Epicyclic Gear Train Ratio Calculator
Willis sun/ring/carrier speed balance; ratio is−(sun−carrier)/(ring−carrier), finite tooth ratio reported even at co-rotation. Caller independently establishes units, regime, calibration and applicability; this does not establish design-code compliance, authenticity, operational safety, treatment efficacy or a validated forecast.
Description
A simple planetary gear relation links sun, ring and carrier speeds.
A simple planetary gear relation links sun, ring and carrier speeds.1
Tooth counts and signed rotational speeds determine the kinematic result rather than losses or torque capacity. Use Epicyclic Gear Train Ratio Calculator to evaluate the supplied inputs under the specific model below.
When to use Epicyclic Gear Train Ratio Calculator
Use Epicyclic Gear Train Ratio Calculator to evaluate the supplied inputs under the specific model below. Establish the units, measurement scope and applicable model or recipe assumptions before entering values.
How to use Epicyclic Gear Train Ratio Calculator and understand its results
- Establish the units, measurement scope and applicable model or recipe assumptions before entering values.
- Enter Sun teeth, Ring teeth, Sun speed rpm, Ring speed rpm using the field table and validation rules below, then run the tool.
- Read Carrier speed rpm, Signed sun relative carrier ratio and interpret units, signs, ordering and placeholders as explained below.
- If the tool reports an input error, correct that field and rerun. A successful false result, empty match list or unknown-evidence placeholder has the specific meaning described here; check the limitations before applying the result.
| Input field | Meaning | Value type | Requirement |
|---|---|---|---|
| sunTeeth | Sun teeth | number | Required; constraints below |
| ringTeeth | Ring teeth | number | Required; constraints below |
| sunSpeedRpm | Sun speed rpm | number | Required; constraints below |
| ringSpeedRpm | Ring speed rpm | number | Required; constraints below |
Enter integer tooth counts from 1 to 100000 with ring greater than sun, and finite signed sun and ring speeds in rpm. The carrier speed is the tooth-weighted speed average. Despite its signed name, signedSunRelativeCarrierRatio always returns the positive ring/sun tooth-count ratio; it is not computed from the supplied speed values. No torque or efficiency model is included.
carrierRpm = (Ns×sunRpm+Nr×ringRpm)/(Ns+Nr); reportedRatio = Nr/Ns Field order, units and branch conditions follow the implementation explanation above.
| Output field | Meaning | Value type |
|---|---|---|
| carrierSpeedRpm | Carrier speed rpm | number |
| signedSunRelativeCarrierRatio | Signed sun relative carrier ratio | number |
{
"input": {
"sunTeeth": 20,
"ringTeeth": 60,
"sunSpeedRpm": 100,
"ringSpeedRpm": 0
},
"output": {
"carrierSpeedRpm": 25,
"signedSunRelativeCarrierRatio": 3
}
}Limitations and assumptions
Tooth counts and signed rotational speeds determine the kinematic result rather than losses or torque capacity. Apply the exact scope and assumptions described above.
All listed fields require explicit values. Unexpected fields, incorrect types, nonfinite numbers and sparse arrays fail validation. Domain-specific bounds, alignments and supported tokens are stated above; extremely large inputs or outputs can also be rejected. These errors differ from successful results such as false, no matches or unknown evidence.
Alternative or Complementary methods
Use DH Transformation Calculator for a related task: A Denavit-Hartenberg transformation maps coordinates between linked reference frames.
Use Transform Function Order Matters Note for a related task: Rotation and translation generally do not commute.
References
-
Epicyclic Gear Train Ratio Calculator — tool.io
Similar or alternative tools
- DH Transformation Calculator
A Denavit-Hartenberg transformation maps coordinates between linked reference frames.
- Transform Function Order Matters Note
Rotation and translation generally do not commute.