straight-line
Peaucellier's cell: exact straight-line motion from pin joints
The rhombus and the two long arms hold |OP| · |OQ| constant at 16 = 5² − 3², which is inversion in a circle about O. Inversion carries circles through the centre to straight lines, and the link CQ makes Q run on exactly such a circle — so P travels on a line, with no approximation anywhere. Measured over 160 solved positions the deviation is 6.5e-16 of the span, which is arithmetic noise rather than a small error.
The paths points tracedraggable: input anglewide
Where it is used
- The straight-line problem The paths points trace
- Peaucellier and the exact answer The paths points trace
- Holding an axle still Machines you have met
- Exact costs more than close The curve as an equation
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