An automatic calibration method of a robot system comprises providing a ball-rod member including a connection rod and a sphere connected to the connection rod, fixing the connection rod to an end execution tool mounted on a flange of a robot, providing distance sensors around a target point, and sensing an actual distance from each of the distance sensors to the sphere. The robot is controlled to move a center of the sphere to the target point in different poses based on the actual distances sensed by the distance sensors. A first transformation matrix of the center of the sphere with respect to a center of the flange is calculated based on pose data of the robot at the target point. A second transformation matrix of a center of the end execution tool with respect to the center of the flange is calculated based on the first transformation matrix.

An automatic calibration method of a robot system comprises providing a ball-rod member including a connection rod and a sphere connected to the connection rod, fixing the connection rod to an end execution tool mounted on a flange of a robot, providing distance sensors around a target point, and sensing an actual distance from each of the distance sensors to the sphere. The robot is controlled to move a center of the sphere to the target point in different poses based on the actual distances sensed by the distance sensors. A first transformation matrix of the center of the sphere with respect to a center of the flange is calculated based on pose data of the robot at the target point. A second transformation matrix of a center of the end execution tool with respect to the center of the flange is calculated based on the first transformation matrix.

A method of calibrating a coordinate positioning machine having a first member that is moveable relative to a second member, wherein the geometry of the machine is characterised by a set of model parameters. The machine is controlled to make point contact between multiple reference surfaces of a tool or artefact mounted on the first member and multiple reference surfaces of an artefact mounted on the second member. At least one of the model parameters is updated knowing or taking into account that the actual separations between the relevant surfaces are zero when making contact, even if the expected separations between the relevant surfaces as derived from the current model parameters are non-zero.