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Universal-joint speed variation calculator

Single Hooke joint instantaneous velocity ratio at one phase.

linkages-universal-joint.napkin / editable
✓ checks pass

SCENARIO COMPARISON

Compare the numbers.

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

ScenarioratiooutputSpeedrpm
0.999399599.64
0.999756599.854

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.

velocity ratio budget1.00 ✓ passes

BASELINE INPUTS

CALCULATED

ratio0.9994
outputSpeed599.64 rpm

Edits change the baseline source.

Calculated from your source · not saved
Baseline · Baseline
velocity ratio budget1.00 ✓ passes
alternative · alternative
velocity ratio budget1.00 ✓ 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.

ratio
ratio = cos(angle)/(1-sin(angle)^2*sin(phase)^2)
output speed
outputSpeed = ratio*inputSpeed [rpm]

Original worked example

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

Given

angle
15 deg
phase
45 deg
input speed
600 rpm

Calculated

ratio
0.999399
output speed
599.64 rpm

Assumptions and limits

Single Hooke joint instantaneous velocity ratio at one phase.

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: Universal-joint speed variation. Inputs: joint angle; input speed and phase. Outputs: instantaneous output speed; ripple. 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 angle, input speed and phase
  • Outputs: instantaneous output speed, ripple
  • Modes: calculate, compare, sweep
  • Drawing: Interactive linkage

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

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