A string of length 4a has one end fixed at the origin and is
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A string of length 4a has one end fixed at the origin and is wound along the arch of the cycloid to the right of the ori
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A string of length 4a has one end fixed at the origin and is wound along the arch of the cycloid to the right of the origin. Since that arch has total length 8a, the free end of the string lies at the highest point A of the arch. Find the path followed by the free end Q of the string as it is unwound from the cycloid and is held taught during the unwinding. (See Figure 11.29.) If the string leaves the cycloid at P; then .arc OP / C PQ D 4a: The path of Q is called the involute of the cycloid. Show that, like the evolute, the involute is also a translate of the original cycloid. In fact, the cycloid is the evolute of its involute.
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