Articles | Volume 8, issue 2
Research article
26 Jul 2017
Research article |  | 26 Jul 2017

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

Jinyong Ju, Wei Li, Mengbao Fan, Yuqiao Wang, and Xuefeng Yang

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.

Short summary
During the mode experiments of the FCRM, we find that the mode characteristics of the FCRM change with the different tip mass. As the direct drive source of the FCRM, the output of the motor also have great influences on the dynamic characteristics of the FCRM. Thus, the nonlinear modelling and dynamic stability of a FCRM with base disturbance and terminal load are analyzed in this paper. During the analysis process, the methods of mechanism modeling and numerical calculation are adopted.