Q. 3 (3 marks) The planetary gearbox shown is used for power assisted steering. The ring gear B has an inside radius r of 55 mm and is driven by the worm gear connected to an electric motor. The planet gears, P each have a radius of 20 mm, while the sun gear has a radius of 15 mm. The carrier C supports the bearings for the planet gears and rotates with the bearings at their centers. The outside radius of the ring gear is 63 mm and the pitch of the worm gear is 6 mm. If the sun gear is rotating anticlockwise at 0.35 radians per second, determine the angular velocity of the worm drive required produce a rotational speed for the carrier C of 1.075 radians per second in the anticlockwise direction. P B Pitch Worm drive