Robot arm reach calculator

Two-link radial reach envelope; no joint limits or collision model.

robotics-arm-reach.napkin / editable

SCENARIO COMPARISON

Compare the numbers.

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

Scenario	maximummm	minimummm
	350	50
	310	10

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.

target reachable250.00 mm✓ passes

target upper reach250.00 mm✓ passes

BASELINE INPUTS

linkA200 mmlinkB150 mmtarget250 mm

CALCULATED

maximum350 mm

minimum50 mm

Edits change the baseline source.

THE SOURCE

Edits below update the same model.

# Robot arm reach
# Scope: Two-link radial reach envelope; no joint limits or collision model.
# Status: illustrative worked example; engineering review pending.
# Inputs are example values. Checks are editable example requirements, not standards.

linkA = 200 mm
linkB = 150 mm
target = 250 mm

maximum := linkA+linkB [mm]
minimum := abs(linkA-linkB) [mm]

check target reachable: target >= minimum
check target upper reach: target <= maximum

scenario alternative: linkA = 160 mm

Calculated from your source · not saved

Baseline · Baseline

target reachable250.00 mm ✓ passes

target upper reach250.00 mm ✓ passes

alternative · alternative

target reachable250.00 mm ✓ passes

target upper reach250.00 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.

maximum: maximum = linkA+linkB [mm]
minimum: minimum = abs(linkA-linkB) [mm]

Original worked example

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

Given

link a: 200 mm
link b: 150 mm
target: 250 mm

Calculated

maximum: 350 mm
minimum: 50 mm

Assumptions and limits

Two-link radial reach envelope; no joint limits or collision model.

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 arm reach. Inputs: link lengths; joint limits; obstacles. Outputs: reachable workspace; excluded regions. 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: link lengths, joint limits, obstacles
Outputs: reachable workspace, excluded regions
Modes: calculate, compare, sweep
Drawing: Robot workspace and trajectory

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