Nonlinear modelling and dynamic stability analysis of a flexible Cartesian robotic manipulator with base disturbance and terminal load

Abstract

Abstract. The flexible Cartesian robotic manipulator (FCRM) is coming into widespread application in industry. Because of the feeble rigidity and heavy deflection, the dynamic characteristics of the FCRM are easily influenced by external disturbances which mainly concentrate in the driving end and the load end. Thus, with the influence of driving base disturbance and terminal load considered, the motion differential equations of the FCRM under the plane motion of the base are constructed, which contain the forced and non-linear parametric excitations originated from the disturbances of base lateral and axial motion respectively. Considering the relationship between the coefficients of the motion differential equations and the mode shapes of the flexible manipulator, the analytic expressions of the mode shapes with terminal load are deduced. Then, based on multiple scales method and rectangular coordinate transformation, the average equations of the FCRM are derived to analyze the influence mechanism of base disturbance and terminal load on the system parametric vibration stability. The results show that terminal load mainly affects the node locations of mode shapes and mode frequencies of the FCRM, and the axial motion disturbance of the driving base introduces parametric excitation while the lateral motion disturbance generates forced excitation for the transverse vibration model of the FCRM. Furthermore, with the increase of the base excitation acceleration and terminal load, the parametric vibration instability region of the FCRM increases significantly. This study will be helpful for the dynamic characteristics analysis and vibration control of the FCRM.

Tip Trajectory Characteristics and Nonlinear Stability Analysis of Robotic Manipulator With Flexible Links-joints

“…The reported studies have been divided into two categories based on the type of joints used to drive the manipulator i.e. revolute [1][2][3][4][5] and prismatic joints [6][7][8][9][10][11]. On many occasions, beam element is often used to model the flexible link and integrating it with rotating hub makes a robotic manipulator with revolute joint [12].…”

Position analysis and nonlinear phenomena of flexible manipulator with generic payload mounted on a moving base

“…Nonlinear equation of motion for a clamped-free flexible Euler-Bernoulli beam rotating in a horizontal plane carrying a moving point mass has been derived by Fung and Yau. 15 Ju et al 16 investigated the influence of base disturbance and point mass payload on the nonlinear response and dynamic stability of the flexible Euler-Bernoulli Cartesian robotic manipulator undergoing large overall motion.…”

“…15 Ju et al. 16 investigated the influence of base disturbance and point mass payload on the nonlinear response and dynamic stability of the flexible Euler–Bernoulli Cartesian robotic manipulator undergoing large overall motion.…”