Solution schemes for the system equations of flexible robots

Abstract

Abstract In this work, a method for generating the dynamic equations of flexible robots with open‐chain linkage mechanisms is developed. A general transformation matrix associated with the elastic deformation is introduced. In determining the elastic response, a method of separation of variables and the Galerkin's approach are suggested for the boundary‐value problem with time‐dependent boundary conditions. Besides the formulation scheme, the present work also studies the difficulty of dealing with the inverse kinematic problem, in which the unknowns involve the rigid‐body displacements and the elastic deflections. Finally, the ideas presented here have been implemented in a computer simulation, and the formulation of the boundary‐value problem has been employed to obtain the equations of motion of a flexible robot. Simulation results are presented.