N=3 2R-Virtual Wheel (Reuleaux triangle, ver. -A)
- Author:
- asifsound
This approximation system is "Planet whose orbit velocity = θ, and self-spin velocity = θ/3".
■ Please gaze the C'1 trace.
Please rotate red A ● from (1,0) to (-1,0) [= 0 ° to 180°].
Gaze the Black point C'1 ● trace carefully, especially its Y value. C'1 is not an exact straight line.
( Y value: -6.46 ～ -6.51 ～ -6.46 ～ -6.51 ～ -6.46 : error rate ≒ 0.05/6 ≒ 1% )
i.e. Chassis body shakes up and down a bit, very frequently.
[This error rate is about the same value of Chebyshev Linkage for quasi-straight line approximation method.]
cf. The Reuleaux Triangle (Square Drill Bit) ---- ①
-- Why does Point C rotate reverse/ against direction? On purpose?
cf. 掘削機 ----- direction of orbital motion is reverse from spin direction. ---- by Gear implementation [ Large gear (r=1) sets outside or inside to center small gear (r=1/3), such difference makes reverse or not rotation. ??? ]
---- This Japanese invention (request ?), it looks having no originality to me. the contents is the same as usual mathematical text common knowledge. Low level contents invention. perhaps, request will be denied.
cf. N=3 2R-Virtual Wheel (Reuleaux triangle) ------- ② [ Chassis body does not shake up/ down. ]
What is rr=7.32 theoretical value?
■ Center curve is not circle theoretically.
From Wikipedia and Reuleaux Triangle (A Wolfram Web Resource.) ※, the center trace is not circle, the fact is 4 elliptical arcs compound figure.
※: The ellipse has center (1,1), semimajor axis a=1+1/√3, semiminor axis b=1-1/√3, and is rotated by 45 degrees.
But, above figure condition is almost exact circle, it's enough to use in real world. Above approximation is very very good.
In general center trace is not circle, but special condition it's circle, isn't it?
■ Slipping?
cf. Reuleaux Polygons
・ Ground touching/ tangent point is different from the point under O or A.
■ Which is low energy consumer, the Gear or the Linkage?
I don't know detail, but feeling is " the Gear consumes much energy. the Linkage does not consume much. Because, gear has much friction.".
■ Why this figure/ picture is approximation?
We can draw an ellipse curve by Linkage easily, so, we can draw exact Reuleaux triangle curve by Linkage.
Please try.