N=3 2R-Virtual Wheel

Pending. There is a logic mis. (i.e. This stage is OK. but, in next stage is NG.) N= odd number is difficult. N=3 is possible, but rigid body (Reuleaux triangle itself.). My now answer is ↓. N=3 2R-Virtual Wheel (Reuleaux triangle) This is typical "Line symmetry linkage" application sample.
Dynamic large radius wheel.  N=3 Polygon wheel. From above "Elementary parts" left figure, we can recognize that the point M1 traces on straight line can be explained easily by line symmetry property. Tip: In above sample, pink bar edge ratio pp=0.26 is assigned. Green bar edge ratio is assigned 0.5. (2:1 is, brings easy calculating) If necessary, please do tuning it. ■ ideal rule 3 Cheese sectors (Black, Blue, Green) are connected by next relation. (1) Each sector's Top B, B', B''' are belong to the r=R circle 120° sector C'''AC', C'AC'', C''AC''' areas. (2) There exists Master and slaves relation between B, B', B'''. The line To Axis A is vertical, such vertex is Master. in above fig. sample, BA is vertical, so, vertex B is master. B', B''' are slaves. Master/ slaves relation are dynamically changed. (3) The line To Axis A,  i.e. BA, B'A, B'''A are dependent. Master and Slave is in Line-symmetry. Slave and Slave has no relations. ex. BA -- C'A---B'A, BA--C'''A--B'''A are line symmetry. B'A and B'''A are slaves, and B'A--C''A--B'''A relation is not line symmetry. Please implementation this, if you can do.