Abstract : To meet the ever-expanding application needs of scroll compressors, this paper, starting from the principle of involute generation, determines the relationship between the number of scroll rotations and the involute development angle of a scroll compressor; based on the working principle of the scroll compressor, the relationship between the number of rotations and the logarithm of the closed compression chamber is determined; furthermore, the formulas for calculating the intake angle of a scroll compressor with varying compression chamber logarithms and the working chamber volume during intake and exhaust processes are derived. Verification shows that these formulas are also applicable to related calculations when the compression chamber logarithm remains constant. Results show that the definition of the number of scroll rotations and the derived definitions and calculation formulas in this paper are highly versatile and suitable for the research and development needs of scroll compressors, and can be directly applied to the design and calculation of scroll compressors. Keywords : Scroll compressor; Compression chamber pair; Number of rotations 1. Introduction The scroll compressor is a new type of high-efficiency positive displacement compressor. The selection of the scroll profile and the determination of the corresponding geometric parameters are not only the basis of its design but also its core. Currently, the most widely used and researched scroll compressor profile is the involute curve of a circle. In the design process, it often employs a structure where compression chambers appear and disappear in pairs, meaning the number of compression chambers remains constant throughout the entire operation of the scroll compressor. However, with the continuous expansion of the application fields of scroll compressors, this structure with a constant number of compression chambers is no longer sufficient to meet current market demands. Consequently, research on scroll compressors with varying compression chamber numbers has gradually emerged, but it remains incomplete, and the terminology used in the analysis process is not clear enough. Therefore, this paper analyzes the scroll profile of the most widely used involute curve of a circle with constant wall thickness. Starting from the working principle of the scroll compressor, it performs a geometric analysis of scroll compressors with varying compression chamber numbers and derives the volume calculation formula for each working process expressed in terms of the number of scroll rotations. This lays a theoretical foundation for future research on scroll compressors with varying compression chamber numbers. [Full text of the geometric theory research on scroll compressors with variable compression chamber pairs available for download.]