Recursive Lagrangian Dynamics of Flexible Manipulator Arms

TLDR

The authors derive nonlinear equations of motion for flexible manipulator arms with rotary joints, modeling joint and link kinematics using 4×4 transformation matrices and small‑deflection shape assumptions, and present the resulting scalar and matrix expressions for implementation. The formulation demonstrates improved computational efficiency relative to rigid‑link models reported in the literature.

Abstract

Nonlinear equations of motion are developed for flexible manipulator arms consisting of rotary joints that connect pairs of flexible links. Kinematics of both the rotary-joint mo tion and the link deformation are described by 4 X 4 trans formation matrices. The link deflection is assumed small so that the link transformation can be composed of summations of assumed link shapes. The resulting equations are pre sented as scalar and 4 X 4 matrix operations ready for pro gramming. The efficiency of this formulation is compared to rigid-link cases reported in the literature.