Robot joint torque calculator

Static horizontal robot joint with point payload, ignoring link mass

robotics-joint-torque.napkin / editable

SCENARIO COMPARISON

Compare the numbers.

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

Scenario	torqueN*m
	7.848
	11.772

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.

actuator capacity7.85 N*m✓ passes

BASELINE INPUTS

payload2 kg0.55reach400 mm200800gravity9.81 m/s^2

CALCULATED

torque7.848 N*m

Edits change the baseline source.

THE SOURCE

Edits below update the same model.

# Static horizontal robot joint with point payload, ignoring link mass
payload = 2 kg in 0.5..5
reach = 400 mm in 200..800
gravity = 9.81 m/s^2
torque := payload * gravity * reach [N*m]
check actuator capacity: torque <= 12 N*m
scenario longer reach: reach = 600 mm

Calculated from your source · not saved

Baseline · Baseline

actuator capacity7.85 N*m ✓ passes

longer reach · longer reach

actuator capacity11.77 N*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.

torque: torque = payload * gravity * reach [N*m]

Original worked example

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

Given

payload: 2 kg
reach: 400 mm
gravity: 9.81 m/s^2

Calculated

torque: 7.848 N*m

Assumptions and limits

Static horizontal robot joint with point payload, ignoring link mass

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 joint torque. Inputs: link masses and centers; payload; pose; acceleration. Outputs: gravity torque; dynamic load estimate. 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 masses and centers, payload, pose, acceleration
Outputs: gravity torque, dynamic load estimate
Modes: calculate, compare, sweep
Drawing: Robot workspace and trajectory

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