This page now treats its two inputs exactly as what they are: declared crank arcs under constant angular speed. The animated clock verifies the full-turn closure and timing arithmetic but does not invent a Whitworth or slotted-lever geometry from arc values alone.
Declared Constant-Speed Crank-Arc Ledger
Enter declared forward and return crank arcs. The worksheet compares their elapsed times for constant crank angular speed and reports any departure from a complete 360-degree cycle; it does not synthesize linkage dimensions or a motion profile.
Equation Used
- The input crank rotates at constant angular speed.
- The two entered arcs are declarations, not outputs of a linkage-closure calculation.
- A complete single-revolution schedule requires their sum to equal 360 degrees; epsilon reports the signed discrepancy.
- The time ratio is forward elapsed time divided by return elapsed time.
- The percentage comparison concerns mean speeds over equal stroke distances only.
- The connected clock animation visualizes the declared schedule and closure; it is not a Whitworth, crank-rocker or slotted-lever synthesis.
- Link lengths, stroke, branch, instantaneous kinematics, accelerations, forces, power, loads, wear, speed limits, machine selection, maintenance and safe operation are excluded.
Retains exact declared arc/time arithmetic, adds an explicit full-turn closure audit, replaces the arbitrary linkage animation with a faithful schedule clock, and removes unsupported machine and field claims.
Quick return requires unequal crank arcs between stroke limits
MIT's machine-elements notes show that offset slider-crank geometry creates unequal input-angle intervals between the two slider extremes. IIT Kharagpur's Virtual Lab likewise states that, for uniform crank speed, stroke-time ratio equals the corresponding crank-angle ratio.
This page does not know any link lengths or offsets, so its animation is a schedule clock rather than a fabricated linkage.
Use this to audit a declared timing schedule
The worksheet compares two declared arcs, checks whether they close one revolution, and converts their ratio into elapsed-time and equal-stroke mean-speed comparisons.
It cannot design, select, operate or troubleshoot a shaping machine or quick-return linkage.
Constant angular speed makes time proportional to angle
For equal reciprocating stroke distances, mean return speed divided by mean forward speed is also q. Instantaneous speed is not uniform and is not calculated here.
A transparent declared schedule
For theta_f=220 degrees and theta_r=140 degrees, q=1.571, the equal-stroke mean return speed is 57.1 percent above the forward mean, the forward share is 61.1 percent and epsilon=0 degrees.
Arc timing does not identify a mechanism
Whitworth, crank-rocker, crank-and-slotted-lever and offset slider-crank mechanisms can all produce quick return, but their link geometry, stroke, velocity and acceleration laws differ.
The former fabricated machine examples, adjustment times, wear diagnoses, tolerances, brand claims, performance and operating advice are removed.
Declared arc-ledger questions
Must the arcs add to 360 degrees?
Yes for one complete single-revolution schedule.
Does q give instantaneous speed ratio?
No.
Does this determine a Whitworth linkage?
No.
Why show epsilon?
It makes inconsistent input schedules visible instead of silently normalizing them.
Quick-return timing references
- MIT 2.017J, Topics in Machine Elements: offset slider-crank stroke-limit angles and quick-return time-ratio expression.
- IIT Kharagpur Virtual Lab, Quick Return Mechanism: constant crank speed and stroke-time ratio as crank-angle ratio.
- University of Utah ME 3200, Quick-Return Mechanism Design: prescribed time ratio, two crank arcs and the 360-degree closure condition.
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