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CALCULATORS / LEAD SCREWS AND LINEAR STAGES

Stage backlash stack calculator

Bidirectional position loss from nut and drivetrain contributions.

screws-backlash.napkin / editable
✓ checks pass

SCENARIO COMPARISON

Compare the numbers.

This source describes an analytical model. Its quantities and checks are the view.

ScenariorotationalLossmmtotalmm
0.01388890.0638889
0.01388890.0538889

All calculated quantities are listed with the inputs. Switch to Source to inspect the equations.

SCENARIOS / CALCULATED VALUESSAME SOURCE

Change an input to see the consequences.

position loss budget0.06 mm✓ passes

BASELINE INPUTS

CALCULATED

rotationalLoss0.013889 mm
total0.063889 mm

Edits change the baseline source.

Calculated from your source · not saved
Baseline · Baseline
position loss budget0.06 mm ✓ passes
alternative · alternative
position loss budget0.05 mm ✓ passes

Illustrative first-order example. Checks are editable requirements, not design standards. The broader topic may require additional equations, data, and validation.

Formula and units

This example uses the following equations. Input names and units match the editable source above.

rotational loss
rotationalLoss = angleLoss*lead/(2*pi) [mm]
total
total = nutLoss+rotationalLoss [mm]

Original worked example

These are the baseline values in the downloadable source. Edits above let you test your own values.

Given

nut loss
0.05 mm
angle loss
1 deg
lead
5 mm

Calculated

rotational loss
0.0138889 mm
total
0.0638889 mm

Assumptions and limits

Bidirectional position loss from nut and drivetrain contributions.

The requirement checks use the limits written in this example. Passing a check does not establish that the model covers every load, material behavior, or operating condition in a real design.

Download this .napkin example ↓

Take it further with your agent

Napkin keeps the inputs, equations, checks and assumptions together in one study. Your agent sets it up; you change the numbers.

Try with Claude ↗

codex 'Use Napkin (https://napkin.engineering/mcp, or the local Napkin plugin) to build a study: Stage backlash stack. Inputs: screw, nut and drivetrain lost motion. Outputs: linear deadband; direction-change error. Model scope: Screw kinematics with efficiency and load assumptions. Read napkin_capabilities and the current snapshot. Ask me for the values that matter, label assumptions with units, author .napkin source, validate it and apply it with napkin_source using the current revision, then open the study. Add checks for the limits I supply. Keep unsupported analyses explicit.'

Claude needs the Napkin connector; Codex needs the Napkin plugin. Set up your agent ↗

The broader study

The topic brief below describes the broader scope. The worked example above states the particular calculation it implements.

  • Inputs: screw, nut and drivetrain lost motion
  • Outputs: linear deadband, direction-change error
  • Modes: calculate, compare, sweep
  • Drawing: Linear-stage animation

EXECUTABLE WORKED EXAMPLE · FIRST-ORDER MODEL · CHECK THE SCOPE & ASSUMPTIONS

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