Engineering optimzation·equivalent-torsional-stiffness-geared-system

Equivalent Torsional Stiffness Geared System

Two gears A and B are mounted on uniform circular shafts with equal torsional stiffness GJ/L. When a torque is applied to gear A, both shafts resist rotation. Given the radii ratio n = R_A/R_B, derive the equivalent torsional spring constant seen at gear A, accounting for the constraint that the gears roll without slip and the reaction forces create moments at both shafts.

✓ All 3 test cases pass.

Inputs

Torsional rigidity (product of shear modulus and polar moment)

GJ parameter for both shafts (equal stiffness)

Shaft length

Length of each uniform circular shaft

Radii ratio

Ratio R_A / R_B of gear radii

Test cases

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#	Inputs	Expected	Got	Status
1	{"GJ":1,"L":1,"n":1}	2	2	✓
2	{"GJ":1,"L":1,"n":2}	5	5	✓
3	{"GJ":10,"L":2,"n":3}	50	50	✓

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Endpoint

POST/api/calculators/engineering-optimzation/equivalent-torsional-stiffness-geared-system/compute

Inputs (3)

GJnumberdefault 1
Lnumberdefault 1
nnumberdefault 2

Example

curl -sX POST http://localhost:3001/api/calculators/engineering-optimzation/equivalent-torsional-stiffness-geared-system/compute \
  -H "Content-Type: application/json" \
  -d '{"inputs":{"GJ":1,"L":1,"n":2}}'

Try it live

Edit the body below, then click Call API.

Request body

Response

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full API docs →

Source: Pattern from: Ch1.pdf. Reproduces a standard equivalent-torsional-stiffness-geared-system computation; problem text paraphrased.

AI disclosure: Calculator code generated by anthropic/claude-haiku-4-5-20251001; verified by 3 test cases.