Chebyshev walker
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