Figure P15.47 is a schematic representation of a conventional three-speed bicycle hub. Sprocket 1 is driven by the chain. Member 2 always rotates with the sprocket, and slides axially to one of three positions (low, neutral, and high) when the gear shift control is actuated. Sun gear 6 is permanently fixed and serves as the reaction member. Freewheeling pawls 3 (attached to annulus 5) and 9 (attached to arm 8) each represent a set of circumferentially arranged members which function as shown in Figure 15.30b. Light torsion springs hold the pawl tips against the notched inner surface of hub 4 (the member to which the wheel spokes are attached). The pawls permit hub 4 to rotate faster (in the clockwise or forward direction) than the member to which they are attached, but not slower; thus they constitute one-way clutches. The tips of pawls 9 always bear on the inner hub surface, but in low gear sliding member 2 disengages pawls 3 by pushing against them as shown in Figure 15.30b. Operation in the three gears is as follows. Low gear. Member 2 is in position L, where it (1) disengages pawls 3 and (2) drives annulus 5. The output member is the arm, which drives the hub through pawls 9. Neutral gear. Member 2 is in position N, where it continues to drive the annulus but release pawls 3, which drive the hub at sprocket speed. (Pawls 9 remain engaged, but "overrun," causing a "clicking" sound as the pawls go over the notches in the hub). High gear. Member 2 moves out of engagement with the annulus and into engagement with the projecting planet pins, which are part of arm 8. Pawls 3 drive the hub at annulus speed, and pawls 9 "overrun." Now for the problem.
(a) The sun and each of the four planets have a pitch diameter and 25 teeth. How many teeth are in the annulus, and what is the diametral pitch of the gears?
(b) What is the ratio of wheel rpm to sprocket rpm for each of the three speeds? Determine these ratios using at least two of the three methods given in the text.
(c) Explain briefly what happens when the bicycle coasts in any gear.
