Fully inverse dynamics of very flexible beam using a finite element approach and lagrange formulation

The problem of fully inverse dynamics of a very flexible planar Bernouli-Euler beam, where all six boundary conditions are imposed on one end, was analyzed and discussed. The problem was solved by using a finite element approach and Lagrange formulation. Theoretically, the solution of a beam divided into n finite elements requires 2n time derivatives of the boundary condition functions. In practice, a much smaller number of time derivatives was required for an accurate solution. The fully inverse solution was verified by comparing the elastic curves of the beam for both direct and inverse dynamics. The developed model can be applied for remote sensing of forces and motion, where accurate measurements of both forces and motion at one end of a beam enable the reconstruction of the elastic curve of the beam and extract the location and the loads applied on the other end. Another application of the proposed model may be in the field of robotics, by predicting the input needed at one end of a flexible arm in order to perform a specific task at the other end of the arm.