Kinetostatics of Wheel Vehicle in the Category of Spiral-Screw Routes

Deterministic mathematical model of kinetostatics of wheel vehicle in terms of different modes of spatial motion in the context of curved route is proposed. Earth-based coordinate system is introduced which pole and axial orientation are determined by the convenience of route description as well as vehicle-related coordinates which pole axial orientation are determined within inertial space with the help of natural trihedral. Turn of the natural trihedral within inertial coordinates is described by means of quaternion matrices in the context of Rodrigues-Hamilton parameters. Rodrigues-Hamilton parameters are in matrix form in direct accordance with specified hodograph. Kinetostatics of wheel vehicle is considered in terms of spatial motion with an allowance for three-dimensional aerodynamic forces, gravity, and tangential and centrifugal inertial forces. In the context of spiral-screw lines deterministic mathematical model of wheel vehicle kinetostatics is proposed in the form of hodograph in terms of uniform motion, accelerated motion, and decelerated motion within following route sections: straight and horizontal; in terms of vertical grade; in terms of horizontal plane. Analytical approach to determine animated contact drive-control forces of wheel vehicle for structural diagrams having one and two support points involving of a driving-driven wheel characteristic is proposed based on kinetostatics equations. Mathematical model of wheel vehicle kinetostatics in terms of spatial motion is constructed on the basis of nonlinear differential Euler-Lagrange equations; it is proposed to consider physically implemented motion trajectories of wheel vehicles in the context of spiral-screw lines; hodograph determines spatial displacement; Rodrigues-Hamilton parameters determines spatial turn; Varignon theorem is applied to identify components of drive (control) force. The obtained results make it possible to solve a wide range of problems connected with dynamic design of wheel vehicles involving controllability, and estimation of dynamic load of both system and support surface.