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I have a 3DOF platform that I'm trying to make more stable. It's difficult to explain in words what the issue is so I've added a GIF below.

enter image description here

Any ideas of how I can get rid of this wobble? The DOF arm tends to cave inwards. I know it's being caused by the very small gap between the screw and the channel but is there any way to prevent this? Since the servo's I'm using don't have a dual shaft going through and through I can't modify the servo arm to be a inverted-U attached on both ends of the servo.

shekit
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If I understand your design correctly you extend the existing play in the mechanism.

If you can’t eliminate the play then you can try to minimise it. See the locking pliers (https://en.wikipedia.org/wiki/Locking_pliers) as an example to reduce the play. The disadvantage of this principe is the distance decrease.