A robotic arm has a pair of gripper fingers designed to grip a variety of containers, including capped and uncapped test tubes as well as containers having unique gripping means. The fingers each have upper and lower projections separated by a groove, the respective projections facing each other when mounted to grippers on the robotic arm. The projections and groove serve to firmly hold the containers as well as self-align the unique gripping means on initially unaligned containers within the fingers as the fingers close around the containers. The fingers have clearance to avoid contact with caps on capped test tubes. Stops are provided at the top of each finger to engage one another and prevent fully closed fingers from deforming. The robotic arm may be transported along a rail mounted above the instrument and a gripper assembly, having a gripper arm, mounted to the robotic arm may be rotated above the instrument to move the container to various locations within the instrument. Side posts on the instruments have a gap between them that permits the gripper arm to rotate and extend outwards to interface with an adjacent instrument or a lab automation transport line.