PURPOSE: To provide possibility of three-dimensional tracing symmetrical about a plane and safely perform precision processing, measurement, assembly, and transport simultaneously without requiring the time and skillfulness by furnishing a mechanism which can make three-dimensional tracing symmetrically about the reference plane between objects.

CONSTITUTION: Two structures 8 movable in the Y-direction are combined with a structure 5 which is movable in the X-direction, and two pulleys 12 having the same outside diameter are fixed to the ends in Y-direction of the X-structure 5 so that the motions of the structures are synchronous and symmetrical to the left and right, wherein the pulleys are restrained by a belt 13 or chain so that their rotating directions and speeds are identical. The belt or chain in its positions point-symmetrical about the center between the pulleys 12 is fixed to the structure 8 movable in the Y-direction, which generates a condition where synchronization symmetrical to the left and right is practicable.