The paper investigates the motion of a spherical pendulum with a movable pivot. The developed and studied dynamic model represents many mechanical systems – a crane with a freely suspended payload, a helicopter carrying a payload, rockets, cable-driven parallel manipulators, etc. The modelled spherical pendulum has six degrees of freedom and comprises two concentrated masses connected through a rope. The mechanical system equations of motion are derived using the Lagrange method. A special feature of the developed model is that it allows the study of the deformation and force in the rope. The motion of the pivot is simulated to follow a spatial straight-line trajectory while the driving forces applied to the upper mass are computed as proportional to the position and velocity errors. The results indicate that when the pivot moves according to smoothly changing trajectories, the swing angles of the pendulum are small, and the dynamic coefficient in the rope is also minimal. The resulting nonlinear mathematical model was linearized, and the linearization error was estimated. The obtained equations were used for modal analysis of the system. The linearized model is especially applicable in developing and testing automatic control algorithms to control the considered system.
Motion analysis of a spherical pendulum with a movable pivot
14TH INTERNATIONAL SCIENTIFIC CONFERENCE ON AERONAUTICS, AUTOMOTIVE, AND RAILWAY ENGINEERING AND TECHNOLOGIES ; 2022 ; Sozopol, Bulgaria
AIP Conference Proceedings ; 3064 , 1
2024-04-10
10 pages
Conference paper
Electronic Resource
English