Physics
Linkages and mechanisms
Four bars and four pins is the smallest machine there is: watch a point on the coupler draw a curve no circle can, see the transmission angle open and close, and find out from Grashof's rule whether anything turns at all.
What happens
Four bars and four pins, the smallest machine there is - a wiper, a pump jack, the piston in an engine are all this one in disguise. Position is not an equation but the intersection of two circles, so when they fail to meet the linkage simply cannot be at that crank angle, and the panel says so instead of smoothing it over: that is the visible face of Grashof's rule, which decides whether anything turns all the way round. The transmission angle says how much of the push actually reaches the rocker - below about 40° a designer starts again, and at 0° the mechanism is at a dead point and cannot be driven from that side, which is why an engine needs a flywheel to carry it past top dead centre. The Peaucellier scene adds the 1864 inversor: eight bars whose pen point draws a mathematically EXACT straight line, and the panel shows the inversion OC·OP = L² − s² holding live. The Chebyshev and Watt buttons dial in the two famous near-straight four-bars.
Equations used in the module
Equations Σr_i = 0 Grashof: s+l ≤ p+q DOF = 3(n−1) − 2j
