Analytical and experimental investigation of the dynamic behavior of a revolute-prismatic manipulator with N flexible links and hubs

In this paper, the dynamic model and vibration analysis of a flexible manipulator composed of N elastic links and robot actuators for which structural vibration is considered are investigated. In view of the concurrent linear and rotary motions of the link caused by revolute-prismatic joints, the interaction of joint’s structural vibration and link fluctuation is taken as an effective model parameter. Utilization of prismatic joint with hub in the manipulator’s structure in question, its significant length and low weight result in the operation of hub akin to a flexible link attached to revolute joint. To model the expressed hub oscillation with respect to the link, the assumed modes method and mode shapes of Euler-Bernoulli beam with independent generalized modal coordinate with respect to the link are employed. Noting the complexity of the present model relative to studied flexible manipulators, the recursive Gibbs-Appell formulation is used to derive the motion equations. Therefore, the dynamic equations of hub are of time-independent form, while these equations are obtained as time-variable for links. Although the obtained equations are simultaneously solved in the coupled form, the derived equations for a single-link flexible manipulator are simulated in three cases of (1) rigid hub, (2) elastic hub, and (3) elastic hub and flexible joints. The simulation results are compared with a similar experimental setup, indicating that the flexible manipulator model with elastic link, hub, and joints yields satisfactory results with an error of less than 1 mm and 1° in the longitudinal and rotational motions, respectively. Moreover, the results of lateral vibration show good accuracy, with the endpoint of the robot having perfect precision with just 1% tolerance.