A minimal-error-model based two-step kinematic calibration methodology for redundantly actuated parallel manipulators: An application to a 3-DOF spindle head

Zero offsets and geometric source errors will significantly degrade the kinematic accuracy of redundantly actuated parallel manipulators (RAPMs). To relieve the influences of these factors, this paper presents a minimal-error-model based two-step kinematic calibration methodology for this type of parallel manipulators. A novel 3-DOF spindle head with a 2UPR&2RPS topology is taken as an example to demonstrate the kinematic calibration methodology. The proposed kinematic calibration methodology includes three critical steps: (1) a set of general principles is proposed to eliminate redundant geometric source errors in the manipulator to derive a minimal error model that includes the least number of geometric source errors; (2) a sensitivity analysis is carried out using the Monte-Carlo simulation to reveal the relative impact of geometric source errors on the terminal accuracy; (3) a hierarchical identification strategy composed of a coarse identification and a fine identification is proposed, based on which a two-step calibration methodology is constructed. Finally, a set of calibration experiments is performed to verify the effectiveness of the proposed calibration methodology.