Dual Cams
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.
Left to Right : Click to enlarge : (i) the author's Dual cam design (never realised). The green cam rotates once a year, the red, twice a year. The upper yellow gear drives a four-year leap year date setting ring (ii) the same design with its centrally mounted lens-ed alidade. The blue potion was a refraction correction which is theoretically incorrect. (iii) another of the author's unrealised designs. In this case the green cam is driven at once per anomalistic year, the red at twice per tropical year. The purple gears rotate the date setting ring at once per calendrical year. You can read a complete story of this unrealised dream below....
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)
Left to Right : Click to enlarge : (i) Bill May - ca 2000 - Equatorial Dial (ii) Inner cam carrying an eccentric pin driving the Hour ring (iii - iv) Outer ring and inner cam, showing month graduations (in 2 different models)
Left to Right : click to enlarge : (i) Pilkington-Gibbs Heliochronometer - ca 1910 - (this dial, still in mint condition) was given to Commander Robert Peary, who first reached the North Pole by the Lord Chief Justice of England, who had previously adjudicated in the international dispute Arctic fishing rights) (ii) the mechanical working of a Pilkington Gibbs - showing the cam and its follower, which is attached to the alidade  (iii - iv) Equation watches using single cams.
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.
Left to Right, click to enlarge : (i) The first prototype (ii) The focussing lens and the Equation cam in the first prototype (iii-iv) Replica of the Equation cam from the first prototype.
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
Right to Left : Click to enlarge : (i - ii) the Pump room clock (iii - iv) the accompanying dial, used to set the clock (v) the single cam Equation mechanism
Profiles are the first cousins to Cams. They serve the same purpose. They can be single or double, as shown below.
Left to Right : Click to Enlarge : (i - ii) The Strasburg cathedral astromonical clock. There are two profiles one each for the eccentricity (rotating once a year) and obliquity effect (rotating twice a year). One rides on top of the other, thus adding the two signals together. (iii - iv) Bill May - 2000 - EoT profile directly driving the equatorial ring of his sundial
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