The present invention relates to a drive train (50) of a hair cutting appliance (10) and to a self-aligning coupling linkage (66) for a drive train (50). The coupling linkage (66) comprises a driving shaft and a non-aligning output shaft (56), said coupling linkage (66) comprising: a first driving coupling element (78) arranged to be driven by a driving shaft (54), particularly by a motor shaft, a transmission shaft (70), particularly a rigid transmission shaft (70), comprising a first drivable coupling element (80) at a first end and a second driving coupling element (86) at a second end thereof, wherein first driving coupling element (78) engages the first drivable coupling element (80) for rotatingly driving the transmission shaft (70), thereby forming a first pivoting joint (76), wherein the second driving coupling element (86) is arranged to engage a second drivable coupling element (88) of an output shaft (56), wherein the first driving coupling element (78) and the first drivable coupling element (80) define a male connector comprising an external polygonal profile (90), viewed in a cross-sectional plane perpendicular to a longitudinal axis, and a female connector comprising an internal polygonal profile (102), and wherein the external polygonal profile (90) of the male connector, viewed in a longitudinal axial section, is at least sectionally provided with convexly shaped flanks (92).