Reciprocal circular motion is a back-and-forth angular movement about a fixed pivot. This calculator shows a four-bar crank-rocker: a rotating crank moves a coupler, which swings the output rocker between two limits. Enter the four pin-centre distances to explore the swing and whether the input can complete a full revolution.
Reciprocal Circular Motion Interactive Calculator
Vary the crank-rocker link lengths and motor speed to see the output swing angle, cycle rate, and linkage motion.
Equation Used
- Rigid pin-jointed planar links with fixed centre distance.
- The input crank must complete a full revolution in the illustrated assembly branch.
- No link thickness, bearing clearance, interference, force, stress, balance or safe-speed prediction.
If the full-revolution closure checks fail, the outputs show zero swing and cycle rate and the diagram identifies the geometry problem. The zero values are an invalid-input indication, not a calculated operating cycle.
How the crank-rocker moves
The frame holds two fixed pivots. The crank rotates about the first and carries one end of the coupler. The coupler’s other end connects to the rocker, which turns about the second fixed pivot. Together these four links form a closed loop.
With crank-rocker proportions, one complete crank turn produces an outward and return sweep of the rocker. At a rocker limit, the crank and coupler are collinear. The rocker changes direction there while the driving crank can continue rotating.
The animation follows one assembly branch. The blue, orange and green links represent the crank, coupler and rocker. Both bearings stay fixed during a cycle. Changing Centre Distance moves their locations for the next geometric calculation.
Measure between pin centres
- Crank length r: first fixed pivot to the moving crank pin.
- Coupler length L: distance between its two moving pins.
- Rocker length R: second fixed pivot to the coupler connection.
- Centre distance C: distance between the fixed pivots.
Link width, offset brackets and bearing clearance are absent from the model. A closed geometric loop does not establish that physical parts will clear one another.
Using an angular sweep
A crank-rocker can provide the repeating motion of a wiping arm, an oscillating paddle or a sweeping guide. The load attaches to the rocker or to another link driven by it; its required travel determines the useful angular range.
For an illustrative wiping arm, start with the required sweep and the available pivot locations. Compare link lengths in the calculator, then examine the full cycle. The tool answers the geometric swing question. Choosing a motor also requires load torque, inertia, friction and duty-cycle information that is not entered here.
Changing Motor Speed adjusts the predicted cycles per minute for valid geometry. It does not resize the linkage or establish a permissible running speed. The displayed animation is slowed so the joints can be followed.
Rocker swing and closure equations
At the two rocker limits, the distance from the first fixed pivot to the coupler–rocker pin is L − r or L + r. Let alpha(d) be the cosine-rule angle in the triangle with sides C, R and d:
The degree conversion applies when acos returns radians. Half Swing is Total Swing divided by two. It is an amplitude about the midpoint of the two limits, not an angle measured from the frame line.
Can the input complete a revolution?
The distance between the crank pin and the second fixed pivot varies from |C − r| to C + r. The coupler and rocker circles must intersect at every input angle. This calculator therefore requires both strict inequalities:
Equality reaches a collinear change point and is excluded from ordinary full-revolution results. A failed check makes the displayed swing and cycle-rate outputs zero; read that as an invalid geometry indication.
The separate Grashof Margin sorts the four lengths into shortest s, longest l and intermediate p and q, then calculates p + q − s − l in millimetres. It is a geometric quantity, not a safety factor. For valid geometry, Cycle Rate equals the entered motor RPM because one crank turn gives one complete outward-and-return cycle.
Worked example using the default inputs
Enter r = 40 mm, L = 180 mm, R = 62 mm, C = 190 mm and n = 90 RPM.
- Closure: |180 − 62| = 118 mm is less than |190 − 40| = 150 mm. Also, 190 + 40 = 230 mm is less than 180 + 62 = 242 mm. Both checks pass.
- Limit angles: L − r = 140 mm gives alpha = 30.29°. L + r = 220 mm gives alpha = 111.03°.
- Swing: Using the unrounded limiting angles gives 80.745°, displayed as about 80.7°. Half Swing is about 40.4°.
- Cycle rate: 90 RPM gives 90 cycles/min. The geometric margin is 62 + 180 − 40 − 190 = 12 mm.
For comparison, r = 40 mm, L = 180 mm, R = 120 mm and C = 200 mm gives approximately 39.29° of swing. Keeping those latter three lengths and changing r to 25 mm gives 24.32°; changing r to 70 mm gives 71.51°. These are calculated geometric comparisons, not tested installation results.
Changing only motor speed leaves these swing angles unchanged. A real drive still needs a separate assessment of its loads, clearances and construction.
Choosing the form of motion
| Arrangement | Output | What sets the motion |
|---|---|---|
| Crank-rocker | Angular sweep about a pivot | Four link lengths, assembly branch and crank position. |
| Scotch yoke | Linear reciprocation along a guide | Crank radius and rotation; a separate linkage is needed for an angular output. |
| Reversing rotary drive | Commanded angular movement | Motor, controller, feedback and the programmed motion. |
The calculator covers the first arrangement. It does not compare costs, lifetimes, bearing service intervals or positional accuracy among these options.
Crank-rocker questions
Why do some inputs produce zero swing and cycle rate?
Zero is the calculator’s indication that the entered links fail its full-revolution closure check or reach an equality/change-point case. It is not a prediction that an assembled machine has zero motion. Adjust the dimensions and read the geometry message.
Does Half Swing give the rocker angle from horizontal?
No. It is half the difference between the two limiting angles. The rocker’s installed angle and the screen angle shown during playback use different references.
Does increasing motor speed change the swing angle?
The ideal swing depends on link lengths, so changing Motor Speed changes Cycle Rate without changing Total Swing. Playback is deliberately slowed for viewing and is not a real-time representation of the entered RPM.
Are the outward and return movements identical?
The rocker travels between the same two limits in both directions, but those strokes can take different amounts of crank rotation and time. Constant crank speed does not make rocker motion sinusoidal or its angular speed constant.
Is a positive Grashof Margin enough to size the drive?
No. The calculator also checks whether this particular input crank can turn fully with the chosen fixed pivots. Neither check predicts required torque, bearing loads, interference or operating speed.
What dimensions should I enter?
Use distances between pin centres for the crank, coupler and rocker, and between the two fixed pivot centres for Centre Distance. Overall plate length or the distance to an external tool tip is not the same measurement.
Can the tool diagnose chatter or choose bearing clearances?
No. It models rigid links and ideal pivots. Chatter can involve clearance, flexibility, loads and dynamics that are not represented. Assess those features in the actual assembly rather than selecting a universal clearance from this calculation.
Technical reference
- Middle East Technical University OpenCourseWare, Four-bar mechanism — crank-rocker classification, Grashof condition and rocker dead-centre positions.
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