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.