My solar orrery is an artistic design to encode the position of the sun into the surface of a cylindrical wooden block such that it could be rotated to a given date and a rotating 24hr dial riding on a stylus on a snaking groove on the surface of the cylinder would point at the sun. While I never constructed it, I have extensively studied and designed the geometry for it to function.
I intended it to be a wood cylinder approximate 1ft long and 8in in diameter with a groove running around the center of its circumference. The geometry of how the cross-section of the cylinder deviates from a circle would be defined by the change in elevation of the sun by date. This is a representation of the cross section of the cylinder:
The deviation of the groove from a straight line around the cylinder would be defined by how fast/slow the sun is at this time of year to adjust for the eccentricity of Earth’s orbit and the obliquity of the ecliptic. This is a representation of the groove:
While you are likely aware that the elevation of the sun changes with the seasons, you may not have been aware that its horizontal position fluctuates as well. As you can see below there are material deviations depending on the time of the year between mean solar time and apparent solar time.
As a result of the combination of these two periodic fluctuations a picture of the sun at noon each day for a year yields the picture below, also knows as an Analemma. In a sense, the geometry of the cylinder is the embodiment of this.
Some screenshots of my work books:
