The principles of Optical Gearing

Optical Gearing has a partly transparent disc rotating on top of a disc with a pattern printed on it. So does a naive circular vernier. The reason that Optical Gearing can make a viable clock display while the vernier cannot is down to the design of the patterns. Here is a picture of the static disc of the circular vernier “unrolled” and stretched into a rectangle:

And here is a sample Optical Gearing design, similarly “unrolled”:

It is this complexity which gives Optical Gearing its power. The two-dimensional nature of the patterns not only makes workable clock displays possible but also allows a great deal of variety in the design of those displays. Translating a chosen design into the patterns needed for the discs is an intricate process involving both mathematics and computation.

Mechanically, on the other hand, nothing could be simpler than an Optical Gearing clock. It is simply one disc rotating on top of another.

Mechanical design

The rotor is partly transparent and partly opaque. It could be a glass disc with an opaque design printed on it, or it could be an opaque metal disc perforated with laser-cut holes. The colour of the opaque parts of the rotor is the colour of the clock face.

The static disc is printed with a pattern in two colours: the colour of the clock face, and the colour of the hands.

If backlighting is used then the static disc, instead of being printed, can be opaque and perforated just like the rotor. In that case the hands of the clock will be bright against a dark background. Backlit designs are usually more appropriate for clocks, especially architectural clocks, than for watches.

Visual design

The hour hand goes round once every 12 hours, the same speed as the rotor. It can therefore be painted on the rotor and it can have any appearance at all. Matching its appearance to the appearance of the minute hand is a matter of artistic judgement.

Alternatively, the hour hand can be displayed in the same way as the minute hand,  by revealing a pattern through perforations in the rotor. This preserves purity because the rotor can then all be one colour. The design shown on this page uses this method.

The minute hand has many options.

It can be the same thickness all along its length.




Here is a close-up view of such a minute hand from 12 minutes to 18 minutes past the hour, speeded up so that one second on the screen represents 10 seconds in real life.

You can see that as time goes on, nothing actually moves. Rather, dots on the leading edge of the hand appear and gradually grow larger, while dots on the trailing edge grow smaller and finally shrink away. This kind of “movement without movement” is part of what makes Optical Gearing unique.

The minute hand can also be made out of a bunch of tapered pointers.


Here is the same close-up view as before.

This time, dots do not appear and disappear. Rather, each line grows to its maximum length and then shrinks back to nothing.

Colour

Colour in an Optical Gearing display can be more than just a decorative element. This is because it introduces richer possibilities of interaction between the rotor and the static disc.

For example, take a ‘dark dial’ design where the hands are light on a dark background. Without colour, this means that a transparent part of the rotor reveals the colour of the static disc. One might say ‘transparent + light = light’, ‘transparent + dark = dark’. These two equations make Optical Gearing work.

Now suppose that we have two transparent colours – say, red and blue – on the rotor and the same two colours on the static disc. Now the rules are different. We have ‘red + red = light (red)’, ‘blue + blue = light (blue)’, ‘red + blue = dark’, ‘blue + red = dark’. There are twice as many interactions, and this doubles the precision and richness of the time display.

Here is an example using three colours rather than two (three is probably the maximum number of coloured dyes one can have such that each dye passes its own colour but blocks the other two).


Here is a similar design, with coloured bands that vary in thickness instead of length:



Technical and contact details

Although the concept is simple, precision in its implementation is vital. The patterns need to be printed exactly as designed, and the axis of rotation needs to pass exactly through the centre. The minute hand rotates 12 times as the rotor and the seconds indicator (if present) rotates 720 times as fast, which means that small errors in printing and assembly will be amplified by a similar amount. Fortunately, it is possible to incorporate self-test patterns into an Optical Gearing design to ensure accurate assembly.

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