I am modeling a screw and nut that are supposed to fit into each other
without collision and stay without collision throughout the process of
moving nut on screw  from top to end.

However, I have used approximation formula that might not be exact:

isosurface {
  function { f_helix1(x,y,z, 1, 20/3*omega1, dy, inner_r+dy+dy*2/3, 1, 1.5,
0) }
         // distance_wind, thicknessm, r, shape, 0, cross-section type
         // 20/3 is an empiric factor connecting number of windings of helix
         // per unit of length with parameter P2 of f_helix1()
         // ***********************************
         // *** WHAT IS THE EXACT VALUE???? ***
         // ***********************************
  contained_by {
     box { <-2, -l/2, -2>, <2, l/2, 2> }
  }
  max_gradient 1.5
}

Later I use this screw from macro:

    object {
       Screw_Approx_Type_01(r_rod, l_rod, omega1, 60+tt)
       rotate y*(-l/l_rod*omega1*360)
       texture {
          //Silver_Texture
          T_Chrome_4D
       }
       translate <0, 0.27-l, 0.0>
    }

..... but it is not exact fit - after 5 turns of screw inside nut, there
seems
to be like if in 25 turns the chrome would meld with chrome, if I am making
myself clear.

So, I'd need a more correct value of 20/3 factor multiplying omega1, but it
is very hard to determine experimentally, if it is linear at all?

Many thanks in forward,
Marvin

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