HYPERSINGULARITIES OF 3-RRR PLANAR PARALLEL ROBOTS

The use of the entire workspace of a parallel robot calls for passing through type II singularities, which can be achieved by removing them from the inverse dynamics solution. Hypersingularities are type II singularities whose removal from the inverse dynamics requires satisfaction of additional higher order derivative conditions other than the acceleration-level ones for maintaining the consistency of the equations of motion. For this reason, the identification of hypersingularities constitutes an important and yet a new subject in the field of parallel robots. This paper contributes to the literature by deriving a condition for their occurrence in one of the mostly used parallel robots in applications, namely the 3-RRR planar parallel robot. It is shown that any type II singular configuration of the considered robot becomes a hypersingularity if the end-effector velocities at that configuration lie on a certain plane in the end-effector velocity space. The orientation of this hypersingularity plane changes according to the singular configuration. However, the said plane always passes through the origin of the end-effector velocity space. These findings are believed to bring new insights into the optimization of the singularity removal process of parallel robots through the minimization of the number of conditions to be satisfied in this regard.