How can one, in a smooth way, produce a semicircle wave, as opposed to a sinusoidal wave ?
Imagining the machinery and linkages behind the movement. I mean the trace. For example a point fixed in wheel of a car may engender a cycloid. Others curves may be a Cyclogon, or a curve produced by a point fixed inside a sharkwheel, when rolling(not gyration).
The motivation behind the question, it is because in the usenet, there is a user called Archimedes Plutonium that has semicircle waves instead of sinusoidal. I have curiosity if it will be possible to produce such kind movement in at least one way. The mechanism that produce the curve does not need to be contained inside a plane.
Other way of thinking on it may be in the sense of producing such movement in a non-trivial way, similar to producing a straight line using the Peaucellier–Lipkin linkage.
Question re-phrased by @Transistor:
Figure 1. A cycloid can be generated by a point on the circumference of a circle. Image source: Britannica.
Can a similar waveform consisting of a series of semi-circles be generated by a mechanical linkage?