We study the spiral arm influence on the solar neighbourhood stellar kinematics. As the nature of the Milky Way (MW) spiral arms is not completely determined, we study two models: the Tight-Winding Approximation (TWA) model, which represents a local approximation, and a model with self-consistent material arms named sPiral arms potEntial foRmed by obLAte Spheroids (PERLAS). This is a mass distribution with more abrupt gravitational forces. We perform test particle simulations after tuning the two models to the observational range for the MW spiral arm properties. We find that some of the currently observed MW spiral arm properties are not in obvious agreement with the TWA model. We explore the effects of the arm properties and find that a significant region of the allowed parameter space favours the appearance of kinematic groups. The velocity distribution is mostly sensitive to the relative spiral arm phase and pattern speed. In all cases the arms induce strong kinematic imprints for pattern speeds around 17 km s-1 kpc-1 (close to the 4:1 inner resonance) but no substructure is induced close to corotation. The groups change significantly if one moves only similar to 0.6 kpc in galactocentric radius, but similar to 2 kpc in azimuth. The appearance time of each group is different, ranging from 0 to more than 1 Gyr. Recent spiral arms can produce strong kinematic structures. The stellar response to the two potential models is significantly different near the Sun, both in density and in kinematics. The PERLAS model triggers more substructure for a larger range of pattern speed values. The kinematic groups can be used to reduce the current uncertainty about the MW spiral structure and to test whether this follows the TWA. However, groups such as the observed ones in the solar vicinity can be reproduced by different parameter combinations. Data from velocity distributions at larger distances are needed for a definitive constraint.