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Solution schemes for the system equations of flexible robots

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.