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.
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.