Application of Hermite splines for load movement on a flexible crane suspension through a curvilinear trajectory

Abstract

Analytical expressions of the coordinates of the load, the suspension point and the rope deviation angle, as well as their first three time derivatives were obtained by setting the desired load movement trajectory on a pendulum type flexible crane suspension using two-point Hermite splines with the quartic highest derivatives. A well-known mathematical model of the oscillatory system described by a linearized differential equation was used. With the described movements, the uncontrollable pendulum oscillations of the load are absent. The load moves exactly along a reference trajectory. The superposition of load movements in two mutually perpendicular planes solves the problem of synthesising the suspension point trajectory, which ensures the movement of load along an arbitrary smooth curvilinear trajectory in the horizontal plane. The second horizontal coordinate of the load was represented as an interpolation polynomial from the first horizontal coordinate. The division of the movement trajectory along the axis of the second horizontal coordinate into several sections of the same length provide the determination of the load movement and its derivatives at reference points, as well as the calculated suspension point trajectory. The developed technique is promising for application in intelligent mechatronic control systems for travelling and bridge-travelling cranes.