How to rotate objects within a radius by controlling the motion of parent object?

There are four child objects of a parent Omega, which rotates around a particular object Theta. The distance from Theta to the child objects should not be greater than a limit, say “alpha”. The parent is controlled by the arrow keys or mouse pointer and can move in all 3 axes. Please advice on how to achieve this so that at any time, the distance from each child object to Theta remains same and not greater than “alpha”?
Hope this image would make it clear.

It hard for me see where the “real” problem is in this question. Let me throw out an idea.

  • At the center of Theta, place an empty game object for each of the “child” objects.
  • Make these empty game objects a child of Theta
  • Take the four child objects and make each one a child of one of the empty game objects.
  • Attach a simple script to each empty game object that rotates so the children will rotate around Theta.
  • Since there is a parent child relationship between all the objects, all the children object will move with Theta. As long as Alpha does not change, and assuming the four were place under the alpha limit at start, they will remain under the limit (since they move with Theta).
  • If you need to bring a child in closer in order to be under the alpha limit, you can use the ray from the empty game object to the child.