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CALCULATORS / CAMS AND INTERMITTENT MOTION

Cam displacement, velocity and acceleration calculator

Simple harmonic rise at a specified normalized phase.

cams-motion-profile.napkin / editable
✓ checks pass

SCENARIO COMPARISON

Compare the numbers.

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

Scenariopositionmmvelocitymm/saccelerationmm/s^2
1062.83192.41736e-14
850.26551.93388e-14

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.

phase within rise0.50 ✓ passes
phase upper bound0.50 ✓ passes

BASELINE INPUTS

CALCULATED

position10 mm
velocity62.832 mm/s
acceleration2.4174e-14 mm/s^2

Edits change the baseline source.

Calculated from your source · not saved
Baseline · Baseline
phase within rise0.50 ✓ passes
phase upper bound0.50 ✓ passes
alternative · alternative
phase within rise0.50 ✓ passes
phase upper bound0.50 ✓ 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.

position
position = lift*(1-cos(pi*phase))/2 [mm]
velocity
velocity = lift*pi*sin(pi*phase)/(2*riseTime) [mm/s]
acceleration
acceleration = lift*pi^2*cos(pi*phase)/(2*riseTime^2) [mm/s^2]

Original worked example

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

Given

lift
20 mm
rise time
0.5 s
phase
0.5

Calculated

position
10 mm
velocity
62.8319 mm/s
acceleration
2.41736e-14 mm/s^2

Assumptions and limits

Simple harmonic rise at a specified normalized 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: Cam displacement, velocity and acceleration. Inputs: rise; dwell; return; cam speed; selected motion law. Outputs: position; velocity; acceleration; jerk plots. Model scope: Specified cam law, follower type and motion constraints. 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: rise, dwell, return, cam speed, selected motion law
  • Outputs: position, velocity, acceleration, jerk plots
  • Modes: calculate, compare, sweep
  • Drawing: Cam and follower animation

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

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