A double-crank, or drag-link, mechanism connects two rotating cranks by a rigid coupler. Two fixed shaft bearings define the frame. Each crank makes a full turn in a nonsingular double-crank arrangement, although the output generally speeds up and slows down during that turn.
Double-crank Mechanism Interactive Calculator
Set the fixed shaft spacing and the three moving pin-centre lengths. Compare the Grashof classification with the actual connected motion and instantaneous output speed.
Equation Used
- Rigid links with ideal revolute joints.
- Positive rotation is counterclockwise.
- Physical thickness and axial offsets are schematic.
- A singular position has no assigned finite instantaneous output speed.
- Zero input rpm stops automatic phase advance but permits manual position inspection.
A positive margin with the frame shortest identifies a nonsingular double crank. Equality is explicitly a change point. Mean output speed is assigned only to a double-crank cycle.
Two shafts and one connecting rod
O and D are the fixed bearing centres. The blue crank rotates about O and carries pin A. The gold coupler joins A to B. The green output crank connects B to the second fixed centre D.
Pin B must lie both one coupler length from A and one output radius from D. The animation solves those intersecting circles at every input angle. It keeps the same oriented assembly branch through the cycle instead of switching to whichever solution is visually higher.
The dashed circular tracks show crank-pin paths. If the selected lengths cannot connect at an input angle, the diagram retains the entered link lengths and marks the separation. The dashed gap is an error preview, not a flexible connecting rod.
Explore a rotating linkage
Use this model to compare the effect of shaft spacing and crank proportions on output rotation. The calculator distinguishes a complete double-crank cycle from a crank-rocker, restricted rocking motion and singular geometry.
The pin-centre model does not include bearing loads, link thickness, out-of-plane spacing or collisions between physical components. A real assembly needs suitable axial offsets and clearance where the drawn members cross.
Closure and output speed
For input angle θ, pin A has coordinates (a cosθ, a sinθ). Pin B satisfies |B−A|=c and |B−D|=b, where D=(g,0). These two distance constraints are the basis of the drawing.
Sort the four lengths as shortest s, longest l and intermediate p and q. The reported Grashof margin is p+q−s−l. With a strictly positive margin and the frame shortest, this model classifies the linkage as double crank. Equality is reported as change-point geometry rather than silently treated as a normal cycle.
For coupler vector w=B−A, input speed ratio is dφ/dθ=[w·(−Ay,Ax)]/[w·(−By,Bx−g)]. Multiply by input rpm for instantaneous output rpm. A zero denominator is singular, so no finite speed is assigned there.
For a nonsingular double crank, one complete input turn gives one complete output turn. Their cycle-average speeds agree; their instantaneous speeds need not. Negative instantaneous output indicates clockwise rotation in this counterclockwise-positive convention.
A clearly separated double-crank example
The default frame is 60 mm, input radius 100 mm, coupler 110 mm and output radius 120 mm. The shortest-plus-longest sum is 180 mm and the other two lengths total 210 mm, giving a 30 mm Grashof margin.
With the shortest link fixed, this configuration permits both cranks to rotate. At 60 input rpm the mean output is also 60 rpm. Scrub the cycle to see the instantaneous output change, or set input speed to zero to stop playback without losing access to the position control.
What a Grashof result does not guarantee
A length classification is not a load-capacity calculation. Small transmission angles can produce unfavorable forces, and real links require clearance at crossings. The model makes no claim about acceptable torque, bearing size or maximum operating rpm.
Change-point dimensions may admit special motion paths, but branch choice at a collinear configuration requires additional physical constraints. This calculator does not hide that ambiguity by reporting an ordinary double-crank mean speed.
Double-crank questions
Why does the green crank change speed?
The connecting rod’s geometry creates a changing angular velocity ratio.
Why do the mean speeds agree?
In the nonsingular double-crank configuration each completes one revolution in the same cycle.
Why are some speed results unavailable?
The current position either cannot connect or has a singular velocity equation.
Can I inspect an invalid set of lengths?
Yes. The separated-link preview retains the requested lengths and identifies the gap.
Does a zero input speed freeze the position control?
No. Playback stops but the cycle slider still permits manual inspection.
References
Carnegie Mellon University: Planar Linkages, sections 5.2.2–5.2.5 on four-bar classification, transmission angle and change points.
Middle East Technical University: Four-Bar Mechanism, Grashof cases and double-crank inversion.
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