In a machining apparatus, a tool has a specified point for machining a workpiece, and a support supports the tool while a position and an orientation of the specified point of the tool are changeable. A actuator actuates the support to move the tool, and a sensor measures a magnitude and an orientation of force upon the force being applied to the tool. A determiner determines, upon the force being applied to the tool, a target orientation of the specified point of the tool according to the magnitude and the orientation of the force measured by the sensor. The force applied to the tool having an orientation to separate the tool from the workpiece. A controller controls the actuator to move the tool according to the determined target orientation.