One chain, four mechanisms — the inversions generator

The same four bars and the same four pins in every panel. What changes is which link is bolted to the bench, and that is not a property of the chain — it is a decision about where the bench is. The four mechanisms are crank rocker, double crank, crank rocker, double rocker: one input turns fully in some and rocks in others, and what each one is *for* is different. What cannot change is the shape of the closed loop, and the two diagonals measure that without reference to which link is held still: swept independently, all four visit the same locus of diagonal pairs to within 2.9e-3, half the sampling resolution. This is why the Whitworth quick-return and the oscillating-cylinder engine are not merely similar to a slider-crank; they are one.