# How to convert 7.62cm linear motion to 150-180° rotary motion

I need to convert 7.62cm/3in linear motion from an actuator to 150-180° (150 is minimum) rotary motion. I am aware of the existence of gears, but would probe here to see if there is some simpler method. I could use rods mounted in some way. It has to be compact and rugged, however. I'd also be interested in formulas for this type of conversion. Thanks!

Edit: I found this contraption for microlinear precision, whilst googling for scotch yoke. Is this a scotch yoke? If not, what is it? I can probably awfulhack one of these with a file, some aluminium rods and strips. But it would be prettier if I bought one.

• You won't need gears as there are commonly used methods often used in backhoes and cherry picker trucks to move the arms almost 180 degrees with a single hydraulic piston. I have not tried the drawing tools here yet so I will leave it to others to provide more detail. But if you search for photos of backhoes or power line maintenance trucks you will see a type of linkage that does what you need. Commented Jun 17, 2017 at 16:01
• @Entrepreneur Well, this is a linear actuator. I suppose the same principle applies. Can you provide a link to what you mention? Commented Jun 17, 2017 at 17:29
• Another simple way to convert linear motion into rotary motion is with a scotch yoke, look up the Bourke Engine to see how these operate. Commented Jun 17, 2017 at 19:38
• it is essentially a rack and pinion with different gear shape than the typcal involute. In this case a cycloid function, which is the second common, but considerablybrarer gear shape. Commented Jun 18, 2017 at 3:03
• This youtube video is crude but you can definitely see the 3 moving parts and how they interact. The red line is the hydraulic cylinder. The white line is a link that connects the 2 green arms. youtube.com/watch?v=tb4jiscwhvw Commented Jun 18, 2017 at 3:21

As suggested a rack and pinion will provide a linear transfer function and avoids complex linkages. A variant on the rack and pinion is to replace the straight rack teeth with a taught cable and the pinion teeth with a pulley. This mechanism is sometimes referred to as a capstan and bowstring.

https://en.wikipedia.org/wiki/Capstan_and_Bowstring

If you need a guarantee against slippage then the cable can be wrapped multiple times and attached to the pulley at the half-way point.

There are commonly used methods used in backhoes and cherry picker trucks to move the arms about 180 degrees with a single hydraulic piston. If you search for photos of backhoes or power line maintenance trucks you may see a type of linkage.

Here is a photo

This video is crude but you can definitely see the 3 moving parts and how they interact. The red line is the hydraulic cylinder. The white line is a link that connects the 2 green arms.