[HugoFara]

Summary

Four of the twelve scripts under docs/examples/ failed — on 1.1.1 too. They are literalincluded in the docs' Examples page, so they were broken there as well.

What was wrong

• The three synthesis demos called len(result) and if result: on a SynthesisResult, which lost __len__/__bool__ before 1.0.
• Once past that, motion_generation_demo stopped on the first double-rocker it tried to animate: every demo drove whatever synthesis returned with a full-turn Crank, which cannot pass the position where coupler and rocker align. fourbar_from_lengths_demo failed the same way on a non-Grashof entry.
• The Grashof-type table in fourbar_from_lengths_demo labelled (2, 4, 3, 1) double-crank and (3, 4, 3, 2) double-rocker — both are change points — and its rocker-crank could not assemble at crank angle 0.
• Three demos ran but always came back empty: five-position approximate function generation (angle pairs starting at 0 give the Freudenstein fit a negative crank length), the straight-line path (three exactly collinear points are degenerate for Burmester theory), and both fixed-ground-pivot demos (arbitrary frame points never lie on the center-point curve; the constraint filters, it does not solve for a frame).

One library change

solution_to_linkage() now honours FourBarSolution.arc_limits. The field existed but nothing in pylinkage read it (the editor server fills it and builds its own mechanism dict). Set it — from crank_angle_limits() — and the linkage is built around an ArcCrank sweeping that range instead of a Crank. The limits are relative to the ground line as crank_angle_limits() returns them, and are placed on whichever side of the ground line the crank starts. Nothing sets the field inside pylinkage, so existing output is unchanged. Tests cover both sides of the ground line and rotated frames.

The demos animate through a small show() helper that does exactly that and prints the swept range when the crank oscillates.

Demo content

• Grashof table lengths now match their labels; the table assembles with the crank vertical.
• Approximate function generation uses five positions in the upper quadrant; the fit is within 0.4°.
• Straight line: middle point bowed by 0.02.
• Fixed pivots (path and motion): synthesize freely, list the pivots the solutions propose, fix one pair rounded to a tenth, re-synthesize. That is the workflow that produces a linkage.
• The five-pose demo still returns nothing; that is what it sets out to show.

Verification

• All twelve docs/examples/*.py run to completion under -W error::DeprecationWarning (matplotlib on Agg).
• Full suite 2561 passed with deprecations as errors; ruff, mypy clean.

[HugoFara]

Also related to #25 by @the-moog . This PR fixes broken example codes.