Wittgenstein's Rod: Clearance and RSS Error-budget Calculator

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Compare diametral ring clearance, pin play and rod straightness. The calculator halves diametral clearance to obtain radial clearance, then combines the three entered error terms by an assumed root-sum-square rule.

Related Resources for Actuator Projects

For separate linkage and actuator projects, check that the required stroke, speed and end positions fit the mechanism geometry. The clearance calculator on this page does not determine actuator travel or force.

With leverage, force is traded against travel. A bracket change that improves force can also increase required stroke, slow the output motion, or move the actuator into a poor mounting angle.

The clean way to review it is to sketch the linkage at the start, middle, and end of travel. At each position, check the line of action, required force, available clearance, and whether the actuator rod remains close to axial loading.

  • Map actuator stroke to the actual output travel before choosing a model.
  • Check for binding, changing leverage, and peak load near the ends of travel.
  • Decide whether timed motion is acceptable or position feedback is required.

For a FIRGELLI design review, calculate the load case with the FIRGELLI actuator force calculator and plan the switching or controller arrangement with the linear actuator wiring diagram generator. If an actuator or cylinder is already installed, the linear actuator replacement finder helps keep the comparison tied to real dimensions.

Wittgenstein's Rod Interactive Calculator

Enter rod diameter, diametral ring clearance, pin play and straightness. Total trace error is a declared RSS budget—not a guaranteed tolerance or motion simulation.

0°

Half diametral clearance
--
Diametral clearance/diameter
--
Entered straightness term
--
Declared RSS budget
--

Equation Used

radial clearance=C/2; clearance ratio=100C/D; total trace error=sqrt((C/2)^2+P^2+S^2).
RSS assumes independent orthogonal-like contributions. Worst-case stack, direction, contact, compliance, wear and measurement uncertainty are not modeled.
  • Clearance is entered diametrally and halved for radial error.
  • Pin play and straightness are entered nonnegative magnitudes.
  • The three terms are combined by a declared RSS rule.
  • Terms are treated as independent for screening.
  • Contact, orientation, compliance, wear, loads and uncertainty are omitted.
Watch the Wittgenstein's Rod in motion
Video: Wittgenstein's rod -- geometry in motion by Nguyen Duc Thang (thang010146) on YouTube. Used here to complement the diagram below.
Same mechanism and inputs as the interactive calculator.

Declared Error-Budget View

The animation separates the rod, clearance ring and three independent budget terms.

What This Calculator Represents

An assumed dimensional error budget using the entered magnitudes. It does not calculate the path of a linkage point.

Error Budget

R=C/2
ratio=100C/D
E=sqrt(R^2+P^2+S^2)

Worked Scenario

At 6 mm diameter, 0.05 mm diametral clearance, 0.01 mm play and 0.10 mm straightness, the RSS total is about 0.104 mm.

Assumptions and Limits

No mechanism closure, contact direction, worst-case stack, load, wear or statistical capability is calculated.

Frequently Asked Questions

Why divide clearance by two?

The input is diametral; the radial allowance is half.

Is RSS worst case?

No.

Are terms statistically verified?

No.

Is contact simulated?

No.

Is straightness solved?

No; it is entered.

Can this set a production tolerance?

Not without engineering validation.

References

Building or designing a mechanism like this?

Explore the precision-engineered motion control hardware used by mechanical engineers, makers, and product designers.

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