How to make a child object follow a target within the constrain of parent object

You can do this a bunch of ways but I would first start by normalising your range of movement between a consistent range probably the most useful would. be 0.0 to 1.0.

That way you have a normalised range of input of your target which goes between 0-1 and you have a normalised range of input of your child objects that go from 0-1.

Explanation

The easiest way to normalise is just to use division and would work like this currentPosition/maxPosition=normalisedPosition

For example:

If our child objects total range of motion is 12 units and our child's position was only 3 units across.

It would mean we are essentially a quarter of the distance across its entire range of movement. So the normalised value would be a quarter. Or: 3 / 12 = 0.25

We could then use that value i.e. 0.25 with any other range.

So, say our targets total range is much larger at 450.

Multiplying our child's normalised position value of 0.25 with the targets total range of 480 gives us 120 i.e 480 * 0.25 = 120.

Meaning our absolute target position for the relative normalised child position would be 120.

Does that make sense and is that what you were trying to achieve?

Clamping

After you have done that you could also clamp the normalised values between 0.0 and 1.0 to stop them moving outside of their bounds.

Reading

https://en.wikipedia.org/wiki/Normalization_(statistics)

Yes that makes sense. But I'm not too good at maths. Can you elaborate it a bit?