In this paper, the conditions are found that give an opportunity to treat a manipulator link as an absolutely rigid body and to use the corresponding simplified model (as proposed in [1, 2]). The conditions that ensure that the deformations of links are small and that the motions of the source and simplified models of a manipulator are close to each other are considered as a criterion of admissibility of such a simplification. This problem reduces to the following problem of motion stability of a flexible manipulator. The set of all possible motions of the simplified model of a manipulator is introduced (a manipulator with absolutely rigid links) [1, 2]. The conditions that provide stable motion of the source model (a manipulator with deformable links) are found. It is established that, in the general case, this requires a sufficiently high level of viscosity of the deformation of the system and the appropriate degree of its stiffness. The specified problem is close to a wide class of problems of stability of an equilibrium position of flexible mechanical systems [3-13]. Its specific feature is the consideration of mechanical systems of the general form (that need not be conservative or dissipative) and the investigation of the stability of a wide variety of possible motions of the system (including its equilibrium positions). The paper also deals with the problem of the realization of constraints of mechanical systems [12, 13]. The case in point is the realization of the constraints corresponding to the concept of a rigid body.
