Lumped mass models of gantry cranes

This chapter discusses the mathematical modeling of gantry crane systems, considering the subsystems of a crane to be rigid bodies. Such a formulation does not reflect the deflections within the individual parts of the crane but only considers their rigid body movements and results in a lumped mass model (LMM). Both the overhead and container cranes, shown in Figs. 1.1 and 1.3, respectively, lie within the category of gantry cranes. In developing the LMMs of gantry cranes, three different approaches for modeling the hoisting mechanism are usually followed: (i) single-rope hoisting mechanism, (ii) multi-rope hoisting mechanism, and (iii) double-pendulum system. The first approach, which considers a single-rope hoisting mechanism, represents the dynamics of a simple overhead crane considering the hook and the payload as a single-lumped mass.