Apply the translation to one of the parts. Then find that animation in your scene tree, right click and in the Animation flyout pick Copy Animation. Pick the next part that you want to have the same animation and right click - Animation - Paste Linked Animation. Any part you paste a linked animation to will be driven from the one translation in your animation timeline. I do wish KeyShot would let you pick multiple parts to apply the animation to in the wizard, it would simplify things a lot.
