The industry often utilizes general-purpose robots, where the motion to be performed is defined in software. In contrast, for special-purpose robots, the task is already considered (at least partially) in the design of the mechanism. This allows for the usage of lighter materials and cheaper actuators, which can lead to a better energy efficiency and is potentially easier to control. Traditionally, either analytic approaches [1] or global optimization [2] approaches are used to retrieve (near) optimal solutions. But the former requires profound expert knowledge, whereas the latter may require sequential simulations. With advances in machine learning, a neural network can learn the relationship between tasks and mechanism design [3,4]. In this work, we investigate different neural network architectures for the direct data-driven synthesis of four-bar linkages. While this is an already-solved task using traditional approaches, it can serve as a test bed to evaluate run times, prediction quality, and simulation cost. We compare the neural network predictions followed by a local post-optimization against solutions found by global optimization. Furthermore, we present a data-driven design assistant for an interactive instantaneous synthesis of four-bar linkages, where in a subsequent stage a desired velocity profile can be defined for the data-driven design of a suitable controller. Our results show that the neural-network approach achieves comparable performance to intermediate stages of the global optimization for a much lower time- and simulation-budgets. A later neuro-initialized optimization can further improve the designs with only few iterations. Utilizing machine learning approaches for the design task allows to outsource the simulation cost into an initial (expensive) training stage. A trained network can then offer almost instantaneous mechanism designs. Finally, ML approaches can scale to more complex mechanisms as long as simulation data can be generated using simulation software.