For a planetary gearset, the sun gear has 24 teeth, and the annulus gear (i.e., ring gear) has 70 teeth. The three pinion gears are grouped with the carrier. Pinion Carrier Sun Center Line (a) What is the DOF (degree of freedom) of the planetary gearset without holding any elements held? What is the DOF (degree of freedom) of the planetary gearset with the annulus gear is held stationary? [2 pts] (b) Draw the equivalent lever analogy of the planetary gearset. [2 pts] (c) When the annulus gear is held stationary, and the input speed of 2000 rpm is applied to the sun gear in clockwise direction, what is the output speed of the carrier and in which direction? [5 pts] (d) When the carrier is held stationary, and the input torque of 300 lb-ft is applied to the annulus gear in counter-clockwise direction, what is the output torque of the sun gear and in which direction? What is the reaction torque on the carrier held stationary? [5 pts] (e) The following gearset is composed of two planetary gears with special connections. S1 is first sun gear with 20 teeth, Al is the first annulus gear with 60 teeth, and C1 is the first carrier. S2 is second sun gear with 40 teeth, A2 is the second annulus gear with 80 teeth, and C2 is the second carrier. A1 A2 60 80 C1 C2 Output 20 S1 40 S2 Input Such a gearset is call as . [2 pts] Applying lever analogy to present these two planetary gears as two levers with solid lines to represent their connections. Combine these two levers into a single lever with the scaled numbers. [7 pts]