Design shafts, bearings, gears, fasteners, springs, joints, and power transmission components.
Course outline only for now. Full chapter-level lessons are still in progress. Use this page for readiness, concepts, worked-example format, practice, review, and portfolio direction. Complete course contents are live today for Math, Physics, and Statics.
01
Readiness check
Before starting, confirm the prerequisite habits.
Trace a torque path through a machine.
Use torsion formulas.
Understand safety factor and fatigue.
Read bearing and gear layouts.
0 or 1 weak itemContinue, but slow down at the worked example.
2 weak itemsReview the foundation page linked in the roadmap before solving practice problems.
3 or more weak itemsStep back to prerequisites; this module depends on them.
02
The core idea
Size common machine elements from load paths, stress limits, stiffness, life, and safety factors.
Machine design is about sizing a real component against a failure mode (yield, fatigue, buckling, wear) by comparing the working stress to an allowable with a defensible factor of safety.
tau = 16T / (pi d^3)
Works when: you identify the governing failure mode first, then size the part so the stress stays below the allowable with a stated factor of safety.
Breaks down when: you check static yield but the part actually fails by fatigue, buckling, or surface wear under cyclic load.
Figure 1. Concept model for Machine Elements. The figure names inputs, computed variables, geometry, and result.
Figure 2. Worked problem setup: A solid steel shaft of diameter 25 mm transmits 180 N m of torque. Estimate maximum torsional shear stress.Figure 3. Calculation model. The result follows from the model, units, and reasonableness check.
A solid steel shaft of diameter 25 mm transmits 180 N m of torque. Estimate maximum torsional shear stress.
Problem A solid steel shaft of diameter 25 mm transmits 180 N m of torque. Estimate maximum torsional shear stress.
Given and find T = 180 N m, d = 25 mm. Find: tau_max.
Assumptions Idealized model, consistent units, and no hidden effects outside the stated scope.
Step Convert T to 180,000 N mm.
Step tau = 16T/(pi d^3).
Step tau = 16(180000)/(pi*25^3) = 58.7 MPa.
Step Check keyways, shoulders, and fatigue before accepting a real shaft.
Conclusion tau = 58.7 MPa. Carry this result into the design decision, not just into the answer box.
05
Misconceptions and diagnostics
Mistake
Symptom
Diagnostic question
Correction
Static check on a cyclic part
Sizes for yield, ignores fatigue
Is the load steady or repeated?
Use the S-N / Goodman approach when loads cycle.
Arbitrary factor of safety
Picks a factor of safety with no rationale
What uncertainty does this factor cover?
Tie the factor of safety to load, material, and consequence uncertainty.
Wrong stress for the element
Uses bending stress on a shaft in torsion
What loading does this element actually carry?
Match the stress (tau = 16 T / pi d^3 for torsion) to the load.
06
Practice ladder
Level 1: direct skill
Redo the worked example with one changed input. Predict the trend before calculating.
Check yourself
The trend must match the governing relation: tau = 16T / (pi d^3).
Level 2: mixed concept
Draw the model from memory, label knowns and unknowns, then write the first equation without looking.
Check yourself
Your first equation should connect the model to tau max.
Level 3: independent problem
Create a similar problem from a real object near you. State assumptions, solve it, and include a reasonableness check.
Check yourself
A valid solution has a sketch, given/find list, governing relation, units, and a conclusion.
Level 4: transfer task
Turn the result into a design decision: what would you change if the output missed its target by 25 percent?
Check yourself
Name the design variable with the strongest influence and justify it from the equation.
07
Working with AI, and proving it yourself
Useful AI role
Ask for a critique of assumptions, units, diagram labels, and missing checks after you have attempted the solution.
Do not outsource
Do not paste the problem and accept a final answer. Your evidence is the model, the checks, and the explanation.
08
Retrieval and spaced review
Closed-notes prompts: name the component's governing failure mode, write the stress it controls, state the allowable and factor of safety, and check the size against it.
TodayRedo the worked example from a blank page.
+1 daySolve Level 1 without notes.
+3 daysSolve Level 2 with changed numbers.
+7 daysConnect this module to another course.
+30 daysAdd a portfolio artifact.
09
Mapping and portfolio task
Course mapping
Machine elements is where mechanics of materials becomes hardware: shafts, gears, bearings, bolts, and springs all reuse the stress formulas, now driven by catalog data and failure theory.
First-pass focus: definitions, model setup, units, and worked examples. Save edge cases for the second pass.
Portfolio task
Create a one-page sizing note for a shaft, bolt, or bearing against its failure mode: sketch, assumptions, equations, result, reasonableness check, limitation, and recommendation.