Planning the right grasp pose and motion into it has been a problem in the robotic community for more than 20 years. This paper presents a model-based approach for a Pick action of a robot that increases the automation of FDM based additive manufacturing by removing a produced object from the build plate. We treat grasp pose planning, motion planning and simulation-based verification as separate components to allow a high exchangeability. When testing a variety of different object geometries, feasible grasps and motions were obtained for all objects. We also found that the computation time is highly dependent on the random seed, leading us to employ a system of budgeted runs for which we report the estimated success probability and expected running time. Within the budget, some objects never found feasible picks. Thus, we rotated these objects by 90 • which lead to a substantial improvement in success probabilities.