A crank pin sliding in a pivoted slotted lever produces unequal working and return intervals. Enter crank radius and fixed-center distance to calculate both crank sweeps, their time ratio and the interval durations at constant shaft speed.
Slotted-Lever Quick-Return Geometry
Enter crank radius, distance between the fixed crank and lever centers, and constant shaft speed. The worksheet derives the two complementary crank sweeps, their time ratio and the duration of each interval. It does not rate force, clearance, cutting speed or machine capacity.
Equation Used
- Crank radius is smaller than the fixed-center distance.
- The crank turns at constant angular speed.
- Pins, sliding block, slot, link and guides are rigid and clearance-free.
- Force, torque, friction, acceleration loading, stroke length, cutting speed and structural limits are excluded.
The crank radius and fixed-center distance determine the two complementary sweeps. At constant crank speed, the larger sweep takes longer.
Crank pin slides in an oscillating slotted lever
A crank rotating about one fixed center carries a block that slides in a lever pivoted at a second fixed center. The lever endpoint drives a guided output through a connecting link. The two lever reversals occur when the lever is tangent to the crank-pin circle.
Because those tangent positions divide one crank revolution unequally, one output stroke takes more crank angle—and time—than the other.
Ideal quick-return timing
Use this calculator to relate the fixed-center geometry to timing. A real shaper or other machine requires a full stroke, force, speed, acceleration and clearance analysis.
Geometry-derived crank sweeps
Timing example
With r=60 mm and d=150 mm, theta=23.58°, the working sweep is 227.2° and return sweep is 132.8°, giving a 1.710:1 time ratio. At 60 rpm the intervals are 0.631 s and 0.369 s.
Why the two sweeps are linked
The lever reverses at the two tangents to the crank-pin circle. Those positions divide one full revolution into the working and return sweeps, so their sum is exactly 360 degrees and both follow from the same radius-to-center-distance ratio.
Quick-return timing questions
Can alpha and beta be entered separately?
No; this mechanism derives them from r/d.
Does the ratio depend on rpm?
No. RPM changes both interval durations by the same factor.
Does this calculate ram stroke?
No; that requires the output-arm, link and guide geometry.
Quick-return references
- IIT Kharagpur / NPTEL, General Purpose Machine Tools: shaper quick-return purpose, forward/return duration ratio and machine-tool context.
- Malla Reddy College of Engineering and Technology, Kinematics of Machinery: labeled crank-and-slotted-lever and Whitworth quick-return constructions.
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