Dynamic modeling of a three degree-of-freedom robotic manipulator

Transfer function models that can provide physical insight into the dynamic behavior of manipulators and establish a foundation for control system analysis and design are identified. Emphasis is directed toward increasing the computational efficiency of the manipulator dynamic equations of motion. A conceptual three-degrees-of-freedom manipulator, which represents state-of-the-art configurations, is designed and simulated on a digital computer. The Lagrangian formulation is applied to develop the complete dynamic equations of motion of the manipulator. The simulation model includes the dynamic interactions of the centrifugal, Coriolis, inertial, and gravitational generalized forces along with the kinematic coupling, and it can accommodate load variations. The simulation model is interfaced to the Steiglitz-McBride identification algorithm to extract, from the complete nonlinear model, simplified linear models that characterize the arm in various regions of the work space. The simplified linear models are second-order discrete-time (input-output) transfer functions.