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Photo comparisons of mice shapes does not tell the full story. We are all well aware that balance plays a key role, along with some other parameters.

Any ideas on how to quantify them?

Some that I can think of:

  • Center of Gravity (CoG) -- significance is obvious
  • CoG-to-sensor moment (offset) -- important also because we subconsciously expect the movement of CoG to correspond to actual measurement
  • Scrollwheel-to-rear length -- especially important for fingertippers, since our button fingers tend to lie on the same axis as the wheels, it can tell us how much space we can have before the butt hits the inside of our palm
  • Radius of Gyration

What others can you think will be important to include in order to characterize the geometry of a mouse? Please provide explanations.
 

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Where does the term radius of gyration come from? It looks like it is basically a different way to express moment of inertia, but even after getting a masters in physics I've never actually heard that term or at least not enough for it to stick. Looking at my books I guess it is mentioned once in each Thornton and Goldstein. Kind of off topic I was just very perplexed at not recognizing a term.

There are many measurements which matter for a mouse shape even beyond what is listed. For example:

width at front, rear, and center
length from highest point to front/rear length
Angle/curvature of the sides (wider at top, wider at bottom, straight, concave, convex)

there are many more you could add in there. W x L x H certainly doesn't even come close to describing a shape though even ignoring weight distribution considerations.
 

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One of my general principles is that for a mouse to have a good shape for a particular grip (there's no such thing as an absolute "good shape"), the following must all fall in the same spot: center of gravity, center of drag, the sensor, and the center of control.

Center of gravity has already been discussed. Center of drag is determined by the friction-- basically a function of the feet. Sensor position is self-explanatory. Center of control is probably the trickiest one to understand: basically, if you look at all the points where your hand naturally holds the mouse, as dictated by the shape of the mouse body and the length of the mouse buttons, the center of control is the exact middle of all of those.

Center of control is why "a good shape" will change based on the grip. Think about the difference between a claw grip and a fingertip grip: a claw grip has an extra point of control at the back of the mouse, where the heel of the hand makes contact, so the center of control will be much further back. Now, a fingertip gripper might respond by trying to hold the mouse further back, but this may be awkward (depending on the shape of the mouse) or even impossible, if the buttons don't extend a long way towards the back of the mouse.

So, while you could, in theory, measure the difference between the center of control and the other centers, or the center, the measurement will vary based on the exact grip being used.

There are also a couple of measurements that can be important for fingertip grip, but less so for the other grips. One is the distance, given a certain hand size, in each of the four primary directions, that the mouse can be moved by finger motion alone using fingertip grip, before the shape and size of the mouse causes at least one of the fingers to lose contact, or the mouse can no longer move, when it is held naturally. A lot of mice designed for palm grip will run into problems with movement in the "downwards" direction, since, when the back of the mouse touches your hand, you can't move it anymore.

Another is more of a checklist than a measurement; it's basically-- whether the mouse can be moved in any direction such that the finger that is propelling it can actually push naturally. This is determined by the curvature of the mouse at the spots where the fingers grip it. With a curve that is good for moving a mouse in a certain direction from a certain contact point, your finger can push the mouse, whereas with a curve that's bad, your finger will simply come off of the mouse unless you expend energy gripping tightly. A well-shaped mouse is one such that, when it is held naturally, it provides at least one good curve, and hopefully a balance of good curves relative to the centers, for moving in all directions. Unfortunately, some mice are shaped such that there's a direction where, when the mouse is held by a fingertip grip user, all of the curves are bad, so moving in that direction is awkward.
 

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