Modeling of a spatial flexible manipulator with the telescopic motion of links.(Russian)Zbl 1137.93358

The aim of this paper is the design of a mathematical model for a manipulator with $$n$$ elastic links modeled by Euler-Bernoulli beams. One of the natural prototypes of such construction is a large turntable ladder. Upon defining the kinetic and potential energies, the author proposes an implicit expression of the Lagrange functional. Integro-differential equations of motion for this system are obtained on the base of Hamilton’s variational principle. Conditions for the existence of a stationary solution are studied, and a scheme for compensating the control forces and torques is proposed.

MSC:

 93C20 Control/observation systems governed by partial differential equations 34A37 Ordinary differential equations with impulses 74K10 Rods (beams, columns, shafts, arches, rings, etc.)