kbd.news is running their Advent Calendar for the second year and I’m honoured they chose my article about Mantis and hexagonal keys in ergo keyboards for opening it. Enjoy the read and have a happy holiday season …
A very interesting read, and really cool looking! I’d really like to try the keycaps in v. 0.3!
I’m curious about this point:
With square keys, each key has eight neighbours, but the diagonal neighbours are about 1.4 times further away than orthogonal ones and therefore harder to reach for the same finger.
Say I arrange square keys in columns with a 0.5u offset. Then each key also only has six neighbors. I wonder how that compares distance-wide to hexagonal keys.
Edit: the Klacker BS does this, but offsets the rows instead.
That’s a cool find. I had not heard of the Klacker BS. The exact spacing and hand angle will be slightly different but pretty close. Column-staggered hexagonal keys give you 18.6mm between columns and 21.5 between rows with a 30° angle. 0.5u row-staggered MX keys with 19mm spacing give you about 17mm between columns and 21.2mm between rows at 26.6°. Also the resulting column-stagger is not exactly 0.5u but about 0.45u.
Klacker BS doesn’t eliminate the top inner index finger key. Moving that to the pinkies like Mantis does, would bring the hands 1u closer together.
Thanks for doing the math! I’m not quite sure I follow: why is the lengths different for row and columns on the Mantis? Are you calculating to the press point of your sculpted keycaps?
I was not considering the press point. I was using the center of each key.
In a column staggered layout I’m calling the distance between the centers of adjacent keys in the same column the row spacing. The column spacing is the distance of imaginary lines drawn along adjacent columns (through the key centres). I measure the shortest possible distance, which is at a right angle to those lines.
In a row staggered point of view it’s the other way around.
The different spacing comes from the hexagonal key shape. If you think of it as row staggered, the keys have 21.5mm horizontal (column) spacing and 18.6mm vertical (row) spacing. Rotate your point of view by 30° and this flips to a column staggered layout. Now the columns are spaced 18.6mm and rows are 21.5mm apart.
Square keys don’t have the same hexagonal symmetry. When you look at it as row staggered, it’s normal MX spacing, 19x19mm. When you look at it as column staggered, you need to do some trigonometry. The column angle is atan(0.5) = 26.6°. the column spacing is 19mm × cos(26.6°). The row spacing is from Pythagoras sqrt(19^2 + (19/2)^2).
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