Abstract
The cinematic and dynamic study of the movement autovehicles is difficult to make because of the various constructive parameters and the disturbing factors, which may appear. That is the reason why the studies with general character must make simplifications, by avoiding the specific constructive peculiarities of each type of autovehicle. In general, the monographs just make a concise analysis of the kinematics of autovehicles, with the purpose of determining the correct rolling condition [1; 2], as represented by Ackerman's relation. There is also a great importance given to the study of the kinematics of the wheels, both motors and pulled wells, [1; 2; 3]. A detailed study on the kinematics of the four-welled autovehicle, among which two of there are directories, is being made in [3].
The travel on an imposed trajectory of an autovehicle, or, in general, of a rolling system is being made by the fulfillment of some cinematic conditions of compatibility of the speeds. The execution of a trajectory imposes a certain variation of the angles of steering of the directory wells, variation which, in practice, is achieved by the human factor.
This variation depends on the imposed trajectory, the constructive parameters of the autovehicle, and on it's initial orientation when compared to the trajectory. The replacement of the human factor with electronic equipments requires the achievement of a database, which would contain the biggest possible number of achievable trajectories.
In the paper there are mentioned the compatibility conditions of the speeds, and the grounds of which one can deduce the differential equation of the variation of the angle between the speed of the mass center and the longitudinal axis of the system (autovehicle). This equation is to be resolved in case of rectilinear and circular/ trajectories.
Through convenient changes of the variable the mentioned differential equation is being transformed into a differential equation of Riccati type.
Keywords: steering, angle, travel, trajectory, speed.