Nonlinear response of a flexible Cartesian manipulator with payload and pulsating axial force

Abstract

In this present work, the nonlinear response of a single-link flexible Cartesian manipulator with payload subjected to a pulsating axial load is determined. The nonlinear temporal equation of motion is derived using D'Alembert's principle and generalised Galerkin's method. Due to large transverse deflection of the manipulator, the equation of motion contains cubic geometric and inertial types of nonlinearities along with linear and nonlinear parametric and forced excitation terms. Method of normal forms is used to determine the approximate solution and to study the dynamic stability and bifurcations of the system. These results are found to be in good agreement with those obtained by numerically solving the temporal equation of motion. Influences of amplitude of the base excitation, mass ratio, and amplitude of static and dynamic axial load on the steady state responses of the system are investigated for three different resonance conditions. For some specific conditions, the results obtained in this work are found to be in good agreement with the previously published experimental work. The results obtained in this work will find applications in the design of flexible Cartesian manipulators with payload.

Dynamic and Stability of Harmonic Driving Flexible Cartesian Robotic Arm with Bolted Joints Based on the Sensitivity and Multiple Scales Method

“…By solving (23), the value of can be obtained, and, according to the relationship 4 = ( / ) 2 , the natural frequency of the flexible CRA can be expressed as Figures 3 and 4 show the influences of the tensional restraint stiffness ( ) and the torsional restraint stiffness ( ) on the mode frequencies. It should be noted that, for the ideal fixed restraint, the natural frequencies of the flexible manipulator can be calculated as 2.448 Hz, 15.339 Hz, and 42.950 Hz.…”

“…Feng and Hu [20] and Li and Zhang [21] studied the principal parametric and internal resonances of flexible beams and plates. For the driving base suffering harmonic excitations, Pratiher and Dwivedy [22][23][24] investigated the nonlinear vibrations of lateral moving CRAs, and in their investigations, however, the motion velocities or motion accelerations of the driving base are assumed as constant neglecting the influence of the motion disturbances; on the other hand, the restraint of the connecting interface is regarded as absolutely rigid and ignores the joint elasticity.…”

Nonlinear Dynamics Analysis of a Large Flexible Slender Truss-Structure Carrying a Manipulator for On-Orbit Assembly

“…1. An appropriate nonlinear PDEs with time-varying coefficients is established by using D'Alembert's principle incorporated with the moment balance method [21], [24]- [27]. The approximate solution is then obtained by using a single-mode discretization via the Galerkin's method with those obtained by directly applying the method of multiple scales.…”

Experimental study of the argumental transverse vibration of a beam excited through intermittent elastic contact by a harmonic axial motion

“…As for the beams receiving axial excitation, a cantilever beam submitted to a harmonic force through its base and to a pulsating axial force through its tip, and carrying a payload at its tip, has been studied in [11].…”