This calculator compares two entered positive angular allocations. It reports their ratio, normalized shares and an equivalent asymmetry angle; it does not derive irregular rocking motion from a linkage.
Irregular Rocking Motion Interactive Calculator
Explore work/return allocation ratios and normalized shares, with a 360-degree closure check disclosed in the interpretation.
Equation Used
- Both entered allocations are positive and use the same angular reference.
- If interpreted as one input revolution, they must sum to 360 degrees and input speed must be constant for angle ratio to equal time ratio.
- Equivalent alpha maps the normalized shares to 180 plus/minus alpha.
- No crank/coupler/rocker/frame lengths, pivot coordinates, branch, stroke extrema, transmission angle, displacement/velocity/acceleration, loads, dwell, interference, strength, wear or safety model.
The entered angles are treated as allocations. Only when they sum to 360 degrees can they directly represent the two portions of one constant-speed input revolution. ‘Slow’ and ‘fast’ stroke behavior is not calculated without input speed and a connected mechanism.
Two-allocation comparison
The page divides one entered allocation by the other and normalizes both by their sum. Equivalent alpha expresses those normalized shares as 180+alpha and 180−alpha degrees.
Hiscox item 1031 shows a crank pin driving an endless groove in a pivoted arm. In the animation, the groove follows an illustrative output law of 0.32 sin(θ) + 0.065 sin(2θ) radians. The changing output angle defines the groove; its proportions and clearance are illustrative. The entered allocations do not control this motion.
Use as phase-budget arithmetic
The results can compare two already-known input-angle or time allocations. They cannot determine those allocations from a linkage or establish rocker motion, quick return, dwell or machine performance.
Closure and constant-speed conditions
When theta_w+theta_r=360 degrees and the input rotates uniformly, their ratio also equals ideal phase-time ratio. Otherwise the displayed shares are normalized arithmetic only.
Equivalent alpha is derived from Q=(180+alpha)/(180−alpha); it is not a physical link angle without a mechanism-specific derivation.
Worked example
For entered allocations 216 and 144 degrees, they close one revolution, ratio is 1.50, normalized shares are 60% and 40%, and equivalent alpha is 36 degrees.
Limits of the allocation comparison
A rocking mechanism needs a defined linkage or cam. Its dimensions and input motion determine the output angle, turning points and speed. Entering two angular allocations does not establish that motion or the loads on its components.
Questions
Does ratio prove a quick-return linkage exists?
No. It only compares entered allocations.
Is alpha a physical rocker angle?
No. It is an equivalent normalized phase parameter.
Do the percentages imply slow and fast output speed?
No. The entered percentages do not set the illustrative grooved-arm motion.
References & Further Reading
Gardner D. Hiscox, Mechanical Movements, Powers, Devices and Appliances (1901), page 259, item 1031: irregular rocking motion.
- Wikipedia contributors. Four-bar linkage. Wikipedia
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