GearboxBigshot's gearbox consists of several intermeshed gears that work together to convert the slow rotation of the hand crank to a very fast rotation of the dynamo shaft.
While there are many types of gears, the most common type is the spur gear, which is generally a cylinder or a wheel that has teeth along its boundary [1]. Gears with compatible teeth can mesh together easily, as Figure 2 shows. One gear's teeth lock between the other gear's teeth so that turning the first gear causes the other gear to turn as well. In Figure 2, Gear B is smaller and rotates faster than Gear A. Point P is where the two gears make contact with one another. Since the teeth on both gears must be of the same size for the gears to mesh together, the smaller gear has fewer teeth than the larger gear. Notice that by the time the smaller gear makes a complete rotation (all of its teeth have passed by point P), the larger gear would not have completed a full rotation (not all of its teeth will have passed by P). The smaller gear, then, makes more rotations in a given period of time; in other words, it spins faster. It can be shown [2] that the speeds of the two gears, A and B, are related by the following equation: (Speed of A * Number of teeth on A) = (Speed of B * Number of teeth on B). (1) The number of teeth on a gear depends on its circumference (the length of its boundary). The gear's circumference, in turn, depends on the gear's diameter (Circumference = 3.14 * Diameter). So, equation 1 can also be written as: (Speed of A * Diameter of A) = (Speed of B * Diameter of B). (2) For example, in Figure 2, the diameter of gear A is 3 times longer than the diameter of gear B, which means that Gear B rotates 3 times faster than Gear A.
In Bigshot's case, the dynamo must be spun at about 100 times faster than the hand crank turns. If we used only two gears to connect the hand crank and the dynamo, then the first gear would have to be about 100 times as big than the second one! The camera, then, would be huge. So, instead of having just two gears, Bigshot uses a series of 8 gears (called a gear train), as shown in Figure 3. The inset at the top-right corner of Figure 3 shows Gear B, which is called a compound gear [3] since it is actually two separate gears (B1 and B2) fixed together. Gears C and D are also compound gears, and are composed of Gears C1, C2, D1, and D2. Gear A, which is directly attached to the crank, drives the smaller gear B1. Since B1 and B2 are connected, B2 will rotate at the same speed as B1. B2, in turn, drives C1, and C2 drives D1. The shaft of the dynamo is attached to Gear E. The sizes of the gears are such that the rotation speed increases with each gear. The overall gain in rotation speed is the product of the speed gains at each stage along the gear train. The larger gears (A, B2, C2 and D2) are 3 times as big as the smaller gears (B1, C1, D1 and E, respectively). Using equation 2, it is easy to see that total speed gain between Gears A and E is 3*3*3*3 = 81, which means that Gear E rotates 81 times faster than Gear A. In other words, each time the hand crank is turned once, the dynamo shaft spins 81 times. For example, if we rotate the crank at 20 rotations per minute, then the dynamo spins at 20*81 = 1620 rotations per minute.
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