First, you need a stable stand. If the stand moves you already lost. AP's are sold when pinned an on a solid base.

Ways to help the base be solid:

Sheet of 3/4" ply or OSB for the base to sit on.
Must be level!
Shim the legs to level the base.
Use the pins that come with your AP cages.
Sometimes you have to look at the floor joist. You may have to block them or support them.

Most important the base support the entire AP cage. You shouldn't have any overhang. Again ply or OSB can be use to prevent this.

This coming from the guy that had to use screw jacks to stop the snake room from bouncing (125 year old farm house).