A drag-link quick-return drive combines a double-crank four-bar with a connecting rod and guided ram. The input rotates uniformly, the second crank rotates at changing speed, and the ram travels out and back in generally unequal times. All five moving-link and frame dimensions below determine the displayed geometry.
Drag-link Quick-return Interactive Calculator
Set the four-bar lengths, ram rod and input speed. The ram follows the linkage geometry; stroke times are measured between its actual left and right endpoints.
Equation Used
- Fixed grounded pivots and rigid links with ideal pins.
- One oriented circle-intersection branch for the four-bar.
- Ram guide passes through output shaft centre; ram rod attaches to the output crank pin.
- Constant input speed; no load, friction, deflection or dynamic capacity model.
- All dimensions are pin-centre distances; drawn link thickness is schematic.
Ideal planar geometry; no loads, interference or operating-speed rating. Rod length exceeds output crank length.
Two linked loops, one driving angle
The frame holds shafts O and D. Input crank OA moves the coupler AB, turning output crank DB. A second rod connects B to the guided ram. Both rods keep their entered pin-centre lengths. The ram centre stays on a horizontal line through D.
The double-crank inversion requires the shortest link to be fixed and a positive Grashof margin. Making the driver shorter than the frame does not give this double-crank arrangement. The model identifies other classifications and retains a geometry preview rather than inventing a full rotation.
The ram reverses when the output crank and ram rod lie along the guide line. Timing is measured between those actual endpoints. A slow portion of the cycle is not a finite dwell.
Study reciprocation with unequal stroke times
Compare the leftward and rightward stroke durations as you change the four-bar dimensions. Assign the intended working direction from your own machine layout; this calculator does not assume that left always means cutting.
The paper by Podhorodeski, Nokleby and Wittchen includes a drag-link-driven slider among quick-return mechanisms and relates the time ratio to input rotation between stroke endpoints. This calculator implements the in-line slider version with the rod attached at the output crank pin.
Changing the ram rod length changes intermediate positions and velocity. With an in-line guide and a rod longer than the output crank, it does not change the total stroke or the two reversal angles. That is a property of this geometry.
Closure, ram motion and endpoint timing
Let O=(0,0), D=(g,0), and A=(a cosθ,a sinθ). Solve |B−A|=b and |B−D|=c using one oriented circle-intersection branch. The input speed is constant. Differentiating these constraints gives the instantaneous output angular-speed ratio.
If φ is the output crank angle and L is the ram rod length, the ram coordinate measured from D is x=c cosφ+√(L²−c² sin²φ). Its displacement from the left endpoint is x−(L−c). With L>c, the endpoints are x=L−c and x=L+c, so the stroke is 2c.
The ram velocity is [−c sinφ−c² sinφ cosφ/√(L²−c² sin²φ)] × dφ/dθ × 2πn/60. Units are mm/s when lengths are in mm and n is in rpm.
A bracketed solve finds the input phases at φ=0 and φ=π. The phase fraction from the right endpoint to the left endpoint, multiplied by 60/n, gives the leftward time. The complementary fraction gives the rightward time. The reported ratio is longer time divided by shorter time. At zero rpm both times read stopped.
Change one quantity at a time
The initial frame is 60 mm, input and output cranks are each 90 mm, coupler is 110 mm, and ram rod is 250 mm. The Grashof margin is 90+90−60−110=10 mm, with the frame shortest. The ram stroke is 180 mm. At 60 rpm, its two stroke times sum to one second.
Increase the rod to 500 mm. The stroke remains 180 mm and the endpoint times stay the same, but intermediate ram displacement and speed change. Increase the input speed from 60 to 120 rpm: all instantaneous velocities double and both stroke times halve.
Increasing the coupler to 120 mm reaches a change-point geometry. Full nonsingular timing is then unavailable. The linkage stays visible and the classification explains why.
What this model establishes
The calculations establish rigid planar positions, ram stroke, velocity and geometric timing. They do not establish drive torque, cutting force, bearing life, safe operating speed or a percentage productivity improvement.
Links are shown in axially separated planes. A projected overlap is not a collision test. The ram rod range stays longer than the output crank so its in-line slider loop can always reach the required output-crank positions; the four-bar itself can still be invalid.
A time ratio near one can result from the chosen dimensions. It is reported rather than forced into a preferred range. Change-point and unassembled configurations are identified separately.
Quick-return questions
Why have the old ratio sliders been replaced?
The earlier driver/frame and coupler/frame sliders did not specify all the links needed to calculate the motion. Entered lengths now constrain every moving pin.
Which direction is the working stroke?
The calculator labels directions left and right. Your tool and process determine which direction does the work.
Why does the ram rod change speed but not stroke?
For this in-line arrangement with L>c, both endpoints occur with the crank and rod collinear. The endpoints remain L−c and L+c while intermediate positions depend on L.
Does a low speed create a dwell?
No. A stationary instant at reversal is not a finite stationary interval.
Can invalid dimensions still be seen?
Yes. A red gap shows where the entered four-bar links cannot meet. Full-cycle values are withheld there.
References
Podhorodeski, Nokleby and Wittchen, Quick-return mechanism design and analysis projects, International Journal of Mechanical Engineering Education 32(2), figures 2 and 3 and the endpoint timing discussion.
Carnegie Mellon University, Introduction to Mechanisms, Chapter 5, four-bar classification, Grashof inversions and slider-crank linkages. The calculator equations above state the specific geometry and differentiation used here.
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