A Whitworth-type quick-return mechanism uses a rotating crank pin, sliding block, pivoted slotted lever and reciprocating carriage. Its defining feature is unequal crank rotation—and therefore unequal time at constant input speed—for the two strokes, not uniform slider velocity.
Uniform Reciprocating Motion Interactive Calculator
Enter crank-pin radius, an assumed slower-stroke crank sweep and an arithmetic comparison percentage. Results are a crank-orbit and timing calculation—not actual ram stroke, velocity, acceleration, force or machine performance.
Equation Used
- R is the entered crank-pin radius and 2R is only its orbit diameter.
- The entered sweep is an assumed slower-stroke driver angle; the complementary sweep is 360 degrees minus that value.
- Input angular speed is constant when interpreting sweep ratio as time ratio.
- The percentage output is only an entered fraction of orbit diameter.
- Link lengths, pivot locations, assembly branch, actual carriage stroke, position law, velocity, acceleration, force, torque, clearance, friction, strength, wear and safety are omitted.
Crank Pin, Sliding Block and Pivoted Slotted Lever
U.S. Patent 3,422,757 describes a Whitworth quick-return mechanism as a disk rotating about one point, an off-axis slide on a pivoted arm and distinct forward and return strokes. U.S. Patent 3,653,869 shows a crank-driven sliding block moving in a slot in a pivoted Whitworth lever that reciprocates a carriage.
The calculator illustrates that topology schematically. It does not solve the carriage position or claim constant output velocity.
What This Calculator Represents
The tool doubles entered crank-pin radius to report orbit diameter, subtracts an entered stroke sweep from 360° to obtain the complementary sweep and divides the two sweeps. With constant driver speed, that angular ratio is also the ratio of elapsed times.
The final value is only an entered percentage of orbit diameter. None of these results establishes actual carriage stroke.
Crank-Orbit and Sweep calculation
complementary crank sweep = 360° - alpha
constant-input-speed time ratio = alpha / (360° - alpha)
selected diameter fraction = 2R × p/100
Worked Arithmetic Example
For entered crank-pin radius 50 mm, orbit diameter is 100 mm. An assumed 220° slower-stroke sweep leaves a 140° complementary sweep and gives a constant-input-speed time ratio of 1.57:1. A 75% comparison fraction of the orbit diameter is 75 mm. These are not solved ram dimensions.
Assumptions and Limits
- Calculated: crank orbit diameter, complementary entered sweep, sweep/time ratio and selected diameter fraction.
- Illustrated: a generic crank, sliding block, pivoted slotted lever and carriage.
- Not calculated: actual carriage position, stroke, velocity, acceleration, jerk, dwell, load, torque, impact, clearance, friction, deflection, wear, motor behavior, tooling, rating or safety.
Frequently Asked Questions
Does a Whitworth mechanism produce uniform slider velocity?
No. Unequal stroke times in a quick-return mechanism do not imply constant slider velocity.
Is 2R the actual ram stroke?
No. It is only crank-pin orbit diameter.
Why can crank-angle ratio represent time ratio?
Only because constant input angular speed is assumed.
Does the entered sweep come from the radius alone?
No. It is entered independently here.
Is the selected diameter fraction a constant-velocity travel band?
No.
Can this calculator design or diagnose a quick-return machine?
No.
References
- U.S. Patent 3,422,757, Sheet feeding apparatus: Whitworth quick-return disk, off-axis slide, pivoted arm and forward/return strokes.
- U.S. Patent 3,653,869, Apparatus for skimming the surface of molten metal baths: crank, sliding block, slotted Whitworth lever and reciprocating carriage.
- Florida International University, Mechanism Design #1: quick-return time ratio as slower-stroke time divided by quicker-stroke time for constant crank velocity.
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