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Abstract. The crossbow evolved from the traditional bow through the incorporation of a stock and trigger mechanism, enabling the crossbow archer to retain the accumulated elastic energy of the bow and string. This design overcame limitations such as difficulty maintaining aim for extended periods, reduced shooting accuracy, and limited range. The shooting process of a crossbow consists of four main steps: string drawing, bolt loading, string releasing, and bolt launching. The principal difference between Eastern and Western crossbows lies in the method of drawing the string. Ancient Chinese crossbows used either manual force or linkage mechanisms. Early European crossbows additionally employed gear mechanisms to facilitate string drawing. The mechanical configuration of a crossbow changes during shooting. Therefore, it is classified as a variable-topology mechanism. This paper applies graph representations to illustrate the mechanical structural changes in historical crossbows from both China and Europe. First, the historical development of crossbows in the East and West is briefly reviewed. Then, the motion characteristics of the earliest documented repeating crossbow, lever-type crossbow, and cranequin crossbow are analyzed. Graph representations and 3D computer models are used to visualize the topological variations in these three crossbow types and their shooting processes. Finally a cross-cultural comparison of ancient crossbows is provided.