A multistage data-driven neuro-fuzzy system is considered for the multiobjective trajectory planning of Parallel Kinematic Machines (PKMs). This system is developed in two major steps. First, an offline planning based on robot kinematic and dynamic models, including actuators, is performed to generate a large dataset of trajectories, covering most of the robot workspace and minimizing time and energy, while avoiding singularities and limits on joint angles, rates, accelerations, and torques. An augmented Lagrangian technique is implemented on a decoupled form of the PKM dynamics in order to solve the resulting nonlinear constrained optimal control problem. Then, the outcomes of the offline-planning are used to build a data-driven neuro-fuzzy inference system to learn and capture the desired dynamic behavior of the PKM. Once this system is optimized, it is used to achieve near-optimal online planning with a reasonable time complexity. Simulations proving the effectiveness of this approach on a 2-degrees-of-freedom planar PKM are given and discussed.