# Chebyshev walker

Author:
asifsound
Chebyshev linkage application.　Piston movement application. Bi-pedal walking apparatus. Catch the Red bullet ● B, then Please rotate it. Chebyshev parts/ leg = 4 bars (each length 4, 5, 5, 2) Crank parts/ leg = 4 bars (each length AR [=rr], RD [=rr], CD [= long], EF [=2.5]) [ Point E is on CD long bar, where ED = 2 ] ( Remark : ED (or E'D) // B''1G [= bottom of the foot]) As a matter of fact, purple method doesn't need long arm. This is great. Please check it out. ( i.e. Do move ▲ C to the right direction. ex. x(C) ≒ -0.8 is OK. )
Perhaps, This is very elegant solution in the world. The hinge elements AR and RD are shrunk in  y < 0 area. (---- This is an important trick.) The direction of Crank rotation  is the same direction of forward movement. This is honest/ natural. --- Like a "Row, Row, Row Your Boat" or Crawl swimming arm movement. ■ Simple structure for implementation in related Axis bar:　Simple chassis/ body structure. ∠DB''2B''1 ≦ 180°,　∠DB'''G ≦ 180°, So, point B''' and segment B''2B''1 doesn't conflict. point B''2 and segment B'''G doesn't conflict. So, 3D structure is very simple. --- i.e. The cross 2 bars are in the same side of chassis. (Between 2 cross bars, there is no chassis. ) Tip: chassis is simpler than orthodox Chebyshev bi-pedal. cf. Chebyshev_walker2 ■ Purple color structure has good property except more 2 bars. Foot trace curve is near the symmetry. Bottom of the foot is always exact horizontal. ■ Compare other known method cf. Kinematics and Dynamics of the Quasi-Passive Biped "PASIBOT” (Spain) ---- No originality, I think so. ---- This is a point symmetry application, so, foot trace shape is identical with Chebyshev curve shape. ( big height stroke ratio tuning cannot be done. [ height/ width ratio is constant. this is bad. ] ) cf. The piston R = L case, please. ---- My apparatus is a typical piston movement. ( i.e. crank clockwise 0° to 180° is mapping to clockwise 0° to 180°, clockwise 180° to 360° is mapping to counterclockwise 0° to 180°. ) ■ About precise number of bars. Crank AR ●-◇ is a part of a bent bar I''AR, so, precisely it's not different bar. Bar DR ●-◇ is a part of a bent bar B''2DR, so, precisely it's not different bar. So, (4 + 4) bars/ leg is (4 + 2) bars/ leg is true, precisely. corresponding to this, (4+6) is (4+4) is precisely. ■ In real world: In big gap barrier _____|‾‾‾‾‾‾ floor case, asymmetry is better than symmetry trace foot. and it has more simple structure. R ◇ tuning mechanism is indispensable. variable hinge length. (Please check R on A' case. very high step. ----- It' easy to jump 10cm high gap. ) cf. Wheelchair operation cf2. How to Use a Wheelchair