Steady and Transient Response Analysis of a Nonlinear Dual Flexible Manipulator

ABSTRACT This paper presented a novel nonlinear theoretical model for the dual flexible manipulator. First, the dual flexible manipulator was simplified as a combination of a rigid joint and an Euler–Bernoulli beam with single‐sided elastic constraints. Considering the axial stretching effect, the nonlinear governing equations of motion for the dual flexible manipulator were established Hamilton's principle. Based on this, the free vibration equation and nonlinear vibration equation for the dual flexible manipulator were established, and the amplitude–frequency relationship was derived using the method of multiple scales. Furthermore, model effectiveness verification was conducted, and the influence of key parameters on the modal characteristics and amplitude–frequency response curves was investigated. The research results show that as the dimensionless load mass and stiffness ratio increase, the modal frequencies of the flexible manipulator system decrease gradually, whereas the dimensionless moment of inertia only affects the low‐order modal frequencies. Changing the value of the dimensionless payload mass causes the flexible manipulator to exhibit either softening or hardening effects, whereas changing the values of the dimensionless moment of inertia and stiffness ratio results in the system exhibiting only a softening effect. The findings provide important guidance for the dynamic design of manipulators with flexible joints.