Robot static stability calculator

Static support-edge tip margin with horizontal acceleration.

robotics-robot-stability.napkin / editable

SCENARIO COMPARISON

Compare the numbers.

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

Scenario	effectiveOffsetm	marginm
	0.0611621	0.138838
	0.0611621	0.0988379

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.

no tipping screen0.14 m✓ passes

BASELINE INPUTS

halfBase0.2 mcenterHeight0.3 macceleration2 m/s^2gravity9.81 m/s^2

CALCULATED

effectiveOffset0.061162 m

margin0.13884 m

Edits change the baseline source.

THE SOURCE

Edits below update the same model.

# Robot static stability
# Scope: Static support-edge tip margin with horizontal acceleration.
# Status: illustrative worked example; engineering review pending.
# Inputs are example values. Checks are editable example requirements, not standards.

halfBase = 0.2 m
centerHeight = 0.3 m
acceleration = 2 m/s^2
gravity = 9.81 m/s^2

effectiveOffset := centerHeight*acceleration/gravity [m]
margin := halfBase-effectiveOffset [m]

check no tipping screen: margin > 0 m

scenario alternative: halfBase = 0.16 m

Calculated from your source · not saved

Baseline · Baseline

no tipping screen0.14 m ✓ passes

alternative · alternative

no tipping screen0.10 m ✓ 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.

effective offset: effectiveOffset = centerHeight*acceleration/gravity [m]
margin: margin = halfBase-effectiveOffset [m]

Original worked example

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

Given

half base: 0.2 m
center height: 0.3 m
acceleration: 2 m/s^2
gravity: 9.81 m/s^2

Calculated

effective offset: 0.0611621 m
margin: 0.138838 m

Assumptions and limits

Static support-edge tip margin with horizontal acceleration.

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: Robot static stability. Inputs: mass distribution; support polygon; payload pose. Outputs: tipping margin; allowable acceleration. Model scope: Rigid links with explicit joints, loads and coordinate frames. 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: mass distribution, support polygon, payload pose
Outputs: tipping margin, allowable acceleration
Modes: calculate, compare, sweep
Drawing: Robot workspace and trajectory

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