For the ideal Scott Russell construction shown, slider A = (C cos θ, 0), output B = (0, −C sin θ), coupler AB has constant length C, and its midpoint M is joined to the fixed pivot O by a crank of length C/2. The ideal output stroke is 2C.
Ideal Scott Russell Right-Angle Linkage
Explore exact ideal Scott Russell linkage closure and selected guide-clearance ratio.
Equation Used
- The slider guides are perpendicular and intersect at the fixed pivot origin.
- The fixed crank joins the origin to the exact coupler midpoint.
- Links are rigid and joints are ideal.
- Clearance propagation, loads, compliance, friction, wear and tolerances are excluded.
The presentation cycles through ideal poses; output tiles report length identities and selected values.
Exact right-angle straight-line geometry
One coupler end is constrained to a horizontal guide and the other to a perpendicular vertical guide. The fixed crank reaches the coupler midpoint, so AB remains C and OM remains C/2 throughout the motion.
The animation preserves those constraints at every frame. The selected clearance and shaft diameter affect only the drawn guide detail and their reported ratio; they do not perturb the ideal linkage solution.
What the calculator determines
Select coupler length C, guide clearance c and shaft diameter d. Outputs are ideal midpoint-crank length C/2, ideal vertical output stroke 2C, the selected clearance, and 100c/d.
No clearance-to-output error propagation, force, torque, stress, friction, wear, backlash, tolerance stack or safe load is calculated.
Ideal closure and selected ratio
A = (C cos θ, 0), B = (0, −C sin θ), M = (A+B)/2, |AB| = C, |OM| = C/2 and output stroke = 2C. The reported clearance ratio is 100c/d.
Selected-input example
For C = 200 mm, the ideal midpoint crank is 100 mm and the output stroke is 400 mm. If c = 0.2 mm and d = 10 mm, the selected clearance ratio is 2%.
Scope and design boundary
The former page treated guide clearance as a one-to-one prediction of output wobble. That is not established by the ideal closure and is removed. Real output error depends on contact state, clearances at multiple joints, load direction, compliance and manufacturing error.
Unsupported material, application, tolerance, maintenance and performance claims are also removed.
Questions
Is the output path exactly straight?
In the ideal rigid, zero-clearance construction, yes: B is constrained to the vertical guide.
Why is the crank C/2?
It joins the fixed origin to the coupler midpoint, whose radius is C/2.
Does selected clearance equal output wobble?
No. The calculator reports the selected clearance and c/d only.
Can this size a real linkage?
No.
References & Further Reading
- Wikipedia contributors. Scott Russell linkage. Wikipedia
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