---
title: "Slider-Crank Workshop Interactive Lab | Sandbox Physics"
description: "The crank turns evenly. The slider does not. Why does uniform rotation produce uneven strokes?"
canonical_url: "https://sandboxphysics.com/labs/slider-crank/"
language: "en"
page_type: "lab"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/labs/slider-crank/"
last_modified: "2026-10-19"
---

Mechanism design · Rotary to reciprocating

# Slider-Crank Workshop

Drive a guided piston with a crank and connecting rod. Change the rod length and guide offset, compare unequal strokes in time, and see why piston force produces no crank torque at dead center.

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

Right-hand slider assembly, rigid rod and ideal guide. Exact geometry and quasistatic constant signed slider force. No gas cycle, pressure, flywheel dynamics, bearing loads or combustion model.

Physics tutorial

## Uniform rotation, uneven strokes

**Background** Rigid links impose geometric constraints before any force calculation.

**Why it matters** Watch the same solved joint positions drive the 3D apparatus, tracer and quantitative views.

Start with the essentials

- **Focus question**: Why does the slider pause at an end while the crank keeps turning?
- **One-sentence intuition**: The connecting-rod constraint makes slider displacement nonlinear in input angle. A finite slider force cannot back-drive the crank at dead center.

### Core mathematical model

#### Right-hand slider assembly

$$
x=a\cos\theta+\sqrt{b^2-(e-a\sin\theta)^2}
$$

The square root must be real. A zero root is a singular vertical connecting rod, not a fabricated clipped position.

#### Velocity and acceleration

$$
\dot x=x'(\theta)\dot\theta,\qquad\ddot x=x''(\theta)\dot\theta^2
$$

Input angular speed is constant during playback. The displayed acceleration is a kinematic result, not a computed force.

#### Signed virtual power

$$
\tau_{\rm in}=-F_x x'(\theta),\qquad\tau_{\rm in}\dot\theta+F_x\dot x=0
$$

At a regular dead center the displacement derivative and required torque vanish. The sign of a constant external force does not reverse automatically.

### Common difficulties

#### Zero is not undefined

**Typical misconception** Every stationary output is a singular solution.

**Better mental model** At an ordinary output reversal the output velocity is zero and the solution can remain regular. At a closure singularity the differential equations cannot uniquely determine the motion.

#### Prescribed motion

**Typical misconception** The animation proves this motor can drive the real mechanism.

**Better mental model** Input speed is prescribed. Link inertia, friction, compliance and collision dynamics are omitted; power balance is quasistatic.

### Run the experiment

1. 01

   #### Turn it

   Play, then pause and drag the gold crank pin in the plan view.

   **What to observe:** The 3D links and all plots share the same input angle.

2. 02

   #### Change a length

   Compare Inline guide, Short connecting rod and Offset guide.

   **What to observe:** A shorter rod changes the speed profile; an offset changes the angular duration of each stroke.

3. 03

   #### Inspect the limiting pose

   Select Dead center and inspect input torque. Then export the full sweep.

   **What to observe:** Missing and singular values remain distinct from valid zero values.

Physical conclusion

Geometry sets the motion and its limits. Quasistatic power transfer does not establish dynamic performance.

Theory & apparatus: [Carnegie Mellon · Planar Linkages](https://www.cs.cmu.edu/~rapidproto/mechanisms/chpt5.html) · [Universidad de Almería · Four-bar mechanisms](https://ingmec.ual.es/tmm/L01_03a_four_bars.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)