A crank-rocker is a four-bar linkage whose input makes complete turns while its output swings between two angles. Two pivots attach to the frame, and a pin-jointed coupler connects the moving links. The entered lengths determine whether that motion is possible.
Crank-rocker Mechanism Interactive Calculator
Adjust all four pin-center lengths. Compare the connected motion, complete input-rotation check, output range and transmission angle.
Equation Used
- Rigid planar pin-jointed links.
- Fixed ground length d, input a, coupler b, output c.
- One oriented intersection branch; no hidden length changes.
- Full-cycle outputs require nonsingular closure through a complete input turn.
- Geometry only; component thickness, collisions, inertia and loads are not evaluated.
Dimensions are pin-center lengths. The drawing uses the same entered values as the calculator.
Four links and four pivots
The input OA turns about fixed bearing O. Coupler AB transfers motion to output DB, which is supported at fixed bearing D. The joint B is the intersection of circles centered at A and D, with radii equal to the coupler and output lengths.
The illustration retains one oriented intersection branch. It does not jump to a different assembly simply because the other intersection is higher on screen. If the joint circles cannot meet, the separated-link preview retains the entered lengths and marks the missing connection.
Oscillating drives
Crank-rockers convert a rotating drive into oscillation, for example in wiper and rocking-beam arrangements. Their output speed varies through the cycle. A particular application also needs checks for load, bearing capacity and component clearance, which are outside this geometry calculator.
Full rotation and transmission angle
Let a be the input length, b the coupler, c the output and d the fixed-pivot distance. During a full input turn, the distance from the input pin A to the output pivot D ranges from |d−a| to d+a. A nonsingular full input turn requires |d−a| greater than |b−c| and d+a less than b+c.
The Grashof margin is p+q−s−l after sorting the four lengths into shortest s, intermediate p and q, and longest l. The identity of the fixed and driven links also matters; a positive margin alone does not prove that the selected input rotates.
For a crank-rocker, the two output limits follow from OA and AB aligning: the distance OB is a+b or |b−a|. The swing is the difference between the corresponding angles from the cosine rule. For a double crank, the output angular range is 360 degrees. The acute transmission angle is the smaller angle between the coupler and output link; its full-cycle minimum follows from the two extreme AD distances.
Example dimensions
With a=40 mm, b=100 mm, c=80 mm and d=120 mm, the Grashof margin is 20 mm. The input can rotate fully, the output swings through 60 degrees, and the minimum acute transmission angle is approximately 51.3 degrees.
Increasing a alone can prevent full input rotation. The calculator then reports limited motion rather than treating a partly sampled path as a complete operating cycle.
Geometry limits
Equality at a closure boundary produces a singular or change-point configuration. A full-cycle angular range and minimum transmission angle are withheld there. A linkage that can assemble at one position may still be unable to make a full input turn.
A small transmission angle reduces the output moment obtained from a given coupler force. This geometric result is not a universal pass/fail threshold. The calculator does not estimate load capacity, friction, inertia or interference between finite-thickness members.
Four-bar questions
Does a positive Grashof margin always make this input a crank?
No. The fixed link and input link must also be identified. The calculator checks the complete input rotation directly.
Why can the result say double crank?
When the frame is the shortest link in an appropriate Grashof linkage, both frame-connected links can rotate. The calculator identifies that different motion.
Why are links separated in some poses?
The entered lengths cannot close at that input angle, or the joint-circle construction is singular. The preview keeps the real lengths visible instead of stretching them.
Is the minimum transmission angle a load rating?
No. It is a geometric indicator of force transmission. Loads and component strength require separate analysis.
Reference
Carnegie Mellon University, Introduction to Mechanisms: Planar Linkages, sections 5.2.2 through 5.2.5, for four-bar classification, transmission angle and dead points. Closure and output ranges here are derived from circle intersection and the cosine rule.
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