Combine three curves made with equations

The only way I can think of is to develop a single equation-driven curve to build the thing. The problem I've always had with this type of thing is the tangency between the two curves doesn't match so any further geometry created using the curves will have a discontinuity.

If you're trying to model a realistic spring that can be adjusted to compress/stretch to fit a particular assembly, you really should do a search here and on YouTube to see some very helpful methodologies people have developed. It's not a simple thing to do, but once you have a robust model it's very nice for all the places you might need to use a spring. Downloaded springs from suppliers are always "dumb" geometry, lack the features needed to place them, etc.

If the three curves are tangent, you can copy them using approximate to create a single curve.

Select first curve and press Ctrl+C and Ctrl+V.

Change curve type to Approximate.

Hold Shift and select remaining curves.

Complete feature

Curves must be tangent for Approximate to work.

A datum graph may be able to control a single curve to create the curve shape you want.

Add small fillet radii at the discontinuities where the curves should "join". Once the radii are present you can create a composite curve (as previously mentioned) by selecting the three curves and the 1 or 2 radii required to get C1 continuity between them. A formed coil will have the bend radii in the actual part so the model should match the formed part more closely.

The spring shown below transitions from a helical path to a planar one at both ends. This model uses curves on each end that match the helix to deal with the discontinuity. This approach can also be used to resolve your issue but is more tedious than adding the fillets between curves.Helical coil with transition to planar ends

@KenFarley 

Thank you for your reply.

The spring will be exported and used in finite element methods. It will not be processed for any Creo assembly at all, so no real functionalities are required.

Thing is, as you can see in the attached picture, the whole curve cannot be modeled within one equation-driven curve because the z-coordinate is seperated into three functions, depending on a parameter. At the bottom and the top, a half of a circle is needed on the same z-coordinate, while between the top and the bottom a helix form is needed. To my knowledge it is not possible to use if-conditions in an equation.

@kdirth @tbraxton 

Thank you for your replies and your suggestions. I will try them out.

After all I found a workaround: It was possible to extract points along all three curves and then create one curve interpolating these points. The result was quite accurate and could be successfully exported.