# Scotch yoke mechanism movement equation

• Lluis
In summary, the Scotch yoke mechanism has a slider that moves from -R to +R (Total: 2R) while the size of R0 does not affect the stroke distance. Changing the length X also does not affect the stroke, which is determined by R and the crank angle. However, modifying R and the stroke can affect the force exerted by the slider. Enough X distance is also needed to accommodate the slider guides without interfering with the rotating disc.
Lluis
TL;DR Summary
How to change Scotch yoke mechanism parameters in order to calculate slider movement
Hi,

I am not an engineer and sorry in advance if I am not correct with the terms. I design out of curiosity this Scotch yoke mechanism (left image) based on a scheme (right image).

I looked for some equations to find if there is a relation between the R0 , R to R0 distance (which changes during rotation) and the X distance. If for example, I will change the parameters R0 , R to R0 distance and the slider horizontal part/s length/s how it will effect the X distance movement?

Any idea how to calculate it?

Thanks a lot.

Assuming the slider is at 0 in the left image, the slider will move from -R to +R (Total: 2R).

The size R0 doesn't affect the stroke distance; it only needs to be large enough to carry the force (depends on the material strength). It's like selecting a bearing for a wheel or a connecting rod: The bearing size doesn't affect the kinematics of the wheel or the connecting rod, it just needs to be large enough to support the load.

Changing the length X doesn't affect the stroke either.
$$\Delta x = R\sin \theta$$
##\Delta x##: Slider displacement
##\theta##: Crank angle (0° when slider is centered as in left image)

Lnewqban
Welcome!
As explained above, the slider stroke is only modified by R.
As R and the stroke get smaller, the pushing/pulling force of the slider gets bigger (greater mechanical advantage), and vice-verse.

Consider that you need enough X distance to accommodate the guides of the slider without interfering with the rotating disc.

## 1. What is the Scotch yoke mechanism?

The Scotch yoke mechanism is a type of reciprocating motion mechanism that converts rotational motion into linear motion. It consists of a sliding yoke that is connected to a rotating crank through a slot. As the crank rotates, the yoke moves back and forth in a straight line.

## 2. How does the Scotch yoke mechanism work?

The Scotch yoke mechanism works by converting the rotary motion of the crank into linear motion of the yoke. As the crank rotates, the yoke slides back and forth in a straight line. This movement can be used to power various machines or devices.

## 3. What is the equation for the movement of the Scotch yoke mechanism?

The equation for the movement of the Scotch yoke mechanism is given by x = r*sin(theta) + (r^2*sin(2*theta))/(2*L), where x is the displacement of the yoke, r is the radius of the crank, theta is the angle of rotation, and L is the length of the slot.

## 4. What are the advantages of using a Scotch yoke mechanism?

One advantage of using a Scotch yoke mechanism is its simplicity and low cost. It also has a high mechanical efficiency and can produce a smooth and consistent linear motion. Additionally, it can handle heavy loads and is relatively easy to maintain.

## 5. What are some common applications of the Scotch yoke mechanism?

The Scotch yoke mechanism is commonly used in various types of engines, such as steam engines and internal combustion engines. It is also used in pumps, presses, and other industrial machinery. In addition, it can be found in household appliances, such as washing machines and air compressors.

• Mechanical Engineering
Replies
17
Views
3K
• Mechanical Engineering
Replies
1
Views
6K
• Mechanical Engineering
Replies
5
Views
987
• Mechanical Engineering
Replies
4
Views
649
• Special and General Relativity
Replies
11
Views
168
• Mechanical Engineering
Replies
3
Views
1K
• Mechanical Engineering
Replies
5
Views
1K
• Mechanical Engineering
Replies
3
Views
1K
• Mechanical Engineering
Replies
4
Views
967
• Mechanical Engineering
Replies
1
Views
3K