Dynamics modelling of a single-link flexible robot

The dynamics modelling of a single-link flexible robot with a rigid mass attached to the tip is addressed. The flexibility is represented by lateral bending motion of the robot link. The model is obtained using a Newton-Euler formulation and the natural frequencies and mode shapes are obtained using a constrained mode approach. The paper models the flexibility effects as an internal disturbance torque generated by lateral bending which affects the rigid body motion. The model is suitable for control system analysis and synthesis. A numerical example is presented for the purpose of illustrating the calculation of natural frequencies, mode shapes, and other modal parameters based on the model developed.