No figure on this site is a drawing that was made once and saved. Each one is a function:
it takes parameters and returns SVG, so the same generator produces the p4 plate and the
p6m plate without either being redrawn.
That is the reason the collection can keep growing without the illustrations drifting apart.
A generator is written once, checked once, and every essay that calls it inherits the same
line weights, the same colour roles, and the same behaviour in dark mode. There are
27 of them so far.
cam-profileroller follower base circle 30 cycloidal, rise 20 over 120°, roller 8 pressure angle 25.5°
coupler-curvesground 4, crank 1, coupler 3.5, rocker 3 5 attachment points, 150 solves each
dead-centres273 of 360 input angle non-Grashof (triple rocker) · s + l exceeds p + q by 0.50 green: assembles · red: refused
drawn-not-solved-0.500 0 0.500 1 0 100 200 300 crank angle (degrees) coupler length error a rigid bar coupler 3.5, worst error 0.890 every frame looks fine on its own
dwell-join-0.008 -0.006 -0.004 -0.002 0 100 110 120 130 140 cam angle (degrees) acceleration (per degree²) dwell begins simple harmonic cycloidal harmonic arrives at 6.85e-3, cycloidal at 2.06e-4 a factor of 33
four-barA B O₂ O₄ crank (input) coupler rocker (output) crank rocker · residual 0.0e+0 positioned by solving, not by drawing
gear-meshpitch point line of action module 1, 20° pressure angle, centre distance 26 contact ratio 1.612
genevadriver 6 slots centre distance 60.00 = crank ÷ sin(180°/6) index 60° per turn
grashof-auditfraction of the input rotation that assembles crank rocker 180/180 predicted: full turn double crank 180/180 predicted: full turn double rocker 32/180 predicted: rocks non-Grashof (triple rocker) 137/180 predicted: rocks prediction from the four lengths · measurement from 180 solves they agree, and the build requires it
grubler-paradoxthe redundant one Grübler: 3(5−1) − 2(6) = 0 Jacobian: 6 − rank 5 = 1
involute-constructionthe traced point tangency base circle r = 9.40 20 teeth, module 1, 20° pressure angle normal meets the base circle to 2.3e-5
mobility-auditGrübler Jacobian triangulated frame 0 0 agree four-bar 1 1 agree slider-crank 1 1 agree Peaucellier cell 1 1 agree parallelogram + third bar 0 1 they disagree — the mechanism moves 3(n−1) − 2j₁ − j₂ · free coordinates − rank(J) one row where the formula loses
motion-laws0 5 10 15 20 0 50 100 150 lift -0.010 -0.005 0 0.005 0.010 0 50 100 150 cam angle (degrees) acceleration (per degree²) constant acceleration simple harmonic cycloidal acceleration differentiated from the displacement above it smoothest is not gentlest
peaucellierP Q O C arm 5, rhombus 3, crank 1.6 deviation 6.5e-16 of span
piston-is-not-harmonic-0.200 -0.100 0 0 100 200 300 crank angle (degrees) piston position − pure sine L/r = 2 L/r = 3 L/r = 4 L/r = 6 solved piston position minus a pure cosine the residual is the second harmonic
planetaryring sun hold the ring sun in, carrier out 4.000 : 1 same direction hold the carrier sun in, ring out −3.000 : 1 output reverses hold the sun ring in, carrier out 1.333 : 1 same direction Willis: (ω_s − ω_c)/(ω_r − ω_c) = −72/24 both derivations agree, and the build requires it
pressure-angle0 20 40 0 50 100 150 cam angle (degrees) pressure angle (degrees) 30° design limit base 16 base 20 base 26 base 34 base 44 base 60 cycloidal rise, 20 over 120° 38° down to 15°
ratio-is-not-constant-0.250 0 0.250 0.500 0 100 200 300 crank angle (degrees) output ÷ input angular velocity a 20:40 gear pair, 0.500 mean 0.000 four-bar 4/1/3.5/3 -0.40 to 0.33 through one turn
slider-crankA stroke = 2.000 = 2 × crank positioned by solving, not by drawing
straight-line-audit10⁻¹⁶ 10⁻¹³ 10⁻¹⁰ 10⁻⁷ 10⁻⁴ 10⁻¹ 0% 25% 50% 75% 100% Watt, 1784 Chebyshev, 1850s Peaucellier, 1864 fraction of the available stroke used deviation ÷ span 120 solved positions per point fifteen decades, and one flat line
structure-or-mechanismmobility 0 — a structure mobility 1 — a mechanism triangle: 2 coordinates, rank 2, 0 free one bar apart
toggle0 15 30 45 60 0 100 200 300 crank angle (degrees) mechanical advantage (clipped at 60) toggle: advantage 1673 worst μ = 46° four-bar 3.4/1.2/3/2.4, 720 solved positions 222° apart
train-ratioreduction ratio 20 → 40 2.00 : 1 reversed 20 → 30 → 40 (idler) 2.00 : 1 same direction 20 → 40, 15 → 45 compound 6.00 : 1 same direction 20 → 60, 20 → 60, 20 → 60 27.00 : 1 reversed product of the stages · sign flips at every external mesh the idler cancels exactly
transmission-angle0 50 100 150 0 100 200 300 crank angle (degrees) transmission angle μ (degrees) 40° design limit ground 4, crank 1, coupler 3.5, rocker 3 μ from 54.3° to 100.3°
two-branchesB open B crossed θ = 75°, both residuals below 1e-12 two solutions, one mechanism
undercut10 teeth undercut 14 teeth undercut 17 teeth undercut 18 teeth clean 24 teeth clean red: the root circle has risen above the base circle threshold N = 2/sin²α = 17.097
watt-erroras traced deviation × 40 worst deviation 8.98% of span an approximation, measured