Non-blind rotary motion deblurring (RMD) aims to recover the latent clear image from a rotary motion blurred (RMB) image. The rotation center is a crucial input parameter in non-blind RMD methods. Existing methods directly estimate the rotation center from the RMB image. However they always suffer significant errors, and the performance of RMD is limited. For the assembled imaging systems, the position of the rotation center remains fixed. Leveraging this prior knowledge, we propose a geometric-based method for rotation center identification and analyze its error range. Furthermore, we construct a RMB imaging system. The experiment demonstrates that our method achieves less than 1-pixel error along a single axis (x-axis or y-axis). We utilize the constructed imaging system to capture real RMB images, and experimental results show that our method can help existing RMD approaches yield better RMD images.