I need to bend one circular iron pipe with 4 cm diameter and 2 mm thickness as a guide rail for an electric stair lifter similar to this picture (the spiral bending part of stair):
How could I bend the metal pipe as a continuous rail guide for the stair lifter device and a normal continuous stair? I tried ordinary bending devices like:
I have made one easy bending multilayer pipe (which I used for house thermal piping "The PEX-AL-PEX pipes") as a pattern for guiding the bending process, but we could not make correct bending diameters and the metal pipe does not fit as a continuous stair. I also tried changing its form from a circular to elliptical cross-section. What mathematical equations must I consider for bending it (what force vectors for 30 cm diameter with 40 cm height?) and how I could make it practical?
I tried to bend my failed sample's metallic pipe with heat and hand pressure to make it fit to the pattern but finally its circular cross-section changed with a very hard process to make an ugly continues spiral sample stair as a guide rail!
Is there a way of welding the pipe so the circular cross-section doesn't change or some kind of professional pipe bending machine used for this application? I have no access to CNC machines or anything similar to this: