The direction shown in the figure is positive, φ R is the included angle between the connecting line between the center of the planetary gear and the center of the gear ring and the positive direction of the coordinate axis X, α Rp1n is the meshing angle, which defines the relative meshing angle φ rp1n：
The projection of the linear displacement XR and yr of the ring gear R on the meshing line is xrsin respectively φ rp1ncos β b、-yrcos φ r p1ncos β b. The projection of the linear displacement XC and YC of planet carrier C on the meshing line is – xcsin respectively φ rp1ncos β b、yccos φ rp1ncos β b. The projection of the linear displacement up1nx and up1ny of the large planetary gear p1n on the meshing line is up1nxsin respectively φ rp1ncos β b、up1nycos φ rp1ncos β b. Under the pure torsion model, the relative meshing displacement between ring gear R and large planetary gear p1n is [rp1n θ p1n+(rr-rp1n) θ c-rr θ r]cos β B-erp1n, so the relative displacement drp1n under the translation torsion analysis model:
