The Influence of the Load Modelling Methods on Dynamics of a Mobile Crane

A mathematical model for the dynamics analysis of a mobile crane is presented in the paper. The proposed model of a mobile crane is in the form of a tree structure of a kinematic chain with closed-loop subchains. The carried load is treated in the two cases, as a lumped mass and a rigid body. The formulated model takes also into account the flexibility of wheels, outriggers, drives and rope(s). Dry friction in joints is also considered. The formalism of joint coordinates and homogeneous transformation matrices are used to describe the kinematics of the crane. The equations of motion are derived using the Lagrange equations of the second kind. These equations are supplemented by the Lagrange multipliers and constraint equations formulated for each cut-joint.