Two-link planar arm reach envelope calculator

Two-link planar arm radial reach envelope; no collision checking.

linkages-workspace.napkin / editable

SCENARIO COMPARISON

Compare the numbers.

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

Scenario	outerRadiusmm	innerRadiusmm
	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 in annulus250.00 mm✓ passes

target outer reach250.00 mm✓ passes

BASELINE INPUTS

linkA200 mmlinkB150 mmtargetRadius250 mm

CALCULATED

outerRadius350 mm

innerRadius50 mm

Edits change the baseline source.

THE SOURCE

Edits below update the same model.

# Mechanism travel envelope
# Scope: Two-link planar arm radial reach envelope; no collision checking.
# Status: illustrative worked example; engineering review pending.
# Inputs are example values. Checks are editable example requirements, not standards.

linkA = 200 mm
linkB = 150 mm
targetRadius = 250 mm

outerRadius := linkA+linkB [mm]
innerRadius := abs(linkA-linkB) [mm]

check target in annulus: targetRadius >= innerRadius
check target outer reach: targetRadius <= outerRadius

scenario alternative: linkA = 160 mm

Calculated from your source · not saved

Baseline · Baseline

target in annulus250.00 mm ✓ passes

target outer reach250.00 mm ✓ passes

alternative · alternative

target in annulus250.00 mm ✓ passes

target outer 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.

outer radius: outerRadius = linkA+linkB [mm]
inner radius: innerRadius = 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 radius: 250 mm

Calculated

outer radius: 350 mm
inner radius: 50 mm

Assumptions and limits

Two-link planar arm radial reach envelope; no collision checking.

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: Mechanism travel envelope. Inputs: joint limits; link geometry; reference frame. Outputs: reachable region; collision candidates. Model scope: Planar rigid-link geometry with explicit joints and branches. 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: joint limits, link geometry, reference frame
Outputs: reachable region, collision candidates
Modes: calculate, compare, sweep
Drawing: Interactive linkage

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