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A scroll air motor, also known as a scroll expander, is a relatively new concept to pneumatic actuators. Its unique structure leads to its feature of high ability in energy conversion. In recent years, scroll air motors have been adopted by combined heat and power boilers, uninterrupted power supplies, and some other energy storage systems as a new mechatronic device for energy conversion. The paper aims to present the work in developing a complete mathematical model of the scroll air motor for analysis of scroll energy efficiency and the factors affecting energy efficiency. The work will be reported in two parts of the paper. The paper describes the derivation of spiral equations, chamber volume calculations, and the driving torque of the scroll air motor. The dynamic process modeling and energy efficiency analysis will be presented in Part II of the paper.