A control device is provided which is operable to change the position of a distal end side link hub by driving each of arms, which are proximal end side links of a plurality of link mechanisms by means of an actuator. When in a series of operations, the position change of the distal end side link hub is mad by an angle greater than a predetermined angle, a relay position setting unit is provided for setting a relay point between a starting point and a terminating point of each of the arms so that the interference of the three axis arms may be relieved. A position change control unit performs a position control so as to pass simultaneously through the relay point so set.