Hi,
How you work out this engineering problem will depend upon the usual
Constraints. How much do you want to spend and how much work you
want to do. If I were creating this design then I would consider a simple
screw system where each "leg" was on a screw and you adjusted the screw
to get the correct distance from the centre. Think like a 3D Printer moves
the print head around, screws and cable drives. In this instance I would
use a small motor screw drive to turn the screws and simply sync them
up until they all worked at the same time.
Here is your issue. Cheaper motor drives may not necessarily all drive at the
same speed. One motor may be say a 1/4 turn slower per minute than another
drive unit. This is not so much of a problem with small threads and small
distances but the more precision you need the tighter the threads and the
more control you will need on your motors. This is one of the reasons that a
Stepper motor is much more expensive than a simpler system. With a stepper
motor you can control exactly how many steps the motor will move. With fine
thread screws you can have very precise accuracy.
I would have a look for basic robot or 3D Printer designs out there and see
what affordable Off The Shelf hardware they use and go from there. Also
remember that you are firing a Rocket so heat shielding will be important
unless you want to rewire and change the system every time you launch.
I would also have a look at the Stiffness of the rail assembly you are using.
It looks a little flimsy to me and may need one or two extra reinforcements.
If a Rocket vibrated enough it may be possible to shake out of the clamps
and get jammed within the rails. This would look fairly impressive until just
after everything goes Boom and you realise that Rocketry is an expensive
hobby. Look at Uncle Elon and how much he spends on his Hobby.
I would probably use a similar design but to reduce vibrations I would use
four triangle sets, at least for the bottom section and three if you joined a
second section to that. You shouldn't need more than that unless it is a
really BIG Rocket. In that case you may consider a Free Standing launch
with drop away stabilisers.
Cheers
Andrew