Modal analysis and dynamic responses of a rotating Cartesian manipulator with generic payload and asymmetric load

Abstract

Here, investigation to explore the effect of generic payload and externally applied asymmetric load on the calculation of modal parameters and dynamic performance of a rotating flexible manipulator under prismatic motion has been established. We thus have developed a dynamic model of a rotating Cartesian manipulator with a payload whose center of gravity doesn’t coincide with the point of attachment, to determine the modal parameters i.e., natural frequency and corresponding mode-shape. These modal parameters are then illustrated graphically upon varying parameters like offset parameters (i.e., offset mass, offset inertia, offset length), mass and stiffness of rotary actuator, and amplitude and frequency of asymmetric load. An investigation into the nonlinear dynamics of the system accounting of geometric nonlinearity has been executed while obtained results have been validated numerically within the permissible error at the assorted critical points in frequency characteristic curves. Current research further investigates the influences of offset parameters, mass and stiffness of the actuator, frequency and amplitude of axial force on the steady state responses for the primary and sub-harmonic resonance conditions to reveal the built-in saddle-node and pitchfork bifurcation due to which the system losses its structural stability. This work enables an insight into the modal characteristics and nonlinear behavior of a rotating-Cartesian manipulator with a generic payload under asymmetric axial force and prismatic motion.

Keywords:

• Cartesian manipulator
• off-set payload
• asymmetric axial force
• modal analysis
• bifurcation
• stability