Mathematical Modeling of a Highly Underactuated Tool for Draping Fiber Plies on Double Curved Molds

In this paper, we present a model based approach for predicting the forward kinematics of a tool for picking prepreg fiber plies from a flat table and draping them onto a double curved mold. The tool consists of suction cups interlinked with springs. The tool has 60 actuated and 240 passive degrees of freedom. The prediction is based on establishing a kinematic model of the total potential energy of the tool and minimizing this energy, under the assumptions that dynamic artifacts can be neglected as the movements are relatively slow, and that the springs interpolate the orientation of the suction cups. Various assumptions and simplifications are presented to increase computational speed.Finally, the model predictions are compared to real configurations measured by a camera. Four configurations are simulated and measured and the largest RMS positional deviation measured is 1.99mm, the largest residual measured is 3.68mm. The tolerance of the layup process is 2.5mm so more work needs to be done to reduce the maximum deviations.