A general approach to solve the singular kinematic problem

A sophisticated and advanced strategy for kinematic calibration of parallel manipulators has been reported. The strategy relies on passing type two singularities (i.e., direct kinematic singularities) and is therefore referred to as singularity-based calibration. Within the parameter estimation process, the singularity-based calibration technique requires to solve a so-called singular kinematic problem (SKP). That is, it involves finding the position of one actuator for which the structure is in a singular configuration of type two under the condition that all other actuators are held at known constant positions. So far, this problem could only be solved for some simple manipulators and structure classes with a maximum of three degree of freedom and thereby limiting the applicability of the singularity-based calibration approach. This article contributes a general approach to close this gap making singularity-based calibration widely applicable. The technique demonstrated by means of exemplarily chosen parallel kinematic structures.