Please, how can I connect these 3 rings as shown in the picture I have attached.
I have 3 rings that I want to put together. I need the rings to move freely but not out of their boundaries.
I don't think that is possible with Solidworks. You could perhaps fake it to a certain degree with angle and/or distance 'limit mates', but fully free moving parts that respect each others boundaries, I've never witnessed anything like that being done in SW.
In assembly can be done. create the ring or rings if are different diameter or thickness and then create planes and drawings in assembly. Mate using that drawings and planes and do a motion study. Actually is not very difficult you need only to know what constrain do you want to have your assembly. good luck
I'm wondering if by "moving freely" you mean moving three parts in an assembly? In a single part to get the stack of rings, you can use Insert>Features>Body Move/Copy three time. Once to triplicate + rotate along Z, and then twice individually on the middle and top bodies along X. In an assembly you should be able to arrange rings into that position also. If your just trying to move them without crossing boundaries, you can enable the 'stop on collision' box during a move.
Were you also thinking of animating or simulating the three rings?