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Variable pitch helical coil with smooth blend.

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CJ.10E-10mm
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Variable pitch helical coil with smooth blend.

I am trying to devise a means of producing a helical coil with a smooth blend in the path between different pitches. I have looked at previous resolutions on this forum but sadly they produce what I would describe as a hinged connection between different pitch helical coils. Please see screenshot attached.

 

So can anyone help me please create a variable pitched helical coil arrangement that has a true blended path and not a 'hinged' path?

 

I have tried using the equation curve but do not have the expertise to write the necessary equation.

 

Any assistance would be most appreciated.

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