The Simscape Multibody software is a set of libraries and mechanical modeling and simulation tools for use with Simulink®. For what concerns the contact library, currently it contains only the models to describe impacts between simple geometries, such as spheres, cylinders and planes. When this environment is intended to be used to simulate the 3D dynamics of a system with a complex geometry, such as a ball screw, the built-in blocks are not sufficient. This paper presents a new contact library, containing blocks specifically designed to handle the contacts between a sphere and the two gothic arc helical grooves of a ball screw, as well as the interaction between adjacent spheres. The developed blocks are exploited to create a first case study dynamic model of a single nut not preloaded ball screw in presence of internal backlash. The results highlight the superiority of this multibody approach with respect to the quasi-static or lumped parameters models in terms of extracted information and understanding of the internal mechanics.