Editing Openai/68fceef0-7248-8013-bf5d-581461dec5bc (section)

=== Assistant: Short answer: I rechecked against solid sources — there’s no essential calculation missing for your pass/fail logic. ===
Short answer: I rechecked against solid sources — there’s no essential calculation missing for your pass/fail logic. Your methods align with standard references.
* Pitch → size/teeth spacing: DP & Module relations and circular pitch are correct for deriving pinion diameter/radius and rack tooth count. gearsolutions.com<ref>{{cite web|title=gearsolutions.com|url=https://khkgears.net/new/gear_knowledge/gear-nomenclature/diametral-pitch.html|publisher=khkgears.net|access-date=2025-11-15}}</ref>
* Torque ↔ line force: Using F=τ/rF=\tau/rF=τ/r at the drum/pinion is standard. Apex Dynamics<ref>{{cite web|title=Apex Dynamics|url=https://www.apexdyna.nl/en/news/calculate-rack-and-pinion|publisher=Apex Dynamics|access-date=2025-11-15}}</ref>
* Static breakaway vs running losses: Treating a starting torque threshold distinct from running efficiency is correct per bearing practice; our “auto τs” is a reasonable parametric stand-in for SKF’s fuller model. SKF<ref>{{cite web|title=SKF|url=https://www.skf.com/group/products/rolling-bearings/principles-of-rolling-bearing-selection/bearing-selection-process/operating-temperature-and-speed/bearing-friction-power-loss-and-starting-torque?Information=true|publisher=skf.com|access-date=2025-11-15}}</ref>
* Angle/projection “loss”: Using the cosine of the deviation to compute effective driving component is textbook.

If you want optional refinements later (not required for your Yes/No outcome):
* Add a mesh efficiency knob tied to pressure angle/μ (spur/rack typically ~94–98%+, high-quality closer to 98–99%). www.cedengineering.ca<ref>{{cite web|title=www.cedengineering.ca|url=https://www.cedengineering.ca/userfiles/M06-031%20-%20Basic%20Fundamentals%20of%20Gear%20Drives.pdf|publisher=cedengineering.ca|access-date=2025-11-15}}</ref>
* If desired, include pulley efficiency (large ball-bearing sheaves ~85–90% each) inside the overall efficiency instead of assuming ideal pulleys. ropelab.com.au<ref>{{cite web|title=ropelab.com.au|url=https://www.ropelab.com.au/pulley-efficiency/|publisher=ropelab.com.au|access-date=2025-11-15}}</ref>

But for now: your calculator’s current torque, friction, tension/angle, and pass/fail checks are complete and properly grounded.