Computational implementation of the rigid finite element method in the statics and dynamics analysis of forest cranes

A general mathematical model of a forest crane for statics and dynamics analysis is presented in the paper. This model allows to take into account the crane's flexible connections with the ground, the flexibility of its links and drives. The rigid finite element method is used to discretize the flexible links. Joint coordinates and homogeneous transformation matrices are used to describe the geometry of the system. Equations of motion are derived using the formalism of Lagrange equations. As an example, a forest crane built of eight links is presented. It is assumed that only one selected link of the crane is flexible. The influence of the flexibility of the link on the movements of load and driving torques in the revolute joints and the driving force in the prismatic joint are analyzed. The results may have practical significance, e.g. in terms of the selection of drives.