You could try creating a 3D Sketch, convert entities (the spiral), exit the sketch, this is your path. Then try a sketch driven pattern using this 3D sketch and the red features. Problem though is I think sketch driven patterns may tend to keep the red part oriented in the same way for every instance. It does not make the red part normal to the spiral path for each instance. I don't find myself in this type of situation hardly ever, so my experience isn't that much. This may work or may hold you over until someone else with more information comes along.
Shouldn't be an issue if you have 2015 - in the mate dialog box go to advanced mates and select the spiral sketch as the pattern sketch
Is every red piece the same orientation on those two top pieces as it goes around curve. It doesn't look so and that's the tricky part.
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