I am trying to describe a space curve that is constructed using piecewise planar circular arcs and a straight line segment. Basically I have three circular arcs, all of same curvature but in three different planes connected together with continuity of tangents and then a straight line segment connecting two open ends of the circular arcs again in a $C^1$ continuous fashion. It is apparent that the torsion, if it can be defined at all, is zero almost everywhere apart from on a finite set of four points where there is a transition from circular arc in one plane to that in another and finally from circular arcs to straight line segments. 
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Is it possible to define a frame for this curve and also describe the torsion at the four points? The curvature is constant on the circular arcs and zero on the line segment. How would one go about trying to describe this curve otherwise? Are there curves of this type that have ben studied elsewhere?