Please indicate flat 2D parameterization of coordinates after isometric development or untwisting of a standard Tangential Developable Helicoid from 3D surface: {x,y,z} = { a ( c - v s) ; a ( s + v c) ; b (u + v)}, which is ruled by generator tangents from a cylinder helix (v = 0). (c = cos(u) , s = sin(u)).
Any web references showing sketches may be given. In this case the development is known to be a flat annular ring but whose inside, outside radii, angle limits etc. are to be identified in terms of a, b, u and v. Engineers are usually more acquainted with development of cones and cylinders than perhaps the developable helicoids. TIA, Narasimham