Identifiability of geometric parameters of 6-DOF PKM systems using a minimum set of pose error data

This paper presents a mathematic proof for the identifiability of geometric parameters of 6-DOF parallel kinematic machines (PKM). Rank deficiency of the identification matrix is justified if the end-effector undergoes all possible degrees of freedom but only a set of position errors normal to a plane is measured. An approach is proposed to tackle this problem, which enables the full set of parameter errors to be identified by only using a minimum set of pose errors: 1) the "flatness" of a fictitious plane generated by the tip of endpoint sensor; 2) the "squareness" of two orthogonal axes; and 3) the orientation of the end-effector at the initial configuration. Consequently, the burden arisen from the orientation error measurement may be dramatically reduced. The proposed method is so general that it can also be used to handle the parameter identification problems of the PKM with fewer than six degrees of freedom.