Parabola approximation by a hyperbola when modeling steering mechanism characteristics of tracked vehicles

Steering control quality improvement and movement safety ensuring of tracked vehicles, primarily high-speed ones, is an urgent problem. Characteristic feature of most tracked and transport vehicles transmissions is an almost linear relationship between values of calculated (maximum) turning radii in gears and movement speed, which leads to underutilization of traction and dynamic capabilities of machines. It would be more advantageous to provide a parabolic view for such a dependence, or at least its non-linear character. Two-stream transmission and rotation mechanisms proposed today with a nonlinear characteristic make it possible to realize only a hyperbolic dependence between these quantities, which makes it urgent to search for constructing methods of the best parabola approximation by a hyperbola. Article shows constructing principle of a hyperbolic swing mechanism diagram for transmission with central gearbox and parallel branch drive through three-link differential mechanism, provides an example scheme for it and proposes a technique for constructing best uniform parabola approximation by a hyperbola on a given interval, based on classical problem of uniform approximation of a function by a polynomial. Construction results can be used to determine main parameters of two-line hyperbolic swing mechanisms for transport tracked vehicles with central gearboxes.