Abstract A study was conducted on three models of the medieval siege engine, the trebuchet. The three models analyzed were the "see-saw", the hinged, and the floating arm trebuchet. Of these models, the mathematical model of each was determined. With his model, the most efficient model was determined to be the floating arm trebuchet, with a range efficiency of 0.8275 and an energy efficiency of 0.8526. The hinged trebuchet achieved efficiencies of 0.8065 for both range and energy efficiency and the "see-saw" with efficiencies of only 0.567 and 0.570, respectively. Then, the floating arm trebuchet's arm length ratio and sling length were then optimized. It was determined that the optimal arm length ratio was approximately 1:2, where the short arm is 1.7 feet and the long arm is 3.3 feet. The optimized sling length was 4.45 feet. Finally, the mathematical models were compared to full scale models. These ranges of the full scale models were surprisingly accurate with what was predicted. The hinged trebuchet model had the largest percentage error at 8.4%.

A method has been developed that employs both procedural and optimization algorithms to adaptively slice CAD models for large-scale additive manufacturing (AM) applications. AM, the process of joining material layer by layer to create parts based on 3D model data, has been shown to be an effective method for quickly producing parts of a high geometric complexity in small quantities. 3D printing, a popular and successful implementation of this method, is well-suited to creating small-scale parts that require a fine layer resolution. However, it starts to become impractical for large-scale objects due to build volume and print speed limitations. The proposed layered manufacturing technique builds up models from layers of much thicker sheets of material that can be cut on three-axis CNC machines and assembled manually. Adaptive slicing techniques were utilized to vary layer thickness based on surface complexity to minimize both the cost and error of the layered model. This was realized as a multi-objective optimization problem where the number of layers used represented the cost and the geometric difference between the sliced model and the CAD model defined the error. This problem was approached with two different methods, one of which was a procedural process of placing layers from a set of discrete thicknesses based on the Boolean Exclusive OR (XOR) area difference between adjacent layers. The other method implemented an optimization solver to calculate the precise thickness of each layer to minimize the overall volumetric XOR difference between the sliced and original models. Both methods produced results that help validate the efficiency and practicality of the proposed layered manufacturing technique over existing AM technologies for large-scale applications.