Machine Kinematics
solved, then drawn
Series

Practice — the series

3 essays on one idea, from the one that introduces it to the one that assumes the rest.
  1. The transmission angle through one turn. μ is the angle at B between coupler and rocker, computed from each solved position rather than from a formula. It runs from 54.3° to 100.3° for these lengths. The shaded band is the usual design rule — keep μ between 40° and 140° — and this linkage stays inside it throughout. The rule is about geometry alone: nothing here knows about friction, and a mechanism with a comfortable μ can still be a poor machine.

    What is still outside

    Eight essays here end by saying that clearance, backlash, friction or wear are not modelled. This field took two of those four, because a tolerance is a set of geometries and a clearance is a short link, and both are questions about where a mechanism can be. The other two are not, and this is the page that says exactly where the line falls and why it is where it is.

    part 1 · practice
  2. a crank rocker with a post: the closest pair at one position. The same four-bar with a post bolted to the frame, just clear of the coupler's path. Every joint is where the solver put it, exactly as in the linkage field; the material is the only thing added. The heavy segment joins the two closest points over every pair of parts that is tested — which excludes pairs sharing a pin, since their material surrounds that pin by construction — and its length is the gap: 0.1809 here, between coupler · post. A negative value is a penetration depth, the distance the pair would have to be moved apart, and it is drawn in the warning colour.

    Where the boundary moved

    Three phases ago this site drew a line around what it computes and listed one thing on the far side as a gap rather than a boundary: interference between links, which needed no new physics, only a body and a test. Here is what that turned out to cost and what it turned out to open.

    part 2 · practice
  3. The output is a band, not an angle. The rocker's angle through one turn of the crank, for a four-bar whose four lengths are each specified to ±0.01. The line is the nominal mechanism; the band is where the output of an actual one lies, found by building all sixteen extreme combinations of the four lengths at every crank angle and solving each. The band is not a constant width: it is 0.73° at its widest, near 30°, and 0.36° at its narrowest — a factor of 2.0. Which of those a designer is told depends entirely on where the mechanism was measured.

    Where the boundary moved again

    The practice field's inventory ended by naming what the work after it should do first: take the feature positions as the variables and derive the lengths. That is done, and it turned out not to be an extension of the tolerance field but half of a different one — because where a length comes from and what a measurement determines are the same question.

    part 3 · practice

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