For the purpose of large-aperture optical system spectral transmittance measurements, a novel double-rotating scanning machine with double-rotating arms (SSMDA) is designed. The sub-aperture scanning beam spot obtained from the SSMDA can cover full aperture of large optical system. By considering the structural parameters errors, mathematical models of the SSMDA based on homogeneous coordinate transformation matrixes are developed. A detailed methodology for analyzing the scanning errors Δηr is proposed and implemented in practical design process. The computational results of scanning errors Δηr carried out on the mathematical models are between -0.007 nm and 0.028 mm while scanning radius ηr≤400.000 mm. The proposed methodology, developed mathematical models and obtained computational results can be not only the design reference for similar machines but also the theoretical and data basis for large-aperture optical system spectral transmittance measurements based on double-rotating sub-aperture scanning method.