PURPOSE: To make possible traverse and vertical movement of a trolley with a simple mechanism without using a large-scaled complicated cam, large-scaled feed arm and a plurality of links.

CONSTITUTION: A liner differential gear comprises a carrier 11 rotatably driven about the axis X, a plurality of planet bevel gears 13 supported by the carrier and freely rotatable about the axis Y radially orthogonal to the axis X, two pinion gears 15, 16 provided on both sides of the carrier to be rotated about their own axes and having on the sides bevel gears 14 meshing with a plurality of the planet bevel gears 13 and two rack teeth 18, 19 respectively meshing with the pinion gears, and guided to move straight in the diametrically opposite direction and parallel to each other.