We discuss nonlinear model predictive control (MPC) for multi-body dynamics via physics-informed machine learning methods. In more detail, we use a physics-informed neural networks (PINNs)-based MPC to solve a tracking problem for a complex mechanical system, a multi-link manipulator. PINNs are a promising tool to approximate (partial) differential equations but are not suited for control tasks in their original form since they are not designed to handle variable control actions or variable initial values. We thus follow the strategy of Antonelo et al. (arXiv:2104.02556, 2021) by enhancing PINNs with adding control actions and initial conditions as additional network inputs. Subsequently, the high-dimensional input space is reduced via a sampling strategy and a zero-hold assumption. This strategy enables the controller design based on a PINN as an approximation of the underlying system dynamics. The additional benefit is that the sensitivities are easily computed via automatic differentiation, thus leading to efficient gradient-based algorithms for the underlying optimal control problem.