{"$schema":"nativecad-dfm-pack/1","id":"power-transmission","title":"Power transmission — gears, sprockets, racks, cams, cranks, belts","sector":"power-transmission","version":"2026-09-04","summary":"Involute gear geometry (spur/helical/bevel/worm/planetary), ANSI roller chain sprockets, racks, V-belt/timing belt sections, crankshaft/con-rod/cam basics, universal joints, servo horn splines, ratchets, flywheels and clutches, with the materials, fits and tests a mechanism designer needs before modelling.","aliases":["spur gear","helical gear","bevel gear","worm gear","planetary gear","gearbox","sprocket","roller chain","rack and pinion","involute","crankshaft","connecting rod","camshaft","cam follower","universal joint","servo horn","ratchet","flywheel","v-belt","timing belt","clutch"],"crossSector":false,"size":"core","sources":[{"id":"iso-21771","title":"ISO 21771 Cylindrical involute gears — concepts and geometry","accessed":"2026-09-04"},{"id":"agma-2005-d03","title":"AGMA 2005-D03 Design Manual for Bevel Gears","accessed":"2026-09-04"},{"id":"agma-6034-b92","title":"AGMA 6034-B92 Enclosed Cylindrical Wormgear Speed Reducers","accessed":"2026-09-04"},{"id":"shigley-mech-design","title":"Shigley's Mechanical Engineering Design — gears, cams, clutches","accessed":"2026-09-04"},{"id":"asme-b29-1","title":"ASME B29.1 Precision Power Transmission Roller Chains","accessed":"2026-09-04"},{"id":"iso-4184","title":"ISO 4184 Classical and narrow V-belts — dimensions","url":"https://www.iso.org/standard/70045.html","accessed":"2026-09-04"},{"id":"iso-5296","title":"ISO 5296 Synchronous belts — pitch T2.5/T5/T10","accessed":"2026-09-04"},{"id":"gates-htd-manual","title":"Gates HTD/GT2 Synchronous Belt Design Manual","url":"https://www.gates.com/","accessed":"2026-09-04"},{"id":"iso-286-2","title":"ISO 286-2 Code system for tolerances on linear sizes","accessed":"2026-09-04"},{"id":"robotdigg-servo-spline","title":"RobotDigg RC Servo Spline Chart","url":"https://www.robotdigg.com/news/168/RC-Servo-Spline-Chart","accessed":"2026-09-04"}],"entries":[{"id":"spur-gear-standard-proportions","kind":"dimension","tier":1,"title":"Full-depth 20° involute spur gear standard proportions","summary":"Standard 20° full-depth system: addendum = 1.0 m, dedendum = 1.25 m, whole depth = 2.25 m, clearance = 0.25 m, where m is module in mm — the four numbers that turn a module + tooth count into a buildable tooth.","applies":["spur gear","gear tooth","involute gear"],"value":{"table":[{"feature":"addendum","multiplierOfModule":1},{"feature":"dedendum","multiplierOfModule":1.25},{"feature":"whole depth","multiplierOfModule":2.25},{"feature":"clearance","multiplierOfModule":0.25}],"unit":"ratio"},"basis":"AGMA 201.02 / ISO 21771 full-depth 20° proportional system, the default for cut and printed spur gearing","sources":["iso-21771"],"tags":["gear","spur","module","addendum","dedendum"]},{"id":"spur-gear-diameter-formulas","kind":"dimension","tier":1,"title":"Spur gear pitch, base, outer and root diameter formulas","summary":"Pitch dia D = m·N; base dia Db = D·cos(20°); outer (tip) dia Do = m(N+2); root dia Dr = m(N-2.5) — 4 formulas from module m and tooth count N that fix every circle on the gear.","applies":["spur gear","gear blank","involute gear"],"value":{"table":[{"circle":"pitch","formula":"D = m*N"},{"circle":"base","formula":"Db = D*cos(20deg)"},{"circle":"outer/tip","formula":"Do = m*(N+2)"},{"circle":"root","formula":"Dr = m*(N-2.5)"}]},"basis":"Direct consequence of the 1.0m/1.25m addendum/dedendum standard proportions applied to the pitch circle D = m*N","sources":["iso-21771"],"tags":["gear","spur","diameter","pitch-diameter","base-diameter"]},{"id":"spur-gear-tooth-thickness","kind":"dimension","tier":1,"title":"Spur gear circular tooth thickness at the pitch circle","summary":"Nominal circular tooth thickness at the pitch circle t = pi*m/2 — half the circular pitch (p = pi*m); a module-2 tooth is 3.1416 mm thick at the pitch line before backlash allowance is subtracted.","applies":["spur gear","gear tooth","rack"],"value":{"value":"t = PI*m/2","unit":"mm"},"basis":"Standard tooth-to-space symmetry: tooth thickness equals space width equals half the circular pitch p = pi*m","sources":["iso-21771"],"tags":["gear","tooth-thickness","circular-pitch"]},{"id":"spur-gear-profile-shift","kind":"rule","tier":1,"title":"Profile shift coefficient to avoid undercut below 17 teeth","summary":"For a 20deg pinion with N < 17 teeth, shift the generating rack outward by coefficient x = (17-N)/17 (in units of module) to eliminate root undercut instead of accepting a weak, undercut tooth — an 8-tooth pinion needs x = 0.53.","applies":["spur gear","pinion","small pinion"],"value":{"value":"x = (17-N)/17","unit":"ratio"},"basis":"Minimum profile-shift coefficient that keeps the involute generated by a rack cutter from undercutting a 20deg-pressure-angle pinion below the 17-tooth limit","sources":["iso-21771"],"see":["robotics/gear-min-teeth-undercut"],"tags":["gear","undercut","profile-shift","pinion"]},{"id":"helical-gear-angle-relations","kind":"dimension","tier":1,"title":"Helical gear helix angle and normal/transverse module","summary":"Helix angles run 15-30deg (20-25deg typical); normal module mn (the cutter's module) relates to transverse module mt by mn = mt*cos(helix) — model the tooth profile in the normal plane, then wrap it around the cylinder at the helix angle.","applies":["helical gear"],"value":{"min":15,"max":30,"typical":20,"unit":"deg"},"basis":"Common helical-gear helix-angle range balancing axial thrust load against the smoother, quieter engagement a higher angle gives","sources":["shigley-mech-design"],"tags":["gear","helical","helix-angle","normal-module"]},{"id":"bevel-gear-tredgold-approximation","kind":"rule","tier":1,"title":"Tredgold approximation for bevel gear tooth form","summary":"Treat a straight bevel gear's tooth as an equivalent spur gear with formative tooth count Nf = N/cos(gamma), gamma the pitch cone angle — a 20-tooth bevel pinion at a 30deg cone angle behaves, for strength and cutter selection, like a 23.1-tooth spur gear.","applies":["bevel gear"],"value":{"value":"Nf = N/cos(gamma)","unit":"count"},"basis":"Tredgold's approximation: the back-cone development of a bevel tooth is (very nearly) a spur tooth of the formative count, letting spur-gear strength and cutter tables apply to bevels","sources":["agma-2005-d03"],"tags":["gear","bevel","tredgold","formative-teeth"]},{"id":"bevel-gear-cone-angle","kind":"dimension","tier":1,"title":"Bevel gear pitch cone angle for 90-degree shafts","summary":"For gears on shafts at 90deg, pitch cone angle gamma1 = atan(N1/N2) for gear 1 (gamma2 = 90deg - gamma1) — a 1:1 mitre bevel pair sits at 45deg each; a 2:1 pair sits at 26.6deg (pinion) and 63.4deg (gear).","applies":["bevel gear","mitre gear"],"value":{"value":"gamma1 = atan(N1/N2)","unit":"deg"},"basis":"Pitch cones of two bevel gears share an apex; for perpendicular shafts the cone half-angles sum to 90deg in the ratio of the tooth counts","sources":["agma-2005-d03"],"tags":["gear","bevel","cone-angle","mitre"]},{"id":"worm-gear-lead-angle-selflock","kind":"rule","tier":1,"title":"Worm lead angle and the self-locking threshold","summary":"Lead angle lambda = atan(lead/(pi*Dworm)); a steel-worm/bronze-wheel drive with lambda below about 5deg is self-locking (the wheel cannot back-drive the worm) at typical 0.05-0.10 sliding friction coefficients — above roughly 11deg it will not self-lock.","applies":["worm gear","worm drive"],"value":{"max":5,"unit":"deg","note":"self-locking threshold; not self-locking above roughly 11deg"},"basis":"Self-locking requires the lead angle to stay below the friction angle (atan(mu)); mu = 0.05-0.10 for a run-in bronze/steel worm mesh gives a friction angle of about 3-6deg","sources":["agma-6034-b92"],"tags":["worm","self-locking","lead-angle"]},{"id":"worm-gear-ratio-and-starts","kind":"dimension","tier":1,"title":"Worm gear ratio from wheel teeth and worm starts","summary":"Ratio = Nwheel / Nstarts; a single-start worm (Nstarts=1) driving a 40-tooth wheel gives 40:1 in one mesh, but halves to 20:1 or 13.3:1 if a double- or triple-start worm (2 or 3 starts) is substituted for the same wheel.","applies":["worm gear","worm drive","worm wheel"],"value":{"value":"ratio = Nwheel/Nstarts","unit":"ratio"},"basis":"Each worm revolution advances the wheel by (starts) teeth, so the ratio is the wheel tooth count divided by the worm's thread-start count","sources":["agma-6034-b92"],"tags":["worm","ratio","starts"]},{"id":"planetary-gear-meshing-condition","kind":"rule","tier":1,"title":"Planetary gear ring/sun/planet tooth-count meshing condition","summary":"For a sun, planets and ring at one common module, the ring tooth count must equal Nr = Ns + 2*Np (sun plus twice the planet count) so the planet meshes with both the sun and the ring at the same centre distance.","applies":["planetary gear","epicyclic gear"],"value":{"value":"Nr = Ns + 2*Np","unit":"count"},"basis":"The planet's centre sits midway between sun and ring centres; equal module and equal centre distance to both forces this tooth-count relation","sources":["shigley-mech-design"],"tags":["planetary","epicyclic","meshing-condition","sun","ring","planet"]},{"id":"planetary-gear-assembly-condition","kind":"rule","tier":1,"title":"Planetary gear assembly condition for k equally spaced planets","summary":"k equally spaced planets assemble only if (Ns + Nr) / k is a whole number — a 20-tooth sun with a 60-tooth ring (sum 80) assembles with 2 or 4 planets but not 3, since 80/3 is not an integer.","applies":["planetary gear","epicyclic gear"],"value":{"value":"(Ns+Nr) mod k == 0","unit":"ratio"},"basis":"Each planet must land on a tooth of both sun and ring when placed at its 360/k angular station; failing the divisibility test means the last planet cannot mesh","sources":["shigley-mech-design"],"tags":["planetary","epicyclic","assembly-condition"]},{"id":"ansi-roller-chain-pitch-table","kind":"dimension","tier":1,"title":"ANSI roller chain pitch by chain number (#25/#35/#40)","summary":"ANSI/ASME B29.1 chain number is 1/8 inch of pitch: #25 = 6.35 mm (1/4in) pitch, #35 = 9.525 mm (3/8in), #40 = 12.7 mm (1/2in) — the pitch every sprocket tooth-spacing formula in this pack takes as p.","applies":["roller chain","sprocket","#25 chain","#35 chain","#40 chain"],"value":{"table":[{"chain":"#25","pitchMm":6.35,"rollerOrBushingMm":3.3,"note":"bushing chain, no roller"},{"chain":"#35","pitchMm":9.525,"rollerOrBushingMm":5.08,"note":"bushing chain, no roller"},{"chain":"#40","pitchMm":12.7,"rollerOrBushingMm":7.92}],"unit":"mm"},"basis":"ASME B29.1 precision roller chain dimension table","sources":["asme-b29-1"],"tags":["chain","sprocket","ansi","pitch"]},{"id":"rack-and-pinion-profile","kind":"dimension","tier":1,"title":"Rack tooth profile: straight flanks at the pressure angle","summary":"A rack tooth is straight-sided (not curved): total tooth height 2.25 m (1.0 m addendum above the pitch line + 1.25 m dedendum below), flanks straight at the 20deg pressure angle from the tooth's vertical centreline, mating any pinion of the same module.","applies":["rack and pinion","rack"],"value":{"value":"height = 2.25*m","unit":"mm"},"basis":"A rack is a gear of infinite radius: its involute flank degenerates to a straight line at the pressure angle, which is why one rack meshes with pinions of any tooth count at the same module","sources":["iso-21771"],"tags":["rack","pinion","straight-flank"]},{"id":"v-belt-section-dimensions","kind":"dimension","tier":1,"title":"Classical V-belt cross-section dimensions (A/B/C)","summary":"ISO 4184 classical V-belt sections: A = 13 x 8 mm (top width x height), B = 17 x 11 mm, C = 22 x 14 mm — pick the section from the sheave's groove angle (typically 34-38deg) and the pulley pitch diameter range the section is rated for.","applies":["v-belt","belt drive","sheave"],"value":{"table":[{"section":"A","topWidthMm":13,"heightMm":8},{"section":"B","topWidthMm":17,"heightMm":11},{"section":"C","topWidthMm":22,"heightMm":14}],"unit":"mm"},"basis":"ISO 4184 / RMA IP-22 classical V-belt cross-section standard","sources":["iso-4184"],"tags":["belt","v-belt","sheave","cross-section"]},{"id":"timing-belt-pitch-htd-t5","kind":"dimension","tier":1,"title":"Timing belt tooth pitch: HTD 3M/5M/8M and T5/T2.5","summary":"Curvilinear HTD belts run 3, 5 or 8 mm tooth pitch (HTD3M/5M/8M); trapezoidal-tooth belts run T2.5 (2.5mm) or T5 (5mm) pitch with about 1.2 mm tooth height at T5 — match the belt pitch to the pulley tooth pitch exactly, they are not interchangeable.","applies":["timing belt","synchronous belt","htd","gt2"],"value":{"options":["HTD3M","HTD5M","HTD8M","T2.5","T5"],"unit":"text"},"basis":"Gates HTD curvilinear tooth series and the ISO 5296 trapezoidal T-series, the two common synchronous-belt tooth families outside 3D-printer-scale GT2","sources":["gates-htd-manual","iso-5296"],"tags":["belt","timing-belt","htd","synchronous"]},{"id":"crankshaft-stroke-throw","kind":"rule","tier":1,"title":"Crankshaft stroke equals twice the crank throw","summary":"Piston/slider stroke = 2 x throw, where throw is the crank radius (the offset of the crankpin centre from the main-journal axis) — a 40 mm throw gives an 80 mm stroke; get the throw wrong by half and the stroke is wrong by exactly double that.","applies":["crankshaft","slider-crank","reciprocating mechanism"],"value":{"value":"stroke = 2*throw","unit":"mm"},"basis":"Simple kinematics of a slider-crank: the slider travels from one extreme (crankpin at top dead centre) to the other (bottom dead centre), a distance of twice the crank radius","sources":["shigley-mech-design"],"tags":["crankshaft","stroke","throw","slider-crank"]},{"id":"servo-horn-spline-dims","kind":"dimension","tier":1,"title":"RC servo output spline tooth count and diameter by brand","summary":"Standard-size hobby servo splines: 25T (Futaba/Hobbico/Savox, ~5.9mm OD; MG996R clone 5.8mm), 24T (Hitec, ~5.9mm), 23T (JR/Sanwa/Spektrum, ~5.9mm) — match the horn's tooth count to the brand, they are not interchangeable.","applies":["servo horn","rc servo","standard servo"],"value":{"table":[{"brand":"Futaba/Hobbico/Savox","teeth":25,"splineOdMm":5.9},{"brand":"MG996R (25T clone)","teeth":25,"splineOdMm":5.8},{"brand":"Hitec","teeth":24,"splineOdMm":5.9},{"brand":"JR/Sanwa/Spektrum","teeth":23,"splineOdMm":5.9}],"unit":"mm"},"basis":"RC hobby servo brands standardised on incompatible spline tooth counts within the same standard-size servo envelope; RobotDigg's spline chart cross-references brand to tooth count","sources":["robotdigg-servo-spline"],"tags":["servo","servo-horn","spline","futaba","hitec","jr"]},{"id":"bore-tolerance-h7","kind":"tolerance","tier":1,"title":"ISO 286 H7 hole tolerance by nominal bore size","summary":"H7 (a hole with zero lower deviation) grows with size: +12/0 um at 3-6mm, +15/0 um at 6-10mm, +18/0 um at 10-18mm, +21/0 um at 18-30mm — the default reamed/bored fit for a bearing housing or a shaft's mating bore.","applies":["bore","bearing housing","hub bore","H7 fit"],"value":{"table":[{"rangeMm":"3-6","upperUm":12,"lowerUm":0},{"rangeMm":"6-10","upperUm":15,"lowerUm":0},{"rangeMm":"10-18","upperUm":18,"lowerUm":0},{"rangeMm":"18-30","upperUm":21,"lowerUm":0}],"unit":"um"},"basis":"ISO 286-2 IT7 grade tolerance values applied to the H fundamental-deviation (hole basis, lower deviation zero)","sources":["iso-286-2"],"see":["robotics/standard-iso-286","robotics/bearing-housing-shaft-fits"],"tags":["tolerance","h7","bore","iso-286"]}]}