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I'm designing something with a vertical linear actuator. It is a quite large actuator lifting a load. I'm anticipating sway from the actuator as it moves up and down so I'm creating a support structure. What is the best way to determine how much this sway will be? I can figure out the weight of the load and the acceleration of the actuator

Thanks for the help!

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A sketch would be helpful here, but you should have an addition linear bearing to stabilize the load and then you decouple any moment loads on the actuator. If space/design allows, you could use your actuator in tension instead of compression which would reduce/remove any buckling conditions

Regarding "sway", you should start with a free body diagram, and then apply some simple statics to get deflections and stresses.

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