Reuleaux triangle Wheel with square drill window.[br][br]No/ Low friction type.[br]i.e. The blue bullet [b]C ●[/b] is a highest position of Reuleaux triangle (= tangent point to the ceiling).[br]I restrict this moving (or trace) by [b]non-friction slider[/b].[br][br]cf.  [url=http://www.etudes.ru/en/etudes/koleso/]Inventing the wheel[/url]  © 2002-2016 Mathematical Etudes  ←　I propose improved type of this wheel.

From this result, I remember my invention few years ago.[br][url=http://www5d.biglobe.ne.jp/~the_imai/etymology/Musashikoganei.html#Cassini_square]"Cassini Square Wheel" [/url] --- DEMO is [url=https://www.geogebra.org/m/GAxQMus6][b]"Cassini Wheel (N=4 4R Virtual Wheel)"[/b][/url] (GeoGebra)[br][br]This is square wheel (is not triangle wheel), but the result is very near. --- This linkage is extension of Chebyshev Linkage family. [br][br]Too many years past, I've forgotten. [br]This apparatus is somewhat great, virtual radius is 4 times of real height.[br]Not, r=R, vs. 2R, It realizes 4R virtual wheel. --- great enough (!?).[br][br][b]■ θ, θ/3 planet orbit simulator is bad.[/b][br]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. [br]But, Using as a explaining method is very convenient method.[br][br][b]■ Square slide/ friction wall (lower horizontal, left/ right both side) should be removed.[/b][br]In this method, Point C is restricted to be made horizontal piston movement, so, square slide guide wall is not needed.[br]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. [br]----- Blue arcs is not also necessary in real implementation.[br][br][b]■ If you use this as caster, this system has no axis.[/b][br]3 hinges make position control, as a result, wheel axis is not needed. [br][br][b]■ Comparison the 2 methods ----- pending.[/b][br]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 (?).[br][br]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.[br]