BetaBetaBetaWorks out the cones and outer circles of a straight bevel gear meshing a mate at a shaft angle: its pitch, tip and root cones, back radii and apex distance.
A tip cone of 90 degrees or more is refused. Example: module 2, 20 teeth meshing 40 at 90 degrees -> pitch cone 26.57 degrees, apex 40 away
The teeth, the mate's teeth and the shaft angle
The radii and distances in model units and the cone angles in degrees
BetaDraws a straight bevel gear's teeth as points on the XY plane around the origin, as seen from the apex on the plane of the outer pitch circle, by Tredgold's approximation.
The flanks run straight to the apex, so the section in a plane nearer it is this outline scaled
by its distance over apexDistance.
The teeth, the mate's teeth, the shaft angle, the turn and the segments per curve
The points of the outline
const sizes = bitbybit.engineering.mechanical.gears.bevelGearSizes({ module: 1, teeth: 20, mateTeeth: 30 });
const outline = bitbybit.engineering.mechanical.gears.bevelGearOutline({ module: 1, teeth: 20, mateTeeth: 30 });
const section = await bitbybit.manifold.crossSection.crossSectionFromPoints({ points: outline, fillRule: Bit.Inputs.Manifold.fillRuleEnum.positive, removeDuplicates: false, tolerance: 1e-7 });
const gear = await bitbybit.manifold.crossSection.operations.extrude({ crossSection: section, height: sizes.apexDistance / 4, nDivisions: 1, twistDegrees: 0, scaleTopX: 0.75, scaleTopY: 0.75, center: false });
BetaWorks out the circles of an involute helical gear's section square to its axis, with that section's module and pressure angle, and how many degrees the teeth turn per model unit along the axis.
Example: module 1, 20 teeth, 20 degrees -> pitch radius 10.64, twist 1.96
The teeth and their lean
The radii, the half tooth angle, the transverse module and pressure angle and the twist
BetaDraws a helical gear's section square to its axis as points on the XY plane around the origin, a closed loop counterclockwise that does not repeat its start.
Extrude it with a twist of twist from helicalGearSizes times the height to make the gear.
The teeth, their lean, the turn and the segments per curve
The points of the outline
const sizes = bitbybit.engineering.mechanical.gears.helicalGearSizes({ module: 1, teeth: 20 });
const outline = bitbybit.engineering.mechanical.gears.helicalGearOutline({ module: 1, teeth: 20 });
const section = await bitbybit.jscad.polygon.createFromPoints({ points: outline });
const gear = await bitbybit.jscad.extrusions.extrudeLinear({ geometry: section, height: 5, twistAngle: sizes.twist * 5, twistSteps: 10 });
BetaWorks out how two external spur gears mesh: centre distance, working pressure angle, contact ratio and ratio, profile shifts included.
The contact ratio counts only involute contact, interferes flags tips reaching past it, and
tipShortening and clearance show how shifts crowd tips into roots.
Example: module 2, 20 and 30 teeth -> 50 apart, contact ratio 1.61
The module, the teeth, the pressure angle, the tooth heights and the profile shifts
The centre distance, working pressure angle, contact ratio, ratio, interference, tip shortening and clearance
BetaWorks out a spur gear meshing inside a ring gear: centre distance, contact ratio, ratio and interference.
The contact ratio counts only involute contact. interferes flags ring tips below the gear's
base circle, or gear tips catching ring tips when the two differ by few teeth.
Example: module 2, 20 teeth in 60 -> 40 apart, ratio 3
The module, the teeth and the pressure angle
The centre distance, contact ratio, ratio and interference
BetaLays out a planetary gear set around a sun at rotation 0: the ring's teeth, where the planets sit, how far each planet and the ring turn to mesh, the ratio with the ring held, and whether the planets mesh, keep clear of each other and interfere.
They mesh when the sun's and ring's teeth together divide by the planets.
The module, the sun's and a planet's teeth, the planets and the pressure angle
The layout and its checks
BetaWorks out the lines of an involute rack: its pitch, its length, how far its tips stand above the pitch line, how deep its gaps reach below it and how thick each tooth is on it.
Example: module 2, 10 teeth -> pitch 6.28, 62.8 long
The teeth and the height
The sizes in model units
BetaDraws an involute rack's outline as points on the XY plane, a closed counterclockwise loop not repeating its start: pitch line on the x axis, teeth along +y, the first tooth's middle on the origin.
A spur gear of the same module meshes with its centre its pitch radius, plus its profile shift times the module, above the pitch line.
The teeth, the height and the segments per curve
The points of the outline
BetaWorks out the circles of an involute ring gear, whose teeth point in toward its centre: the pitch and base circles, the tip circle inside them, the root circle beyond, and half the angle a tooth spans at the pitch circle.
Example: module 1, 40 teeth -> pitch radius 20, tip radius 19, root radius 21.25
The teeth
The four radii in model units and the half tooth angle in radians
BetaDraws the teeth of an involute ring gear as points on the XY plane around the origin: the edge of the hole inside the ring, a closed loop counterclockwise that does not repeat its start.
Cut it from a circle larger than twice the root radius to make the ring; segments sets how
many points stand for each curve.
The teeth, the turn and the segments per curve
The points of the outline
BetaWorks out the circles of an involute spur gear: the pitch circle meshing gears roll on, the base circle its flanks unwind from, the tip and root circles, and half the angle a tooth spans at the pitch circle.
Example: module 1, 20 teeth -> pitch radius 10, tip radius 11, root radius 8.75
The teeth
The four radii in model units and the half tooth angle in radians
BetaDraws the outline of an involute spur gear as points on the XY plane, a closed counterclockwise loop that does not repeat its start, ready to extrude in any kernel.
The flanks follow the involute within a ten-thousandth of the module; segments sets the
points per curve. Tips that reach only inside the base circle are refused.
The teeth, the turn and the segments per curve
The points of the outline
BetaGives the module of an inch gear from its diametral pitch, in the model's unit, so the gear methods can size it.
The module is the pitch diameter over the teeth, the inverse of the diametral pitch: 1 / DP inches, or 25.4 / DP millimetres. Example: 10 DP -> 0.1 inches, or 2.54 millimetres
The diametral pitch and the unit
The module in unit
Involute gears by their numbers, with no CAD kernel needed: the circles of spur and ring gears, and their outlines as points on the XY plane for any kernel to extrude.
occt.parts.mechanical.gearsbuilds the same teeth as solids. Gears mesh when they sharemoduleandpressureAngle: two spur gears half the module times their teeth together apart, a spur gear in a ring half the module times the difference.