---
title: "Crank-Shaper Quick Return Interactive Lab | Sandbox Physics"
description: "A steady motor. A slow cut. A fast return. Why does a steady motor give the ram a fast return?"
canonical_url: "https://sandboxphysics.com/labs/crank-shaper-quick-return/"
language: "en"
page_type: "lab"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/labs/crank-shaper-quick-return/"
last_modified: "2026-10-22"
---

Machine kinematics · Slotted rocker

# Crank-Shaper Quick Return

A crank pin slides in a real rocker slot and drives a horizontal ram through a connecting rod. Tune the crank radius to change the time ratio, then test which dimensions change stroke without changing timing.

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

Ideal rigid planar links, open slot and horizontal prismatic guide. Constant prescribed input rotation. The working stroke is a kinematic label; no cutting load, material removal, inertia, friction or motor dynamics.

Physics tutorial

## Equal distance, unequal time

**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**: Which dimension changes the return time without changing motor speed?
- **One-sentence intuition**: The rocker reaches its extremes where its slot is tangent to the crank circle. Those points divide the turn into unequal angles.

### Core mathematical model

#### Crank pin and rocker direction

$$
\mathbf A=(0,-d),\quad\mathbf P=(r\cos\theta,r\sin\theta),\quad\mathbf B=\mathbf A+L\frac{\mathbf P-\mathbf A}{|\mathbf P-\mathbf A|}
$$

The crank pin slides along the rocker slot; the rocker tip stays at fixed distance from its pivot.

#### Right-hand ram branch

$$
H=L-d,\quad Q_x=B_x+\sqrt{c^2-(H-B_y)^2},\quad Q_y=H
$$

The positive square root selects the displayed connecting-rod assembly. Output displacement is the horizontal coordinate minus the rod length.

#### Quick-return time ratio

$$
\alpha=\arcsin(r/d),\quad\frac{T_{\rm work}}{T_{\rm return}}=\frac{\pi+2\alpha}{\pi-2\alpha}
$$

For constant shaft speed the two input angle intervals set the two durations.

#### Stroke and time scaling

$$
S=2L\frac rd,\quad v=\omega\frac{dQ_x}{d\theta},\quad a=\omega^2\frac{d^2Q_x}{d\theta^2}
$$

These stroke extrema hold throughout the permitted rod-length box, where ram position is monotone in rocker angle.

### 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.

#### Constant input is not constant output

**Typical misconception** The working stroke has constant cutting speed.

**Better mental model** Both output speeds vary continuously. Quick return compares full stroke durations, not a constant speed ratio at every instant.

### Run the experiment

1. 01

   #### Run one turn

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

   **What to observe:** The same ram stroke takes different times in opposite directions.

2. 02

   #### Change the radius ratio

   Compare mild and strong quick-return presets.

   **What to observe:** A larger radius ratio creates a stronger timing asymmetry and a longer stroke.

3. 03

   #### Separate stroke from timing

   Change rocker length and connecting rod length independently.

   **What to observe:** Rocker length changes stroke; rod length changes curve shape. Neither changes the ideal time ratio.

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)