedom into the translational configuration space for planar assembly tasks. The resulting representation helps the visualization and understanding of motions in a simple and easy graphical way. The aim is the developing of motion planning algorithms in a two-dimensional parametrized space for planar assembly tasks (3 DOF) and in a three-dimensional parametrized space for assembly tasks in space (6 DOF). The method has been successfully applied to the problem of contact identification in the presence of uncertainty for planar assembly tasks. The extension to six degrees of freedom is under development.