Identification and compensation of position independent geometric errors of dual rotary axes for hybrid-type five-axis machine tool based on unit dual quaternions

•A universal kinematic model and PIGEs redefinition are proposed based on the UDQ.•A general irregular trajectory equipartition method is proposed.•The installation error of the DBB is obtained using the least square circle/sphere fitting method.•A compensation strategy of orientation errors is proposed in combination with the UDQ kinematic model. This paper presents a novel synchronous motion trajectory based on the unit dual quaternion (UDQ) to identify the position-independent geometric errors (PIGEs) of the dual rotary axes of a hybrid five-axis machine tool using a Double ball-bar (DBB). A general irregular trajectory equipartition method is presented to deal with the asynchronous matching between DBB data sampling and trajectory points. The kinematic model is effectively simplified by redefining the PIGEs of linear/rotary axes. The installation errors of the DBB are obtained by circular/spherical fitting trajectories, which are brought into the error model for elimination. The simulation of the UDQ kinematic model combined with preset error value shows that the non-uniform variation of DBB motion will lead to the deviation of PIGEs decoupling results. A compensation strategy of major orientation errors based on the UDQ is proposed, which is verified by simulation and compensation experiments.