A Whitworth turning-block quick-return mechanism places a sliding block on a rotating crank pin inside a slotted member turning about an offset fixed pivot. At constant crank speed, unequal crank angles give unequal stroke times.
Swinging-block Linkage Interactive Calculator
Vary crank radius r and centre offset d. For d/r below one, the calculator shows the larger and smaller crank-angle intervals and their ideal time ratio; otherwise it reports invalid geometry.
Equation Used
- The crank turns at constant angular speed.
- The entered centre offset satisfies 0 <= d/r < 1.
- Links are rigid and joints are ideal, without clearance or friction.
- Ram linkage dimensions, displacement, velocity, acceleration, force, stress, wear and safety factors are omitted.
How the Turning Block Creates Quick Return
The crank pin carries a sliding block inside a slotted lever. The lever pivots about a fixed point offset from the crank centre. As the crank turns, the block slides along the slot and changes the angular position of the slotted member. The numerical tool compares angle intervals; it does not solve a complete ram linkage.
Cornell's Reuleaux collection identifies the turning-block slider-crank, also called a Whitworth quick-return mechanism, as a machine-tool quick-return arrangement. The diagram does not specify manufacturing tolerances, hardness, maintenance intervals or a particular machine design.
What This Explanatory Model Is Useful For
The calculator isolates the ideal geometric source of quick return: one stroke occupies a larger crank-angle interval than the other. Under constant crank speed, the larger interval takes proportionally longer.
Assembly orientation determines which physical stroke corresponds to the larger interval. A complete machine also needs the rocker-to-ram linkage dimensions and dynamic analysis.
Ideal Constant-speed Angle Partition
For entered crank radius r and centre offset d, with d/r below one:
The two intervals sum to 360 degrees. When d is zero, both are 180 degrees and Q = 1. As d approaches r, the ideal smaller interval approaches zero; real mechanisms cannot use that singular limit.
Worked Example: Entered Geometry
For r = 50 mm and d = 25 mm, d/r = 0.5 and alpha = 30 degrees. The larger crank interval is 240 degrees, the smaller interval is 120 degrees, and their ideal constant-speed time ratio is 2.00:1.
If d is 50 mm or more for that radius, this formula has no valid real quick-return geometry and the calculator reports an invalid input.
Model Boundary
- Calculated: ideal offset angle, complementary crank-angle intervals and their constant-speed time ratio.
- Geometry boundary: the entered offset must be smaller than the crank radius for this convention.
- Not calculated: rocker angle, ram stroke, displacement, velocity, acceleration, force, torque, bearing or slot pressure, clearance, friction, wear, stress, fatigue, lubrication or safe operating speed.
Frequently Asked Questions
Why must d/r be less than one?
This angle construction requires asin(d/r) to be real and the offset pivot to lie inside the crank circle.
Why are the outputs called larger and smaller rather than forward and return?
Assembly orientation determines which physical stroke is the working stroke; the geometry alone only fixes the two angle intervals.
Does the ratio depend on crank rpm?
The ideal ratio does not, but equating angle ratio with time ratio assumes constant crank speed.
Does this calculate ram stroke?
No. Ram motion also depends on rocker length, connecting link and attachment geometry.
What happens at d = 0?
The angle intervals are equal and the time ratio is 1:1.
Can the calculator size the block or slot?
No. Component design requires forces, pressure, material, lubrication, wear and fatigue analysis.
References
- Cornell University Reuleaux Collection, Turning Block Slider-Crank: historical identification and Whitworth quick-return use.
- Florida International University, Mechanism Design notes: quick-return time ratio as the ratio of crank angles under constant speed.
- University of California, Davis, Whitworth Quick Return Mechanism: mechanism layout and motion project.
- Gardner D. Hiscox, Mechanical Movements, Powers, Devices and Appliances: historical mechanism collection.
Building or designing a mechanism like this?
Explore the precision-engineered motion control hardware used by mechanical engineers, makers, and product designers.
