# Crank\-Slider Mechanism Explainer

How a crank\-slider turns a spinning wheel into straight back\-and\-forth motion, with its stopping points at the dead centres explained\. Turn the crank yourself and follow the slider's speed\.

By brave\-comet\-48fa366f

Topic: Machines

[Open the interactive Jig](https://ask.jig.com/j/6AOT61Dl9TlR)

## Transcript

### 1. Round and round, back and forth

This little machine turns a spinning wheel into a straight push and pull\. It is called a crank\-slider\. Its trick hides inside car engines, pumps and sewing machines\.

Drag anywhere to turn the model and look around it\.

### 2. The crank goes in a circle

The crank is an arm that turns around a shaft\. Here it is the big wheel, with a pin fixed near its edge\. Watch the glowing ring: the pin travels around it, again and again\.

### 3. The connecting rod rocks

The connecting rod joins the crank pin to the slider\. One end rides around the circle and the other end stays on a straight line\. So the rod rocks up and down as it pushes and pulls\.

On this model the rod is 3\.5 times longer than the crank arm, like in many car engines\. It never tilts more than about 17 degrees\.

### 4. The slider only goes straight

The slider is trapped between two rails, so it can only move back and forth\. The distance between its two ends is the stroke\. The stroke is always twice the length of the crank arm\.

A typical car engine has a stroke of about 95 mm and a connecting rod about 152 mm long\.

### 5. Dead centres: the stopping points

Twice in every turn, the crank and the rod line up straight\. At that instant the slider stops before it changes direction\. These are the dead centres\. A heavy wheel keeps turning and carries the machine past them\.

### 6. Turn it yourself

Move the slider below to turn the crank by hand\. A small turn moves the slider a lot in the middle of its path, but hardly at all near the ends\. Find the two dead centres, where the slider stands still\.

### 7. Rising and falling

The chalkboard draws where the slider is as the crank turns\. Green means the slider moves right, orange means it moves back\. Where the line turns over, the slider is at a dead centre and its speed is zero\.

Mathematicians call a rising part increasing and a falling part decreasing\.

### 8. Solve: where does f go up and down?

Your problem asks where f\(x\) = \-x⁵/5 \- 17x⁴/4 \- 70x³/3 \+ 6 increases and decreases\. Look at its slope, like the slider's speed: f'\(x\) = \-x²\(x \+ 7\)\(x \+ 10\)\. It is zero at \-10, \-7 and 0\.

Answer: f decreases on \(\-∞, \-10\), increases on \(\-10, \-7\) and decreases on \(\-7, ∞\)\. At x = 0 it only pauses for an instant\.

### 9. A turning point everywhere

Rising, stopping and falling happen in every turn of this machine\. Engines use it to turn pushes into spinning wheels\. Pumps and sewing machines use it the other way round, turning spinning into pushes\.