Themes
Solved, not drawn
Every mechanism on this site is positioned by solving its loop-closure equations, not by placing the links where they look right. A figure that could not be solved is not published, which means a linkage that would jam cannot be drawn moving.
Two routes to the same number
Mobility from Grübler's formula and mobility from the rank of the constraint Jacobian are computed independently and must agree. Where they disagree the formula is wrong and the mechanism is more interesting.
The crank is the argument
A mechanism is not a state, it is a relation between an input and an output. The figures are draggable because turning the crank is the explanation rather than a decoration on it.
The singularities are the point
Dead centres, toggle positions and the configurations where a mechanism locks or changes branch are treated as the subject rather than as edge cases. They are where the mechanical advantage goes to infinity and where the machine stops working.
Exact and approximate
Watt's straight line is not straight and Peaucellier's is. The difference is measurable, it took ninety years to close, and the error curve of an approximation is a more interesting object than the approximation.
The constant that is not constant
A velocity ratio quoted as a number is a claim that it does not vary through the cycle. For gears that claim is true and is the whole reason the involute exists; for most other mechanisms it is false, and the variation is measurable.
Somebody had a problem
Every mechanism in the canon was invented to solve something specific — a piston that had to move straight, an indicator that had to trace, a film that had to stop thirty times a second. The problem explains the shape.