A method for processing medical samples in an analytical medical laboratory system comprising: transporting by an input module gripper each of a plurality of specimen containers from an input module to a distribution area module; detecting information about the specimen containers by measuring liquid levels within the specimen containers during the transport to the distribution area module; loading, by a distribution area gripper in the distribution area module, the plurality of specimen containers into a centrifuge adapter which is placed on an adapter shuttle (224, 225), wherein the first specimen container gripper sequentially loads single specimen containers of the plurality of specimen containers into the centrifuge adapter until the plurality of specimen containers are loaded; transporting, by the adapter shuttle (224, 225), the centrifuge adapter from the distribution area module to a centrifuge module, which comprises a centrifuge (206-1, 206-2); loading, by a centrifuge adapter gripper, the centrifuge adapter into the centrifuge (206-1, 206-2); centrifuging, by the centrifuge (206-1, 206-2), the centrifuge adapter; and transporting, by the centrifuge adapter gripper, the centrifuge adapter from the centrifuge (206-1, 206-2) to the adapter shuttle (224, 225); and unloading, by a centrifuge tube gripper in the centrifuge module, the plurality of specimen containers from the centrifuge adapter, wherein the centrifuge tube gripper sequentially unloads single specimen containers of the plurality of specimen containers until the plurality of specimen containers are unloaded, and transporting, by the centrifuge tube gripper, each of the plurality of specimen containers to a carrier on a conveyance system of the analytical medical laboratory system. transporting by an input module gripper each of a plurality of specimen containers from an input module to a distribution area module; detecting information about the specimen containers by measuring liquid levels within the specimen containers during the transport to the distribution area module; loading, by a distribution area gripper in the distribution area module, the plurality of specimen containers into a centrifuge adapter which is placed on an adapter shuttle (224, 225), wherein the first specimen container gripper sequentially loads single specimen containers of the plurality of specimen containers into the centrifuge adapter until the plurality of specimen containers are loaded; transporting, by the adapter shuttle (224, 225), the centrifuge adapter from the distribution area module to a centrifuge module, which comprises a centrifuge (206-1, 206-2); loading, by a centrifuge adapter gripper, the centrifuge adapter into the centrifuge (206-1, 206-2); centrifuging, by the centrifuge (206-1, 206-2), the centrifuge adapter; and transporting, by the centrifuge adapter gripper, the centrifuge adapter from the centrifuge (206-1, 206-2) to the adapter shuttle (224, 225); and unloading, by a centrifuge tube gripper in the centrifuge module, the plurality of specimen containers from the centrifuge adapter, wherein the centrifuge tube gripper sequentially unloads single specimen containers of the plurality of specimen containers until the plurality of specimen containers are unloaded, and transporting, by the centrifuge tube gripper, each of the plurality of specimen containers to a carrier on a conveyance system of the analytical medical laboratory system.