N=3 2R-Virtual Wheel (Reuleaux triangle, ver.-Window)
Reuleaux triangle Wheel with square drill window. No/ Low friction type. i.e. The blue bullet C ● is a highest position of Reuleaux triangle (= tangent point to the ceiling). I restrict this moving (or trace) by non-friction slider. cf. Inventing the wheel © 2002-2016 Mathematical Etudes ← I propose improved type of this wheel.
From this result, I remember my invention few years ago. "Cassini Square Wheel" --- DEMO is "Cassini Wheel (N=4 4R Virtual Wheel)" (GeoGebra) This is square wheel (is not triangle wheel), but the result is very near. --- This linkage is extension of Chebyshev Linkage family. Too many years past, I've forgotten. This apparatus is somewhat great, virtual radius is 4 times of real height. Not, r=R, vs. 2R, It realizes 4R virtual wheel. --- great enough (!?). ■ θ, θ/3 planet orbit simulator is bad. When rotate the crank, Pink horizontal line is oscillating little by little. So, this crank approximation method is not fit for real implementation. --- I think so. But, Using as a explaining method is very convenient method. ■ Square slide/ friction wall (lower horizontal, left/ right both side) should be removed. In this method, Point C is restricted to be made horizontal piston movement, so, square slide guide wall is not needed. If you make a straight line slider by Chebyshev Linkage, you only have to set the Chebyshev 4 corner L,M,U,U' (same square format, by chance) to the square frame corresponding corner positions , and connect the Point C to C. ----- Blue arcs is not also necessary in real implementation. ■ If you use this as caster, this system has no axis. 3 hinges make position control, as a result, wheel axis is not needed. ■ Comparison the 2 methods ----- pending. To realize same rotation, this square drill window version needs straight line ruler, but other method does not need it, so this method is inferior than others methodologically (?). ---- this is mistaken opinion (?). More check is needed. ----- This method needs the horizontal chassis, but from the view of confliction, it's easy method than the method without Chebyshev Linkage.