The 'purest' way to produce the EoT mechanically is with 2 cams, the output of which are added together. One cam turning once a year simulates the Eccentricity Effect. The other turning twice a year simulates the Obliquity Effect. For astronomical clocks, designed to work in the longer term, this has the added advantage that the Eccentricity cam can be driven once per Anomalistic year (the time from one mean perihelion to the next = 365.259 636 days). While the Obliquity cam can be driven twice per Tropical year (the time from one mean vernal equinox to the next = 365.242 189 days)
The output from each cam is then added with a 'wiffletree' or other mechanism (as shown in the following video.
Another double cam system can be found in Bill May's work. Here one cam sits inside another. This produces an effect similar to that of of two gears (see Gears page). The inner (circular) cam carries an eccentric pin that connects to the equatorial ring of a dial. The inner cam is carried eccentrically inside the outer ring. The inner cam is turned wide in the year (Obliquity effect) ; the outer ring once (Eccentricity effect)
THE CLOCK OF THE LONG NOW
The Clock of the Long Now longnow.org/clock/ is an extraordinary project to build a clock which - with appropriate maintenance - will run for 10,000 years. A prototype (some 3 metres tall) has been completed and has toured the science museums of the world. A second prototype is being built inside a mountain in Texas. The final clock will be built in Mount Washington in Nevada, The clock runs with a torsion pendulum, but needs to be corrected every now and then. This is done whenever the sun is shining at noon. A lens focuses the sunlight onto a bar which heats and bends. This resets the clock to mean noon, via an Equation of Time cam, which must reflect the 10,000 year design life of the clock.
THE TOMPION CLOCK IN THE PUMP ROOM, BATH, UK
This is a perfect example of a Clock and Sundial, both made by Thomas Tompion, clockmaker to King Charles II. The Clock was set by the sundial, just a few steps away outside the window. The Clock had a cam driven Equation mechanism to allow the clock to be set directly using the sundial
Profiles are the first cousins to Cams. They serve the same purpose. They can be single or double, as shown below.