Distort UV to curve around a pivot point?

So I have a mechanic in my project that allows the player to build conveyor belts, and I have to say, they’re coming along awesome so far!

But now I’ve come to setting up the corner pieces, which also work awesome, but I’m trying to alter the material I am using for the belts to curve along with the turn.

Does anyone know of any way I can bend a material around a pivot point?

Good day.
Instead of relying on material math to do the turn, I suggest you unwrap conveyor corner piece keeping UVs for moving part straight. That way you do not need to worry about turns. Belt will always flow following the turn, provided your mesh has enough vertices.

Sketchup is not bad for prototyping some geometry but it sucks as a tool for creating final models. You probably need to revise your workflow. You can use some free applications like blender for retopology and unwrapping. My personal pipeline is sketchup → test in ue4 with complex collision → retopo in 3dsmax → unwrapping lowpoly → creating highpoly in zbrush → baking maps and texturing in substance.
So dont try to find an easy way to make a good product ;-D

I have never touched sketchup, yet I have no doubt that it has sufficient functionality for what was laid out above. As long as it allows moving vertices and assigning UV coordinates to them, it is already enough.

It is not UV unwrap that you need to bend. It is the model. Just take straight conveyor piece and bend it 90 degrees, leaving UVs untouched.

There are probably other ways, but they likely to be inferior in all respects.
Flow maps, for example.

I had a feeling someone would suggest that! The reason why actually I’m resorting to material math to make the turn for me is because we are using sketchup as our 3d-modelling program, and I don’t believe that sketchup supports the curving of UV maps.