Dynamic analysis of a single link flexible manipulator using Lagrangian-assumed modes approach

In the present work, a dynamic model of a single link flexible manipulator is obtained using the Lagrangian-assumed modes method. Two equations are obtained which need to be recursively solved. First equation gives the relationship between the joint torque and the joint variable. The second equation is a differential equation that is used to find out the elastic displacement of the link. This differential equation is different from the standard Euler-Bernoulli beam equation and is non-linear. The effect of joint variable on the elastic displacement is considered. An analytical approach is given to obtain the solution of the differential equation. The response of the single link flexible manipulator system is obtained under a step torque input. Validation of the mathematical model is also done.