This partial calculator applies an entered constant angular ratio to a selected input angle. It reports selected output angle, input turns, output-to-input angle magnitude, and an ideal lossless torque ratio. It does not define a rack, linkage, road-wheel angle, steering effort, vehicle response or safety.
Steering Gear - Selected Constant Angular-Ratio Ledger
Explore a selected constant angular-ratio mapping between abstract input and output shafts.
Equation Used
- Input angle and constant positive angular ratio are entered values.
- Input and output signs use one selected coordinate convention; topology-dependent reversal is not modeled.
- Ideal torque ratio assumes lossless power transfer and no assist.
- No road-wheel angle, linkage geometry or vehicle response is inferred.
- Backlash, friction, compliance, loads, limits and safety are excluded.
The secondary figure is a two-dial angular ledger, not a rack-and-pinion or vehicle steering design.
Selected angular-ratio ledger
For the selected sign convention and constant ratio R, output angle is input angle divided by R. Input turns are input degrees divided by 360. Output-to-input angle magnitude is 100/R percent. The ideal torque ratio equals R only under lossless power transfer.
What the calculator determines
Use it to inspect a selected two-shaft angular mapping. No steering mechanism topology or vehicle geometry is inferred.
Selected relationships
theta_out=theta_in/R; turns=theta_in/360; angle magnitude=100/R; ideal torque ratio=R.
Selected-input example
At 360 degrees selected input angle and ratio 12, selected output angle is 30 degrees, input rotation is one turn, output-to-input angle magnitude is 8.333 percent, and the ideal lossless torque ratio is 12.
Not a steering-system model
Gear topology, direction reversal, variable ratio, rack travel, pinion pitch radius, tie rods, Ackermann geometry, compliance, backlash, friction, assist, tire forces, steering effort, limits, vehicle motion and safety are excluded.
Questions
Is selected output angle a road-wheel angle?
No. NHTSA's road-wheel relationship applies to an identified overall steering ratio; this ledger has no vehicle geometry or measured system.
Is the torque ratio actual steering assistance?
No. It is the reciprocal angular ratio under an ideal lossless assumption and excludes friction and power assist.
Does the sign specify gear direction?
No. Input and output signs share a selected coordinate convention; topology-dependent reversal is unresolved.
Authoritative references
- NHTSA-hosted steering-system definitions — defines mean steering ratio as steering-control angular displacement divided by mean swept steering angle.
- NHTSA steering-response report — states the simplified road-wheel steer angle relationship as handwheel angle divided by steering ratio in its test context.
- NASA Gear Design — discusses fixed gear-train speed ratio and practical gear limits absent from this abstract mapping.
References & Further Reading
- Wikipedia contributors. Rack and pinion. Wikipedia
Building or designing a mechanism like this?
Explore the precision-engineered motion control hardware used by mechanical engineers, makers, and product designers.
