Orient along a CRV maintaining same angle throughout

Hi I have what I think is a very simple problem yet I am having a little trouble with it. I want to orient objects on a curve (based off a curved surface, that is 3 dimensional and not just a flat 2D profile), that maintain the same angle throughout. For simplicity sake lets just say I want to orient diagonal lines along a curve upon which the point of contact maintains a same (X) angle in relationship to the base curve. The base curve once again is not flat but curves in all XYZ dimensions. What would be the best way to go about doing this? My hinch is that you would start by dividing the base curve and using those points to evaluate tangency and rotating a line normal to that portion (X) degrees and orienting the module along that rotated line. The only tricky parts are when testing to see the amount of rotation, the module must consistently maintain the (X) angle in relationship to the left side of the base curve, and also how to make a line rotate normal in the direction of the base curve/surface. THANKS!.