In an apparatus for determining whether a manipulator is operable, a rotational angle calculator performs, based on a length of each of first and second links at a specified temperature of a manipulator, a calculation operation to calculate a target rotational angle of at least one of the first and second links based on a joint. The target rotational angle of at least one of the first and second links based on operation of the joint is required for a predetermined point of the manipulator to be moved toward a setting movement position. A determiner determines, based on the target rotational angle of at least one of the first and second links, whether the predetermined point of the manipulator is movable to the setting movement position at the specified temperature of the manipulator.

A method includes: receiving a substrate on a first stage by a holder of a substrate transfer mechanism; causing the substrate to pass through a first measurement part, and measuring a first true deviation amount between the holder and the substrate at a first position; causing, when transferring the substrate toward a second stage, the substrate to pass through a second measurement part, and measuring a second true deviation amount between the holder and the substrate at a second position; reflecting a difference between the first and second true deviation amounts to a physical model to correct the physical model; calculating a position correction amount of the holder on the second stage from a thermal displacement amount of the holder at the second position; and controlling the substrate transfer mechanism based on the position correction amount to perform a position correction of the holder.

A method for predicting a thermal error of a spindle of a computer numerical control (CNC) machine tool based on twin feature transferring of a virtual-real prototype, is provided, including: first, building a spindle physical prototype experiment table, and screening temperature sensitive points outside the physical prototype spindle, so as to establish an autoregressive distributed lag model; second, determining a temperature synchronization lag point on the physical prototype spindle corresponding to the temperature sensitive point outside the physical prototype spindle, so as to construct a thermal error analysis model; thereafter, establishing a virtual prototype and transferring the twin feature of the physical prototype, and by integrating a twin coupling relationship between the physical prototype spindle and the virtual prototype spindle, realizing the thermal error prediction. The present disclosure improves the accuracy of the thermal error prediction under the condition that it is difficult to arrange sensors on the spindle.