Lagrangian dynamics of flexible manipulators using angular velocities instead of transformation matrices

An approach that uses angular velocities and 3×3 rotation matrices to represent the link kinematics of flexible manipulators efficiently is presented. A truncated method expansion is used to model link deflection. A recursive computational procedure is presented that is similar to the Newton-Euler dynamics formulation for rigid manipulators. The full nonlinear inverse dynamic equations are calculated in recursive form for manipulators with an arbitrary number of flexible links. Kinematics are computed recursively from the base to the tip, and torques are computed on the return recursion. On the basis of this formulation, a fast and accurate simulation algorithm is presented. It is shown that this method offers significant improvement in computational speed without degrading numerical accuracy. The modeling accuracy of the method and some practical implementational problems are discussed.