# N=2 Polygon wheel by Chebyshev (rabatment)

- Author:
- asifsound

N=2 Polygon wheel by Chebyshev (rabatment)
Probably this is the most compact Chebyshev linkage leg or wheel.

Please reduce the number of bars.
■ Number of 1 leg bars (biped type)
Chebyshev linkage -- 4
base horizontal --2-1 = 1
crank + line symmetry (= vertical lifting) 3
[ here, 2 crank bars D'L', L'M''' are belong to each Chebyshev upper base bar, so not indepentent bars. No count as independent bar. ]
total = 4 + 4 bars/ leg
Find the method to reduce 4 to 2.
If not found, Prove "4 is minimum".
cf. Chebyshev N=2 Polygon Wheel --- 4 + 0.5 bars/ leg --- WHY? too simple !!! & only 2D (great).

**■ About rough implementation for M, M' ----- This is considerable good.**Black and Blue linkages are connected by one relation. To keep this relation, above rough implementation coordinator is easily thought. This coordinator is needed 2 sets for black and blue frames. 1set / black, 1 set/ blue. (∵ Axis D ◯, M ◯ are both need to be lifted. ) Real 3D implementation is somewhat complicated. ★ Someone, Please consider how to change 2 sets to only one set. I don't like 2 sets. Perhaps, it may be possible. Big circle centers (2 sets) are on the ceiling of chassis.**■ 2D/ 3D figure layer (top view)**Green Chebyshev frame --◎-- Coordinator for Green --◎ (on chassis/ pelvis, vertical slider part) crank --◎-- Coordinator for Black --◎ (on chassis/ pelvis, vertical slider part) Black Chebyshev frame --◎-- Implementation looks like easy. (?) ∵ is simple. has symmetry. cf. Chebyshev_walker (GeoGebra) --- almost same (but, left is more honest than above.)