For the ideal Whitworth geometry with crank radius r smaller than fixed-center spacing d, α = asin(r/d). The two crank arcs are 180° + 2α and 180° − 2α, so their constant-speed time ratio is the same angle ratio.
Slider-Crank Inversion and Quick Return
Explore exact ideal Whitworth long-arc/short-arc timing with explicit feasibility handling.
Equation Used
- Crank speed is constant.
- Crank pin is ideal and slides on the pivoted lever centerline.
- Valid tangent-angle timing requires r smaller than d.
- Ram linkage dimensions, dynamics, friction, loads and ratings are excluded.
Select r smaller than d for this tangent-based quick-return model. At r ≥ d, the illustration is hidden and timing outputs are zero.
Crank pin sliding in a pivoted slotted lever
The rotating crank pin remains on the selected crank circle while its block slides along the pivoted lever. The lever tip connects to a horizontal ram through a constant-length rod. Tangent positions of the crank pin reverse the lever and define the long and short crank arcs. Ram dimensions are illustrative and vary with the selected proportions; they are not dimensions for a particular machine.
What the calculator determines
Select crank radius, fixed-center spacing and constant crank speed. For r < d, the calculator reports long-arc/short-arc ratio, their ideal times and geometry margin d − r. If r ≥ d, tangent changeover geometry does not exist and timing outputs are zeroed rather than clamped.
Ideal tangent-angle ledger
α = asin(r/d); long arc = 180° + 2α; short arc = 180° − 2α; Q = long/short; times = (60/N)(arc/360°).
Selected-input arithmetic
For r = 40 mm, d = 100 mm and N = 60 rpm, α is about 23.58°, the arc ratio is about 1.71, and the two ideal times sum to one second.
Timing reference only
The arc ratio does not determine ram stroke or cutting direction without the full lever, link and guide dimensions. Acceleration, inertia, force, slot friction, clearances, singular behavior, stress and ratings are excluded.
Questions
Why is r ≥ d invalid?
For r>d the pivot is inside the circle; at r=d the arrangement is singular. Neither gives the two distinct tangent positions required by this model.
Is the long arc always the cutting stroke?
No. Which stroke is cutting depends on assembly orientation and machine use, so outputs are labeled long and short arcs.
References & Further Reading
- University of AlmerÃa, Other well-known mechanisms, quick-return diagram, and Example 2.3, crank pin and slotted-bar position analysis. Wikipedia contributors. Slider-crank linkage. Wikipedia
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