Like many flightless, obligatory walking insects, the stick insect Carausius morosus makes intensive use of active antennal movements for tactile near range exploration and orientation. The antennal joints of C. morosus have a peculiar oblique and non-orthogonal joint axis arrangement. Moreover, this arrangement is known to differ from that in crickets (Ensifera), locusts (Caelifera) and cockroaches (Blattodea), all of which have an orthogonal joint axis arrangement. Our hypothesis was that the situation found in C. morosus represents an important evolutionary trait of the order of stick and leaf insects (Phasmatodea). If this was true, it should be common to other species of the Phasmatodea. The objective of this comparative study was to resolve this question. We have measured the joint axis orientation of the head-scape and scape-pedicel joints along with other parameters that affect the tactile efficiency of the antenna. The obtained result was a complete kinematic description of the antenna. This was used to determine the size and location of kinematic out-of-reach zones, which are indicators of tactile acuity. We show that the oblique and non-orthogonal arrangement is common to eight species from six sub-families indicating that it is a synapomorphic character of the Euphasmatodea. This character can improve tactile acuity compared to the situation in crickets, locusts and cockroaches. Finally, because molecular data of a recent study indicate that the Phasmatodea may have evolved as flightless, obligatory walkers, we argue that the antennal joint axis arrangement of the Euphasmatodea reflects an evolutionary adaptation to tactile near range exploration during terrestrial locomotion.