隨著現代數學的進步，複雜的物理現象和工程問題可以透過提供相應分析方法的數學模型解決。各種可處理複雜方程式的機械式計算器於 19 世紀至 20 世紀相繼問世，儘管現已被電子式計算機取代，但其工作原理和設計方法仍然是構成科技文明進步並推動計算機技術發展的重要基礎。
西班牙發明家 Leonardo Torres Quevedo 於西元1893至1920年間陸續設計的三台機械式計算機，皆用於求解複雜方程式，分別求解多項式相加、一元二次方程式的複根、八次方程式的根。其中一個典型的例子「機械式一元二次方程計算機」為二次方程式計算器，用於求複數根。儘管歷史文獻與Torres的學術論文和計畫報告仍然存在，然而多為概念原理與範例說明，對其機構的研究有限，影響對其概念原理和具體示例的理解，導致構造與零件並不明確。
本研究提出一套系統化的復原方法，針對Torres發明之複雜計算機械式計算機進行史料研究。解析裝置所運算之方程式，了解數值與機構之轉換關係以利復原設計。並針對「機械式一元二次方程計算機」中的六大機構進行分析與分類，區分輸入動力源、計算系統、傳動系統及輸出結果系統等四個動力傳遞子系統，根據文獻之圖片與文字記載進行復原設計，構造明確部分進行直接進行機構尺寸演算；構造不明部分則以兩台參考裝置的相似機構為基礎，進行機構設計合成方法、機械設計方法，以及目標方程與機構之關係演算，進行機構與尺寸合成，以推測出符合當代工藝技術之可行設計。
本研究針對「機械式一元二次方程計算機」中的六大機構提出可行機構，從中篩選出符合目標方程與機構之關係的最合適機構，包含耦合運動曲線、平移變量ρ計算機構、旋轉變量α計算機構、剪刀機構。其次建構3D模型與運動模擬，藉由製造公差分析設置最佳公差參數，以提高計算機精準度。最後製作實體原型機，驗證所提出的可行復原設計與製造之合理性。本研究所提出之復原合成流程，可應用於其它計算機之復原研究。

With the advancement of modern mathematics, complex physical phenomena and engineering problems can be addressed using mathematical models that provide corresponding analytical methods. To solve complex equations, mechanical calculators were designed during the 19th and 20th centuries. Although mechanical calculators have been replaced by electronic computers precently, these operation principles and design methods constitute an important foundation for the advancement of technological civilization and the development of computer technology.
Spanish inventor Leonardo Torres Quevedo designed three mechanical calculators between 1893 and 1920 for solving complex equations, including polynomial addition, complex roots of quadratic equations, and roots of eighth-degree equations. One typical example is the Quadratic Equation Calculator “Máquina para Resolver Ecuaciones de Segundo Grado”, created by Spanish inventor Leonardo Torres Quevedo, which was used to determine complex roots. Though Torres's academic papers and project reports still exist, there’s limited research on mechanism. This scarcity primarily affects the understanding of their conceptual principles and specific examples, leaving the structures and components unclear.
This research provides a systematic reconstruction method. Beginning with research on literature, the equations are analyzed to understand the relationship between numerical values and mechanism transformations. Six major mechanisms in the “Mechanical Quadratic Equation Calculators” are analyzed and classified into four power transmission subsystems, including input power source, calculation system, transmission system, and output result system. For the parts with unclear structures, the mechanical design and dimensional parameters are reconstructed referring to the other two calculators made by the same inventor. The reconstructed calculator meets the requirement that the output motion of the mechanisms represents the solutions of the target mathematical equations, and it also aligns with the technology available at that time.
Feasible mechanisms are proposed for six major mechanisms in the “Mechanical Quadratic Equation Calculators”. The 3D models and motion simulations are created, and the manufacturing tolerance is analyzed to obtain the optimizing parameters for improving calculator precision. Finally, the prototypes testing is made to evaluate the rationality of the proposed reconstruction designs and manufacturing. The desing procedure proposed in this research can be applied to the reconstruction of other calculators.

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