This page now limits itself to the exact timing arithmetic supported by its two controls. The connected clock shows declared forward and return crank arcs under constant angular speed; it does not pretend those two angles define a slotted lever, Whitworth chain, ram stroke or rectilinear path.
Declared Two-Arc Time-Share Ledger
Enter declared forward and return crank arcs. The worksheet compares their constant-speed elapsed times and equal-stroke mean speeds. Check that the displayed arcs total 360 degrees before interpreting them as one full crank revolution.
Equation Used
- The input rotates at constant angular speed.
- Alpha and beta are user declarations, not results of a linkage closure.
- A complete single-revolution schedule requires alpha+beta=360 degrees.
- Time ratio means forward elapsed time divided by return elapsed time.
- The mean-speed comparison assumes equal travel distance in the two directions.
- The clock animation is a connected timing visualization, not a rectilinear linkage model.
- Link lengths, stroke, line guidance, instantaneous kinematics, acceleration, force, power, loads, wear, machine performance, operation and safety are excluded.
Keeps exact declared two-arc time-share arithmetic, replaces the invented rectilinear linkage view with a schedule clock, and removes unsupported geometry and machine claims.
Unequal input arcs can create unequal stroke times
MIT's machine-elements notes derive quick return from unequal crank-angle intervals between reciprocating limits. IIT Kharagpur states the same timing principle for a constant-speed crank.
Because this worksheet has no link lengths, offsets or ram geometry, it displays only the two-arc timing schedule.
Use this as a declared time-share ledger
The calculator reports the ratio and shares of two declared input-angle intervals plus an equal-stroke mean-speed comparison.
It cannot generate or validate reciprocating rectilinear motion.
Constant-speed arc timing
For equal travel distances only, mean return speed divided by mean forward speed is q.
A transparent declared example
For alpha=216 degrees and beta=144 degrees, q=1.500, forward share=60.0 percent, return share=40.0 percent and equal-stroke mean return speed is 50.0 percent higher. The arcs total 360 degrees.
Timing declarations are not mechanism geometry
A physical quick-return machine needs a selected linkage type, complete dimensions and closure analysis before stroke, velocity or acceleration is known.
The former fabricated geometry, machine examples, wear limits, tolerances, performance, adjustment, maintenance and troubleshooting claims are removed.
Two-arc ledger questions
Do alpha and beta have to total 360 degrees?
Yes to represent one full revolution.
Does the time ratio give instantaneous speed?
No.
Does this prove straight-line ram motion?
No.
Why keep both time shares?
They expose exactly how the declared total is divided.
Timing references
- MIT 2.017J, Topics in Machine Elements: quick-return angle intervals and time ratio.
- IIT Kharagpur Virtual Lab: uniform crank speed and crank-angle time ratio.
- University of Utah ME 3200: two quick-return crank arcs and full-turn closure.
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