In this article we describe and build a model of a historical weighing device proposed by the Spanish engineer Dario Bacas in the second half of the 19th century. The balance was named "goniobarimeter" by its inventor, and the weighing principle is based on a curious, and not very well known, property of the cycloid. The simplicity of the design makes it especially suitable for a hands-on educational project with pre-university physics students. (Contains 6 figures.)