Follow the load path
Identify how force and torque pass through shafts, bearings, gears, fasteners and supports. Check alignment, lubrication, fatigue and assembly access as well as nominal stress.
Opening Lilerno
lilernoEngineeringlilernoEngineeringOpening Lilerno
Chapter 20 · Guided self-study
Intro + external course studyConnect geometry and component choices to loads and service conditions.
Build the idea
An original introduction, worked example and practice, followed by a curated reading sequence. The external courses supply deeper teaching and problem sets.
This guide is an orientation, not a complete university module. Practical work needs suitable facilities, safety review and supervision.
Start with these prerequisites
Shared science foundations
Detailed machine design connects loads to geometry, interfaces and service life. A downloaded CAD object supplies geometry, not proof of suitability.
Module lens
An ideal external gear pair trades speed and direction through pitch geometry.
Identify how force and torque pass through shafts, bearings, gears, fasteners and supports. Check alignment, lubrication, fatigue and assembly access as well as nominal stress.
For an ideal external gear pair, speed magnitudes vary inversely with tooth counts and rotation directions oppose. Torque capacity still depends on material, tooth geometry, width, manufacturing and operating conditions.
See the relationship
Change one quantity, watch the graph respond, then explain the result in your own words.
Predict → change → explain
Increase the output tooth count. What happens to output speed?
Axes: Output tooth count → Signed output speed (rpm). Bounds may rescale when inputs change.
Ratio = 3:1; output = -300 rpm. Minus denotes the opposite direction.
Ideal external gear pair; input has 20 teeth. Pitch circles are schematic, not manufactured tooth profiles. Torque capacity and losses are not modelled.
Original Lilerno illustration. Inputs are illustrative; this is not experimental evidence or a design rating.
| Series | Output tooth count | Signed output speed (rpm) |
|---|---|---|
| Output speed | 20 | -900 |
| Output speed | 20.75 | -867.5 |
| Output speed | 21.5 | -837.2 |
| Output speed | 22.25 | -809 |
| Output speed | 23 | -782.6 |
| Output speed | 23.75 | -757.9 |
| Output speed | 24.5 | -734.7 |
| Output speed | 25.25 | -712.9 |
| Output speed | 26 | -692.3 |
| Output speed | 26.75 | -672.9 |
| Output speed | 27.5 | -654.5 |
| Output speed | 28.25 | -637.2 |
| Output speed | 29 | -620.7 |
| Output speed | 29.75 | -605 |
| Output speed | 30.5 | -590.2 |
| Output speed | 31.25 | -576 |
| Output speed | 32 | -562.5 |
| Output speed | 32.75 | -549.6 |
| Output speed | 33.5 | -537.3 |
| Output speed | 34.25 | -525.5 |
| Output speed | 35 | -514.3 |
| Output speed | 35.75 | -503.5 |
| Output speed | 36.5 | -493.2 |
| Output speed | 37.25 | -483.2 |
| Output speed | 38 | -473.7 |
| Output speed | 38.75 | -464.5 |
| Output speed | 39.5 | -455.7 |
| Output speed | 40.25 | -447.2 |
| Output speed | 41 | -439 |
| Output speed | 41.75 | -431.1 |
| Output speed | 42.5 | -423.5 |
| Output speed | 43.25 | -416.2 |
| Output speed | 44 | -409.1 |
| Output speed | 44.75 | -402.2 |
| Output speed | 45.5 | -395.6 |
| Output speed | 46.25 | -389.2 |
| Output speed | 47 | -383 |
| Output speed | 47.75 | -377 |
| Output speed | 48.5 | -371.1 |
| Output speed | 49.25 | -365.5 |
| Output speed | 50 | -360 |
| Output speed | 50.75 | -354.7 |
| Output speed | 51.5 | -349.5 |
| Output speed | 52.25 | -344.5 |
| Output speed | 53 | -339.6 |
| Output speed | 53.75 | -334.9 |
| Output speed | 54.5 | -330.3 |
| Output speed | 55.25 | -325.8 |
| Output speed | 56 | -321.4 |
| Output speed | 56.75 | -317.2 |
| Output speed | 57.5 | -313 |
| Output speed | 58.25 | -309 |
| Output speed | 59 | -305.1 |
| Output speed | 59.75 | -301.3 |
| Output speed | 60.5 | -297.5 |
| Output speed | 61.25 | -293.9 |
| Output speed | 62 | -290.3 |
| Output speed | 62.75 | -286.9 |
| Output speed | 63.5 | -283.5 |
| Output speed | 64.25 | -280.2 |
| Output speed | 65 | -276.9 |
| Output speed | 65.75 | -273.8 |
| Output speed | 66.5 | -270.7 |
| Output speed | 67.25 | -267.7 |
| Output speed | 68 | -264.7 |
| Output speed | 68.75 | -261.8 |
| Output speed | 69.5 | -259 |
| Output speed | 70.25 | -256.2 |
| Output speed | 71 | -253.5 |
| Output speed | 71.75 | -250.9 |
| Output speed | 72.5 | -248.3 |
| Output speed | 73.25 | -245.7 |
| Output speed | 74 | -243.2 |
| Output speed | 74.75 | -240.8 |
| Output speed | 75.5 | -238.4 |
| Output speed | 76.25 | -236.1 |
| Output speed | 77 | -233.8 |
| Output speed | 77.75 | -231.5 |
| Output speed | 78.5 | -229.3 |
| Output speed | 79.25 | -227.1 |
| Output speed | 80 | -225 |
| Chosen pair | 60 | -300 |
Save your place when you finish reading.
Original Lilerno example
An ideal 20-tooth gear drives a 60-tooth gear at 900 rpm input.
Use output speed magnitude = input speed × input teeth/output teeth.
900 × 20/60 = 300 rpm.
The external gears rotate in opposite directions.
Test the model
Open learning, traceable sources
Work in this order. These links open the publisher’s material; free access does not always permit republication.
MIT OpenCourseWare · Spring 2009
Start with: Mechanisms and design development
Follow a mechanism from requirement to calculation and drawing.
BelfrySCAD / BOSL2 contributors
Start with: Gear parameters and documented examples
Inspect an existing parametric construction. Identify module, tooth count and pitch diameter.
FreeCAD-library contributors (community-maintained)
Start with: Bearings, fasteners, couplings and pulleys
Inspect one part's geometry, author and licence. Verify dimensions against a real specification before use.
Recall, then record
Close the explanation and answer these in your own words. Return tomorrow, then again later in the week.
What is geometry and what is a rating?
Where does the load go?
How would you assemble and inspect it?
Prepare a paper assembly drawing and load-path diagram. Record model provenance and all missing service-condition data.
Self-reported tasks, not an assessment of mastery or university credit. Reading a page does not complete a chapter.
Loading local record…
Open learning, traceable sources
Original Lilerno lessons and diagrams, supported by these references. Free access does not always permit republication. Links open the publisher’s material.
Inspect editable bearings, fasteners, couplings and pulleys. Download individual parts rather than the entire large library. Geometry is not a certified load rating.
Repository assets: CC BY 3.0. Attribute each model's author from file properties and commit history; retain notices and identify modifications. No files are mirrored by Lilerno.
Open source ↗Rights / publisher record ↗Existing OpenSCAD gear constructions and documented parameters. Compare tooth count, module and pitch diameter; verify design assumptions before fabrication.
BOSL2 code is BSD-2-Clause; retain copyright and licence notices when redistributing code. Documentation and dependency notices must also be checked. Linked only.
Open source ↗Rights / publisher record ↗Mechanical design, mechanisms, and project thinking.
CC BY-NC-SA, except marked exceptions; external study only.
Open source ↗Rights / publisher record ↗