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I woke up last night with the design of a simple mechanism to find the symmedian point.

Three rods joined by pivots to make a triangle. Each rod can slide in the pivot but be locked to the desired triangle by a set screw. Each rod has another free slider and this has another small rod at right angles with a spring on the outside of the triangle; the spring is unloaded when the small rod is flush with the slider. The small rods can be extended putting the springs in compression and then joined by a pivot. The energy at equilibrium is proportional to the sum of squares of the extension so at the equilibrium position the small rod join at the symmedian point.

The sliders have to be free running and I imagine where the small rods join there is a hole for a pencil mark. The spring constants have to be matched and the springs linear over the range.  If they are not matched you get a weighted symmedian. Of course there are mechanisms using only linkages and not springs but the ones I thought of were rather complicated.

Hope you  enjoy this idea and please let me know if you foresee any problems. Feel free to make one (with attribution!). I ccd Peter Moses, one of the world's few experts on triangle centres. Peter, does it make sense?

Bill Lionheart