This crank-and-rod linkage turns a continuous input rotation into an oscillating output when its four pin-center lengths permit crank-rocker motion. The rod joins two moving pins; the input and output shafts are supported on a fixed frame.
Crank to Oscillating Rod Reciprocating Interactive Calculator
Set four pin-center lengths and follow the connected rod and oscillating output. Compare angular range, one-way tip arc and complete input-rotation closure.
Equation Used
- Rigid planar pin-center geometry.
- One oriented assembly branch.
- Nonsingular full input turn required for full-cycle outputs.
- Arc is one-way output travel for a crank-rocker, one circumference for a double crank.
- Clearance, load, speed and wear not evaluated.
Tip arc is one-way travel along a circular path, not a straight-line stroke.
Follow the two supported shafts
The blue crank OA rotates about bearing O. The gold rod AB pushes and pulls the green output arm DB about bearing D. Both fixed bearings belong to the same frame. The pale green trace is the path of output pin B over a complete input revolution.
All moving links retain their entered lengths. The same oriented circle-intersection solution locates B at every connected pose, preventing a jump between two different assemblies. Where closure is impossible, separated links and a red gap identify the missing joint instead of stretching a rod to hide the problem.
Angular reciprocating motion
The output of a crank-rocker swings along an arc. It is not a straight-line ram, and its speed is not generally sinusoidal. This geometry is useful when studying rocking arms and oscillating drives. A slider-crank is a different arrangement for a directly guided linear output.
Calculate sweep and tip travel
Use input radius a, connecting-rod length b, output-arm length c and fixed bearing separation d. The distance from moving crank pin A to fixed bearing D ranges from |d−a| to d+a. For nonsingular full input rotation, that entire interval must lie strictly between |b−c| and b+c.
For a crank-rocker, output extrema occur when the input and rod align. The corresponding OB distances are a+b and |b−a|. The cosine rule in triangle ODB gives the two output limits. Their difference is the angular range Δβ. One-way output-tip arc travel is cΔβ, with Δβ in radians; a full outward-and-return cycle travels twice that arc.
The minimum acute transmission angle is evaluated from the extreme AD distances using triangle ADB. The full-turn closure deficit is max(0, |b−c|−|d−a|, d+a−b−c). It describes failed triangle inequalities, not a single recommended machining correction. A zero value may still be a singular equality, which the status identifies.
Example dimensions
The default input radius is 90 mm, rod length 240 mm, output arm 180 mm and bearing separation 200 mm. This geometry permits a nonsingular full input rotation. Its output range is approximately 74.3 degrees, corresponding to about 233.5 mm of one-way travel along the output pin’s circular arc.
Changing any link length recalculates closure, sweep and transmission. When the selected input cannot complete a turn, the full-cycle measurements are withheld; a connected instant alone does not establish a working cycle.
What the drawing establishes
The animated dimensions are pin-center lengths. Bearings, rod thickness and frame detail show the physical arrangement but are illustrative. Members can pass in different planes; the model does not test collisions or specify bearing widths.
A double-crank geometry produces full output rotation rather than oscillation and is labeled accordingly. A change-point configuration is singular. Neither the transmission-angle result nor the closure deficit establishes load capacity, operating speed, component life or a universal service limit.
Oscillating-rod questions
Is tip arc the same as linear stroke?
No. It is distance along a circular path centered on output bearing D.
Why do the links remain visible when they cannot connect?
The preview retains each entered length and marks the unclosed connection. That is a geometry diagnostic, not a functioning linkage at that angle.
Why can zero closure deficit still show a warning?
Zero includes equality at a circle-tangency or change-point boundary. A nonsingular full turn requires strict inequalities.
Does increasing crank radius always give a usable larger sweep?
No. It can prevent full input rotation. Check the complete closure result as well as the output travel.
Reference
Carnegie Mellon University: Planar Linkages, sections 5.2.2–5.2.5, for four-bar classification, transmission angle and dead points. The calculator derives closure, tip arc and output limits from circle intersection and the cosine rule.
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