A crank pin running in a lever slot can make the lever traverse one stroke while the uniformly rotating crank sweeps a larger angle than it uses for the opposite stroke. This calculator evaluates that ideal tangent-angle timing construction.
Variable Rectilinear Motion Interactive Calculator
Enter crank-pin radius r and fixed center distance L with r<L. Results are ideal input-angle intervals and their ratio—not ram displacement, velocity, force, stress or machine capacity.
Equation Used
- The driver center and slotted-lever pivot are fixed a distance L apart.
- The crank pin travels on a circle of radius r with r<L.
- The lever slot passes through its fixed pivot and the crank pin without clearance.
- Input angular speed is uniform, so angular-sweep ratio equals ideal time ratio.
- Output link geometry, ram stroke, displacement, velocity, acceleration, force, friction, backlash, stress, wear and safety are omitted.
Documented Slotted-Lever Quick-Return Topology
U.S. Patent 479,742 describes a uniformly driven disk pin working in a slotted bar whose rotation center is offset from the driving-shaft center, producing unequal motion during opposite parts of the cycle. NASA mechanism reports also distinguish crank-slider and offset quick-return arrangements.
What This Calculator Represents
The tool constructs the two tangents from the fixed lever pivot to the crank-pin circle. Their half-angle alpha divides one crank revolution into work and return sweeps of 180 degrees plus and minus 2alpha.
Ideal Tangent-angle Timing Calculation
work sweep = 180 deg + 2alpha
return sweep = 180 deg - 2alpha
ideal timing ratio = work sweep / return sweep
L is fixed center distance, not lever length. Under uniform crank speed, elapsed time is proportional to crank angle.
Worked Idealized Example
For crank-pin radius 130 mm and fixed center distance 320 mm, alpha is about 24.0 degrees. The ideal work sweep is about 227.9 degrees, return sweep about 132.1 degrees and timing ratio about 1.73:1.
Model Boundary
- Calculated: tangent construction angle, two crank sweeps and ideal timing ratio.
- Illustrated: fixed driver center, offset lever pivot, crank pin and slotted lever.
- Not calculated: output link closure, ram position, stroke, velocity, acceleration, force, stress, clearance, wear, capacity or safety.
References
- U.S. Patent 479,742, Conveyer and screen: quick-return slit-bar motion with an offset slotted-bar shaft and uniformly driven disk pin.
- NASA mechanism report: four-bar, offset slider-crank and offset quick-return mechanisms.
- U.S. Patent Application 2018/0206449: distinguishes crank-slider, Whitworth slotted-rod, Scotch-yoke and cam-slider reciprocating systems.
Frequently Asked Questions
Is L rocker length?
No; here L is the fixed distance between the two rotation centers.
Why must r be smaller than L?
So real tangents exist from the lever pivot to the crank circle.
Does the ratio equal elapsed-time ratio?
Only for uniform crank angular speed and the defined intervals.
Is ram stroke calculated?
No.
Are forces or stresses included?
No.
Can this size a machine?
No.
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