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The work is devoted to improving the reliability and manufacturability of mechatronic machine designs with parallel kinematics by replacing statically indeterminable manipulators with statically determinable mechanisms. A technique is proposed in which the design of statically determinable manipulators of technological mechatronic machines with parallel kinematics is performed by modifying the structure of prototypes and includes three steps: identifying and analyzing redundant links, eliminating redundant links, checking the correctness of eliminating redundant links. To determine the number of degrees of freedom of the mechanism, identify redundant links, and verify the solution, the authors use the proposed methodology for structural analysis of parallel structure mechanisms. In structural analysis, a manipulator is represented by a hierarchical structure and is considered as a parallel connection of elementary mechanisms with an open kinematic chain; as a kinematic chain consisting of leading and driven parts; as a set of links and kinematic pairs; as a kinematic connection of the output link and the rack. The article implements the following techniques for eliminating redundant links: mobility increase in kinematic pairs; introduction of unloading links and passive kinematic pairs to the kinematic chain; exclusion of extra links and pairs from the kinematic chain; increase in mobility in some kinematic pairs simultaneously with the exclusion of other kinematic pairs that have become superfluous. The authors developed several variants of structural schemes of self-aligning manipulators based on the Orthoglide mechanism, which retain the basic functional proper ties of the prototype. To increase the number of self-aligning mechanism diagrams, the redistribution of mobilities and links within the connecting kinematic chain and between connecting kinematic chains is used. The proposed methodics allow to determine the number of degrees of freedom of the mechanism, the number and type of redundant links, eliminate redundant links and, on an alternative basis, build structural diagrams of statically determinable mechanisms of technological mechatronic machines with parallel kinematics.

The aim of the study is to develop and analyse computer models for determining the natural frequencies and oscillation modes of a planar parallel manipulator using the Universal Mechanism software package. The article is devoted to solving the problem of ensuring vibration resistance of robot manipulators. The novelty of the work lies in developing and analysing a computer model of a planar manipulator, in which solid bodies form joints with the number of freedom degrees in relative motion from 1 to 4; in determining the influence of the mass and link elasticity, as well as the type of kinematic pairs on natural frequencies and oscillation modes. As a result of the study, computer models of a planar manipulator with three degrees of freedom are developed. For these models natural frequencies and vibration modes are determined, the values of natural frequencies are compared with the known analytical solution, the influence of inertial and elastic properties of links, the number of excess links to natural frequencies and oscillation modes are established. The proposed computer model can be used to determine with sufficient accuracy the natural frequencies and oscillation modes of a planar parallel manipulator; a planar manipulator with weightless elastic rods and an elastic drive has six natural oscillation frequencies. Natural forms retain their shape for different values of the inertial and elastic parameters of the links. Oscillations of the platform on these forms in the horizontal and vertical planes are independent. The values of natural frequencies, at which the platform oscillates in the horizontal motion of the mechanism links, depend on the ratio of the drive stiffness coefficients and the bending stiffness of the rods. The values of natural frequencies, at which the platform oscillates in the vertical plane, depend on the bending and torsional stiffness of the rods and on the type of kinematic pairs in the mechanism scheme.