jats:titleAbstract</jats:title> jats:pDetecting cosmological signals from the Epoch of Reionization (EoR) requires high-precision calibration to isolate the cosmological signals from foreground emission. In radio interferometry, the perturbed primary beams of antenna elements can disrupt the precise calibration, which results in the contamination of the foreground-free region, or the EoR window, in the cylindrically averaged power spectrum. For the Hydrogen Epoch of Reionization Array (HERA), we simulate and characterize the perturbed primary beams that are induced by feed motions, such as axial, lateral, and tilting motions, above the 14 m dish. To understand the effect of the perturbed beams, visibility measurements are modeled with two different foreground components, point sources and diffuse sources, and we find that different feed motions present a different reaction to each type of sky source. HERA’s redundant baseline calibration in the presence of nonredundant antenna beams due to feed motions introduces chromatic errors in the gain solutions, producing foreground power leakage into the EoR window. The observed leakage from the vertical feed motions comes predominantly from point sources around the zenith. Furthermore, the observed leakage from the horizontal and tilting feed motions comes predominantly from the diffuse components near the horizon. Mitigation of the chromatic gain errors will be necessary for robust detections of the EoR signals with minimal foreground bias, and this will be discussed in a subsequent paper.</jats:p>