finkle

Good question!

It looks like Creative Commons non-commercial, according to the download page.

When referring to length, a given spring does not care about total length (ignoring situations where you'll introduce buckling or other modes of loading). Changing the number of coils means you'd be using a different spring design. For a given spring design, it's the same stiffness whether it's 5mm long or 10mm. That makes the math of splitting it in series simple.

I am curious about the full impact of the dead coils (I like that term). I was treating then simply as a rigid connections, effectively splitting the spring into series, reducing the effective stiffness. Can you elaborate on how they would work to increase the stiffness?

Your explanation on the effect of diameter makes a lot of sense, especially given how tight tolerances must be at this scale. I just assumed you wouldn't want to get the spring too thin for strength reasons.

The way the spring is designed is very akin to taking two separate springs, and attaching them in series. On a highly technical level, this creates a quite different response to motion than a single spring would have. On a lower tech level, it's approximately the same as regular spring with a different stiffness value.

I'd like to think that some engineers went down the rabbit hole, doing differential equations or modal analysis to solve some complex design problem. More likely it was just a cheap or easy way to solve a manufacturing or supply problem.

Edit: Upon further reflection, spring stiffness does not care about length. The primary concerns are thumb travel (deflection) and force to click (deflection times stiffness). I suspect that deflection is pretty well set by ergonomic factors. This design would reduce the effective spring stiffness by half (and therefore the force). The most obvious other way to reduce stiffness would be reducing wire thickness, which could reduce reliability.

Noise, on the other hand, is an expected result of clicky-pens. People don't like products behaving unexpectedly. If the design made the pen quieter, you can bet they would advertise it on the packaging.

I kind of hate how much thought I've put into this.