---
title: "Cam Motion Designer Interactive Lab | Sandbox Physics"
description: "A shaped edge writes a motion program. Can a follower stop while the cam keeps turning?"
canonical_url: "https://sandboxphysics.com/labs/cam-motion-designer/"
language: "en"
page_type: "lab"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/labs/cam-motion-designer/"
last_modified: "2026-10-22"
---

Machine kinematics · Roller envelope

# Cam Motion Designer

Turn a real cam profile beneath a guided roller. Design rise, dwell and return, compare cycloidal and quintic motion, and see why a shorter rise makes acceleration and pressure angle grow.

> Interactive simulation: open this page in a web browser to change the parameters and run the model.

Ideal planar cam and translating roller, with externally maintained contact and prescribed constant shaft speed. No spring sizing, contact force, friction, roller spin, elastic deformation or separation dynamics.

Physics tutorial

## Motion is a geometric program

**Background** A rotating shaft can create motion that is very different from uniform rotation.

**Why it matters** Connect each visible part with the output curve it creates.

Start with the essentials

- **Focus question**: Can a follower stop while the cam keeps turning?
- **One-sentence intuition**: A circular dwell segment keeps the follower still. The remaining profile encodes a chosen displacement law.

### Core mathematical model

#### Cycloidal rise

$$
s=h\left(u-\frac{\sin(2\pi u)}{2\pi}\right),\quad u=\theta/\beta
$$

This applies over the rise interval; the return reverses it and the dwells have fixed displacement.

#### Quintic rise

$$
s=h(10u^3-15u^4+6u^5)
$$

Both laws join a dwell with zero velocity and acceleration; jerk need not be continuous.

#### Roller-center pitch and true edge

$$
\rho=R_b+a+s,\quad\mathbf p=(\rho\sin\theta,\rho\cos\theta),\quad\mathbf c=\mathbf p-a\mathbf n
$$

The cam frame rotates opposite to the input during construction. The normal is outward from the pitch curve; rotating the edge forward places the contact against the roller.

#### Pressure angle and offset regularity

$$
\tan\varphi=-\frac{s'}\rho,\quad\kappa=\frac{\rho^2+2(s')^2-\rho s''}{(\rho^2+(s')^2)^{3/2}},\quad m=1-a\kappa
$$

Primes differentiate with respect to shaft radians. The minimum margin readout scans one turn; independent geometric tests check contact and offset regularity across control bounds.

### Common difficulties

#### A kinematic model is not a force model

**Typical misconception** Smooth motion proves the real drive can run at the selected rate.

**Better mental model** Contact loads, inertia, friction, elastic deformation and drive design need separate models. Parts have schematic thicknesses.

#### The roller center is not the cam edge

**Typical misconception** The pitch curve can be manufactured directly as the roller cam.

**Better mental model** The material edge must be offset inward along the pitch normal by the roller radius. A radial subtraction is generally wrong.

### Run the experiment

1. 01

   #### Run one turn

   Choose the motion-plane view and run or drag the coral crank.

   **What to observe:** The cam keeps turning through each dwell while lift and velocity stay fixed.

2. 02

   #### Make the rise shorter

   Keep the lift, shorten the rise angle, then enlarge the base circle.

   **What to observe:** A short rise magnifies speed and acceleration. A larger base reduces pressure angle without changing the lift program.

3. 03

   #### Compare motion laws

   Compare cycloidal and quintic presets at the same dimensions, then double shaft rate.

   **What to observe:** Both laws reach the same lift and dwell. Doubling shaft rate doubles velocity and quadruples acceleration.

Physical conclusion

An imposed input rate turns geometric derivatives into velocity and acceleration.

Geometry & apparatus: [CMU · Cams](https://www.cs.cmu.edu/~rapidproto/mechanisms/chpt6.html) · [NITK Virtual Labs · Crank and Slotted Mechanism](https://mm2-nitk.vlabs.ac.in/exp/crank-slotted-mechanism/theory.html)

Motion & dynamics · Starter path

## From a falling ball to an orbit

Measure gravity, split motion into components, add contact forces and collisions, then carry the same laws into orbit.

[Start here → **Free Fall & Measuring Gravity** Capture a few drops and fit the camera positions to estimate gravitational acceleration. Then add air damping and watch the fit drift from the truth. Observe · 14 min](https://sandboxphysics.com/labs/free-fall/)

1. [1 Free Fall & Measuring Gravity](https://sandboxphysics.com/labs/free-fall/)
2. [2 Projectile Flight Designer](https://sandboxphysics.com/labs/projectile-flight/)
3. [3 Inclined Plane & Friction](https://sandboxphysics.com/labs/inclined-plane/)
4. [4 One-Dimensional Collision Bench](https://sandboxphysics.com/labs/collision-bench/)
5. [5 Mass–Spring Oscillator](https://sandboxphysics.com/labs/mass-spring/)
6. [6 How Orbits Take Shape](https://sandboxphysics.com/labs/orbit/)

[View the full path →](https://sandboxphysics.com/topics/mechanics/#starter-path)