Hart's A-frame Wheel
- Author:
- asifsound
- Topic:
- Square
Sqaure wheel by Hart's A-frame Linkage.
Literally, this is "Invention of Square Wheel"
cf. related word : "Reinventing the wheel" (wikipedia, Reinventing the square wheel)
Hart's A-frame is an exact straight line drawing apparatus.
■ Characteristics:
① Shape is an exact square wheel. (size is changing: big ⇔ small. □OIO'I' is square. CO ⊥ CI )
② Foot trace is exact straight line. (+/- 45° line or horizontal.) ---- not cycloid curve.
③ Long stride.
Tip: This method cannot be applied to Chebyshev linkage. (∵ Chebyshev shape is a left/ right symmetry, so, #4 foot goes under ground.)
■ max span this A-frame
Suppose, B(0,2+y), End(x, y(B)) [End is bent bar angle 180°, stretched.]
where,
x2+y2=(4+3)2=72=49 ①
x2+(y+2)2=(6+2)2=82=64 ②
②-①
4y+4=64-49=15 then y=11/4=2.75
so, 2+y=4.75
x=√(49-121/16)=√(784-121)/16=(1/4）√663=6.437196595