Methods of positioning a gripper to pick or place a specimen container from a sample rack. One method includes providing a robot including the gripper, the gripper moveable in a coordinate system by the robot and including gripper fingers, providing a sample rack including receptacles containing specimen containers, providing data, obtained by imaging, regarding the specimen containers in the sample rack, and dynamically orienting the gripper based upon the data. The data may include population and/or configuration data and the dynamic orientation may include gripper finger opening distance, gripper finger rotational position, and/or gripper offset distance. Gripper positioning apparatus for carrying out the method are disclosed, as are other aspects.