Rubik's Brain Racker/Delta Ball
The Rubik's Brain Racker was also known as the Delta Ball. It is a moving piece puzzle. The metal ring at the top of the puzzle is attached to one of the triangular pieces - it can be twisted and the red number 1 removed. There are a series of different goals to be achieved by moving the pieces around. The different goals (referred to as levels) involve different arrangements of the coloured triangles.
Like most moving piece puzzles, you can solve the different situations fairly easily just by concentrating on what you are doing. The puzzle seems like a nice idea, particularly the removable/locking piece. It isn't a twisty puzzle though and seems to have been produced with the mass market rather than the specialist puzzle market in mind.
The usual puzzle shops don't seem to stock these items as new and they may not be produced in significant numbers any more. There are plenty around on ebay though if you are really taken by the puzzle. You could, of course, look into something similar but more challenging like the Impossiball from Meffert's which can be optionally used as a sliding piece puzzle.