N=3 2R-Virtual Wheel (Roly-poly toy wheel)

This is related to Reuleaux triangle. cf.  N=3 2R-Virtual Wheel (Reuleaux triangle)  (Geogebra) ■ Rolling toy (1) Rolling Triangle (straight edge + circle corner) ------ exact straight line drawing mechanism is needed. mapping from circle to line is needed, "Inversor Linkage" concept is needed for this, perhaps. Rolling Reuleaux triangle is "straight edge + circle corner" case. (2) Rolling Square (straight edge + circle corner) ----- this can be realized by "Chebyshev Linkage", perhaps.. Please try , if you want. --- But, my feeling is , It may be impossible (?).
Comment above Pink bent bar is typical Hart's A-frame. sample length is, (2/3)√5, (1/3)√5 [long: short= 2:1 sample], Purple bar is length 1 [half of 2] which locates under (1/6)√5 from bent point [it locates at middle of √5 overall.]. When bent bar is stretched [i.e. 180° bent], this Pink & purple apparatus looks like a letter "A" figure. "A-frame" name comes form this fact.