Researchers from the US National Institute of Standards and Technology published instructions for a very precise LEGO watt balance to measure the kilogram unit of mass. You also need strong neodymium magnets. From New Scientist:
Finding the mass requires two measurements. First place a weight on one of the pans, moving the coil past the magnet and inducing a voltage. Then run a current through the coil, creating an electromagnetic force on the pan that counteracts the weight. Comparing these two gives you the weight's mass, which can be compared to the Planck constant.
"DIY device to define the kilogram – using Lego"
"A LEGO Watt Balance: An apparatus to demonstrate the definition of mass based on the new SI" (arXiv.org)
