Apparatus for rotating a table 1 comprises a motor 32 driving a worm gear 33 which engages a worm wheel 35b from which motion is transmitted through a gear train 30 to (an inner ring gear 1g of) the table 1. Torque can also be transmitted from the table 1 to the worm gear 33 via the worm wheel 35b, such as when the table is moved manually or movement of the table is obstructed. This is possible because the worm gear 33 has a lead angle gamma sufficiently large to transfer torque from the worm wheel. The table 1 is supported by bearing balls 21 retained by an annular cage comprising a series of arcuate parts (23, Figure 15). <IMAGE>