Due to the simplified tooth profile and the complicated load distribution along the contact line, the traditional analytic method cannot satisfy the accuracy requirement while carrying out addendum modification of the helical gears. To overcome this disadvantage, a new way based on cross-section method is presented to calculate the deformation of helical tooth tip. First, the tooth is divided into copies of cross-section along face width and the moment of inertia for each section is calculated. Also, the load is distributed according to length of the contact line, and the effect of deflected load is taken into account as well. Based on these works, a general formula of helical tooth tip deformation is deduced. Then, this formula is applied to calculate the addendum modification width ac. In addition, considering that tooth tip modification will shorten the meshing line, three models used to control length of the remaining meshing line are proposed and addendum modification height hc is defined accordingly. Finally, an instance is given to verify the good agreement between results of this study and those of a finite element model. Apart from this, engineering application of this method is provided.

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Both the ultrastructures and dynamics of living erythrocyte membranes provide critical criteria for clinical diagnostics. However, it is challenging to simultaneously visualize these features at the single-molecule level due to the rigid photophysical requirements of different single-molecule imaging techniques. Herein, we rationally developed a far-red boron dipyrromethene membrane (BDP-Mem) probe that not only retained consistent and intensive single-molecule emission but also possessed the capability to photoswitch on cellular membranes. We also constructed a microfluidic platform for the noninvasive trapping and long-term imaging of nonadherent erythrocytes. By combining these advantageous technologies, super-resolution reconstruction and single-molecule tracking of living human RBC membranes were achieved at the molecular scale in a high-throughput fashion. Our integrated paradigm defines a quantitative approach for analyzing living RBC membranes under physiological and pathological conditions, improving imaging precisions and revealing new perspectives for future disease diagnostic approaches.