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Reverse SPIRAL parametric equations

Question asked by Ivan Furfaro on Jul 29, 2020



I'm having trouble understanding which are the equations used in the Solidworks function "Helix/spiral" in order to generate a "reverse direction" SPIRAL given only the 4 inputs that Solidworks uses:


1) outer radius (it's imposed when creating a circle in the sketch)

2) pitch

3) revolutions

4) start angle


I need to implement the same equations of my Solidworks design in a firmware with parametric equations (x,y), by giving these 3 inputs to build a reverse spiral (so that builds the spiral from the outside to the inside as Solidworks does).



I have already tried to implement classics parametric equations in my firmware (I can do the same in solidworks with the "equation driven curve"):


x(t) = (Ro-Ri)*/(pi/2)*cos(N*t + fi);

y(t) = (Ro-Ri)*/(pi/2)*sin(N*t + fi);


where Ro is the outer radius, Ri is the inner radius, N is the revolutions, fi is the initial angle...But these equations build a classic spiral from the inside to the outside (the initial angle fi rotates the spiral in a controlled way, but it's the angle at the center of the spiral, while I want to impose the angle of the point on the outer radius, exactly how Solidworks does). Plus, I would need to know other parameters not required by the "Helix/spiral" Solidworks function, so I think I am complicating my life... 


Can someone please help to understand how to implement the right parametric equations for a reverse spiral?


Thank you very much