This partial calculator is explicitly a user-selected timing schedule: one 180-degree forward segment and one 180-degree return segment divide a cycle by an entered time share. It does not reconstruct non-circular gears, pitch curves, tooth generation, contact or a physical quick-return drive.
Partial · Selected Two-Segment Angular Schedule
Explore a user-selected time split for equal 180-degree forward and return segments without inventing non-circular gears.
Equation Used
- Forward and return segments each cover 180 degrees in magnitude.
- Speed is idealized as constant inside each segment.
- Endpoint reversal is instantaneous and therefore not a physical acceleration model.
- Pitch curves, gear contact, teeth, center distance, inertia, torque, impact, wear and safety are excluded.
The secondary figure is a timing dial, not a non-circular gear pair.
Supported two-segment schedule
For cycle speed n, cycle time is T=60/n. If selected forward time share is s, forward time is sT and return time is (1-s)T. Because each segment covers the same 180-degree magnitude, the selected average return-to-forward angular-speed ratio is s/(1-s).
The animation uses ideal constant speed within each segment and an instantaneous reversal at the endpoints; it is a schedule, not a machine dynamics model.
Use and boundary
Use the ledger to compare a selected time allocation for equal angular excursions. Do not use it to design non-circular gears, predict tooth contact or infer acceleration, torque, impact or achievable motion.
Selected timing identities
T=60/n; t_forward=sT; t_return=(1-s)T; average return/forward speed ratio=s/(1-s).
Default selected-value example
At 10 cycles/min and s=0.70, cycle time is 6 s, forward time is 4.2 s, return time is 1.8 s and the selected average return-to-forward speed ratio is about 2.333.
Unsupported gear synthesis removed
The former arbitrary axis-ratio calibration, elliptical mesh drawing and non-integrated output angle were removed. No axis ratio, pitch curve, center distance or tooth geometry is produced.
Questions
Does this design quick-return gears?
No.
Why is the return faster?
The same 180-degree magnitude is assigned less time by the selected schedule.
Are endpoint accelerations finite?
No. Instantaneous reversal is an idealization, so the schedule is not a dynamics model.
References
- OpenStax: Rotation Angle and Angular Velocity
- Determining the Geometry of Noncircular Gears for a Given Transmission Function — documents why a physical gear pair requires a defined transmission function and compatible pitch curves.
References & Further Reading
- Wikipedia contributors. Non-circular gear. Wikipedia
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