A D-class drag link is a double-crank four-bar linkage: two shafts in fixed bearings are connected by cranks and a coupler. With a strict Grashof geometry and the shortest link fixed, both cranks can revolve. Constant input speed generally produces variable output speed.
Drag-link Mechanism Interactive Calculator
Set the four pin-centre distances and input speed. Inspect the assembled links, variable output rpm, and the time needed for each marked output half-turn. Invalid geometries remain visible as previews.
Equation Used
- Fixed frame and ideal revolute pins; constant input rpm.
- One continuous oriented intersection branch in the nonsingular double-crank case.
- Lengths are pin-centre distances, independent of schematic link thickness.
- Output half-turns are measured from the input-0° pose, not an unspecified working stroke.
- No friction, elastic deflection or inertial loads.
Rigid ideal planar geometry. Speed extrema sampled; no load, collision, dwell or operating-speed rating.
Four actual links determine the motion
The frame fixes the two shaft centres O and D. The blue input crank OA drives the gold coupler AB, which turns the green output crank DB. Each entered dimension is a pin-centre distance; the closure calculation preserves those distances at every connected position.
The output pivot B is found by intersecting a circle about A, of radius equal to the coupler length, with a circle about D, of radius equal to the output crank length. The same oriented intersection branch is retained throughout a nonsingular revolution.
Linkages that cannot complete that revolution are identified separately. A red gap marks an unassembled preview position; it is not another flexible link or a prediction that a real drive would pass through the position.
Explore a nonuniform rotary drive
The calculator lets you compare continuous input rotation with geometry-dependent output rotation. Adjust all four link lengths and the input rpm. The speed curve and two output half-turn times update from the resulting geometry.
The green and gold arcs split the output revolution into two equal 180° motions, starting from the output pose at input angle 0°. Their time ratio is tied to that specified datum. It does not assign a working stroke, return stroke, contact time or dwell to an unspecified machine.
Although output speed changes within a revolution, a nonsingular double-crank drive completes one output revolution for each input revolution. The mean speeds therefore agree.
Classification, closure and timing
Sort the four lengths into shortest s, longest l and intermediate p and q. The displayed Grashof margin is p+q−s−l. A positive margin with the shortest link fixed gives the double-crank case. Zero margin is a change-point geometry; a negative margin does not give a full revolving crank. Lengths that cannot form a quadrilateral are identified first.
For input angle θ, A=(a cosθ,a sinθ) and D=(g,0). The position B obeys |B−A|=b and |B−D|=c. If w=B−A, differentiating the coupler-length constraint gives dφ/dθ=(w·JA)/(w·J(B−D)), where J rotates a vector by 90°. The current output rpm is this ratio multiplied by input rpm.
For a valid double crank, solve for the input fraction f at which the continuously unwrapped output advances 180° from its input-0° pose. The first half-turn takes 60f/n seconds and the second takes 60(1−f)/n. The displayed longer-to-shorter ratio is max(f,1−f)/min(f,1−f).
The speed curve and peak sample 1440 input angles. Half-turn timing uses a bracketed angular solve. At zero rpm the times read stopped, while the geometric time ratio remains available.
A configuration close to the Grashof boundary
The starting dimensions are g=60 mm, a=90 mm, b=119.5 mm and c=90 mm. Their margin is 90+90−60−119.5=0.5 mm. The frame is the shortest member, so the ideal linkage is a double crank.
At 60 rpm input, the sampled output peak is about 300.4 rpm. The marked half-turns take about 0.168 s and 0.832 s, giving a longer-to-shorter ratio of 4.953. The small positive margin gives strong speed variation. Changing a link by enough to reach zero margin changes the classification to a change point. The calculator then withholds nonsingular double-crank timing instead of reporting a misleading cycle result.
Doubling the input rpm doubles each instantaneous output rpm and the sampled peak, while halving both half-turn times. Changing the rpm does not alter the geometric time ratio or the pin trajectories.
Scope and interpretation
This model calculates rigid planar linkage geometry and angular speed. It does not calculate torque, bearing pressure, fatigue, backlash or permissible machine speed. Large speed variation is not a demonstration of acceptable dynamic loading.
The shaft bearings are fixed to the frame; links are drawn in offset planes so they can pass in a side view. Actual link thickness, axial clearances and hardware collisions are not assessed.
A speed minimum is not a finite dwell. The calculator describes ideal linkage motion; selecting a machine speed also requires analysis of loads, bearings and link strength.
Drag-link questions
Why must the shortest link be fixed?
For a strict Grashof four-bar, that inversion is the double-crank case. Fixing a different member can give a crank-rocker or double-rocker.
Is the displayed time ratio a universal quick-return ratio?
No. It compares two equal output half-turns from the marked starting datum. A machine’s working interval needs its own specified boundaries.
Why do results disappear at a change point?
The geometry is singular and a continuous nonsingular branch is no longer guaranteed. The entered links remain visible, but full double-crank timing is not claimed.
Why does output rpm vary if it makes one turn per input turn?
The coupler changes leverage through the cycle. Faster and slower portions still total one output revolution.
Can I inspect the drive with its input stopped?
Yes. Zero rpm stops playback; the cycle-position control still displays selected configurations.
References
Carnegie Mellon University, Introduction to Mechanisms, Chapter 5: Planar Linkages, defines four-bar members and the Grashof inversions. The position, differential speed and half-turn timing calculations implement the explicit constraints described above.
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