Scotch yoke mechanism movement equation

AI Thread Summary
The discussion focuses on the Scotch yoke mechanism and its movement equations, specifically the relationship between the parameters R0, R, and the slider's horizontal distance X. It is clarified that R0 does not influence the stroke distance, which is solely determined by R, with the slider moving from -R to +R. The equation Δx = R sin θ is provided to calculate slider displacement based on the crank angle. Additionally, adjusting the length X does not affect the stroke but must be designed to avoid interference with the rotating disc. Overall, the mechanical advantage increases as R and stroke decrease, emphasizing the importance of proper design for load support.
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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.
scotchYolk.jpg
 
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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)
 
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.
 
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