The machine needs to consist of five sections, in reverse order:

1. a number of bins to collect the sorted pieces
2. a 'diverter' to direct each part into the correct bin
3. a sensor and controller which can determine the correct bin (by piece colour) and control the diverter
4. a feeder to feed parts to the sensor one at a time, and then on to the diverter
5. a drum, bucket or hopper to hold a mass of Lego pieces

After a bit of thought and some inspiration from here and here, the concept is:

- a "drum feeder" to hold the bulk pieces and supply them at a rate (controlled by the rotation of the drum and the size of the scoops) to the feeder.

- a "vibratory linear feeder" to simultaneously separate the pieces and transport them to the sensor and beyond.

- a colour sensor e.g. TCS34725 module connected to an Arduino Nano to estimate/classify colour, and control the diverter and linear feeder

- a rotary diverter powered by a NEMA 17 stepper to divert pieces into one of eight collector tubes

- a circle of tubes which allow pieces to slide (under gravity) to eight bins/bags.

I hope to use 40mm plastic pipe for most of the build, as it's cheap and large enough for most Lego pieces to fit through.