Nonlinear dynamic analysis of the extended telescopic joints manipulator with flexible links

摘要

In this paper, the open-chain arm containing flexible links connected through telescopic joints is investigated so as to replacerobotic chains with revolute joints. In this manipulator, telescopic joints are considered by a simultaneous motion combinationof the prismatic and revolute joints. In comparison with revolute–prismatic joints in which prismatic joint hubs areutilized, telescopic joints lack the hub, and the linear motion is generated via a gear. Accordingly, the flexible link is notplaced inside the hub. In fact, the link is merely divided into two sections each at a time step. The front section which is consideredin the motion equations is placed at the back of the hinge’s point. This part solely creates vibration, which probablyaffects the motion of other sections. This type of manipulator’s joints due to the structure benefits consists of the optimumweight, simple mechanism, extended workspace acceptable for robotic tools, industrial machinery, and domestic systems.To derive motion equations of N-link flexible manipulator with telescopic joints system, the Euler–Lagrange formulationis employed. The obtained equations are in the time-varying form, and the manipulator link length changes during motion.The derived equations are simulated for a two-link system with different elasticity values, and the results are then analyzedto verify the outcomes. The bifurcation analysis has also been used to prevent unstable vibrations and chaotic responses. Itshould be noticed that this type of manipulator can be used in a fast and precise mechatronics’ system for utilization in spaceexploration, space station, and spacecraft as well.