A double rocker is a four-bar linkage whose two frame-mounted arms both oscillate. This calculator solves their motion from four pin-centre lengths. The output angle follows the coupler constraint; it is not a separately chosen swing.
Double-rocker Mechanism Interactive Calculator
Enter four pin-centre lengths to solve a connected four-bar linkage. The input rocks within its feasible interval; the output follows the rigid coupler. Classification and both displayed sweeps update with the geometry.
Equation Used
- All entered lengths are pin-centre distances.
- Input position is prescribed; no motor or inertia model is included.
- Display uses the middle 90% of the feasible positive-angle interval.
- One continuous circle-intersection branch is retained.
- Output sweep is sampled and not claimed as an exact analytic extremum.
- Geometry that changes linkage class is labeled; impossible assemblies remain visible as previews.
Output swing is geometry-derived and sampled over the displayed interval. Playback timing, bearing sizes and link thickness are illustrative.
Four rigid links, one connected motion
The fixed pivots O and D are carried by a frame. Input arm OA drives the gold coupler AB, which moves output arm DB. Each pin joins the same two members throughout the animation, and all four pin-centre distances remain constant.
The input is prescribed to rock back and forth inside a feasible angular interval. The solver finds B as the intersection of a circle centred at A with radius AB and a circle centred at D with radius DB. One oriented intersection branch is retained.
The displayed reversals use the middle 90% of the positive-angle feasible interval. This keeps the animation away from the interval boundaries, where links may align. The two geometric limits are still reported separately.
Explore a coupled rocking motion
Change the fixed-pivot spacing or any moving-link length to see how the connected motion changes. The shaded frame, bearing supports and distinct link colours separate fixed and moving members.
The entered dimensions may stop describing a double rocker. The classification updates accordingly. A limited rocking demonstration of a crank-capable linkage does not mean that its cranks have lost their ability to rotate.
No motor, driving torque or force capacity is calculated. The animation prescribes input position and solves output position.
Closure and angular limits
For fixed spacing g, input length a and input angle θ, A=(a cosθ, a sinθ) and D=(g,0). The separation d between A and D satisfies d²=g²+a²−2ga cosθ.
The two circles can intersect when |b−c|≤d≤b+c. Combining that with |g−a|≤d≤g+a gives the permitted distance interval. Applying the cosine relation gives the lower and upper input-angle limits in 0° to 180°.
The displayed input uses 5% inward clearance at each angular end. Output sweep is the range of unwrapped output angles from 601 equally spaced input samples over that displayed interval. It is labeled sampled rather than an exact analytic extremum.
Classification uses the shortest and longest link lengths and the choice of fixed link. Change-point equality is identified separately; dimensions that cannot close the quadrilateral are not reported as a working linkage.
A connected double-rocker example
The starting design has 200 mm fixed-pivot spacing, a 150 mm input arm, a 70 mm coupler and a 160 mm output arm. The shortest link is the coupler. Its shortest-plus-longest sum is 270 mm, smaller than the other two lengths summed to 310 mm; with this fixed link, the mechanism is a double rocker.
The calculator finds a feasible angular interval from these lengths and draws the coupled motion within it. The input and output swings are generally different and their instantaneous relationship is not constant.
Entering four equal lengths produces change-point geometry. Making one length greater than the sum of the other three makes assembly impossible; the component-length preview remains visible.
What the animation does and does not establish
A connected drawing establishes planar pin-centre closure for the shown branch and interval. It does not establish collision clearance, bearing loading, force transmission under load or a suitable drive arrangement.
The 5% angular margin is a demonstration choice, not a mechanical safety factor. A full mechanism can have other assembly branches or motion intervals beyond the positive-angle interval used here.
The output sweep is numerically sampled. Use a refined analytic or numerical analysis when exact extrema are needed for detailed design.
Double-rocker questions
Why are the two rocker swings linked?
The coupler connects the two arms, so the four lengths and one input position determine the other arm. Independent arbitrary swings would stretch or disconnect a rigid link.
Why do the displayed arms reverse before the geometric limits?
The illustration leaves 5% of the feasible angular span at each end to avoid displaying toggle endpoints as normal driven travel.
Why does the classification change?
Changing the lengths can produce a crank-rocker, double crank, change point or impossible assembly instead of a double rocker.
Is the output sweep exact?
It is sampled at 601 input positions and labeled accordingly.
Does this calculate a driving actuator?
No. This is a planar linkage position model with prescribed rocking motion.
Reference
Carnegie Mellon University, Introduction to Mechanisms, Chapter 5: Planar Linkages, sections 5.2.2–5.2.5: four-bar definitions, classification, transmission angles and dead points. The circle-intersection position solution and sampled sweep calculation are derived from the entered pin-centre lengths.
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