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Synthesis of a seven-link spatial statically determined mechanism without redundant (passive) connection with an additional moving link of a machine for processing parts, followed by an analytical study of its main structural and geometric parameters. Methodology.  An  analytical  research  method  was  used  based  on  the  geometric  and  structural synthesis  of  a  spatial  seven-link  statically  defined  mechanism  with  an  additional  movable  link  without redundant communication of the machine for processing parts; 3D modeling of the machine was performed in the SolidWorks 2016 computer-aided design system. Results.  On  the  basis  of  structural  synthesis,  the  design  of  a  seven-link  spatial  statically  defined mechanism  with  an  additional  movable link  of  the machine for processing  parts is  proposed,  there is  no redundant  connection  in  the  kinematic  chain  of  the  spatial  mechanism,  3D  modeling  of  the  machine  is performed  in  the  CAD  system  SolidWorks  2016.  Analytical  studies  of  the  main  geometric  and  design parameters of the developed machine are carried out. Scientific novelty. The relationship between various geometric parameters of the spatial seven-link statically determined mechanism is established, which makes it possible to calculate the optimal ratio of the lengths of the links of the mechanism to ensure the smooth functioning of the machine without jamming its spatial mechanism.  Practical significance. A new design of a machine for processing parts has been developed, based on  a  seven-section  spatial  statically  determined  mechanism  with  an  additional  moving  link  without redundant  communication.  Mathematical  dependences  are  obtained  for  calculating  its  basic  design  and geometric parameters. These dependencies can be used by the corresponding machine-building enterprises at the design stage of this type of equipment.

Synthesis  of  a  seven-link  statically  determined  spatial  hinge mechanism  with  an  additional movable crank link without redundant (passive) connection of the tumbling machine with a complex spatial movement of the working vessel with subsequent analytical study of its design and geometric parameters.  Methodology. The analytical method of research is used on the basis of geometric and structural synthesis of a spatial seven-link hinge mechanism with an additional movable crank link without redundant connection of the tumbling machine with a complex spatial movement of the working vessel. The machine was simulated in the SolidWorks-2016 computer-aided design system.  Tumbling  types  of  equipment  with  containers,  which  perform  a  different  character  of movement, are analyzed. On the basis of structural synthesis, the design of a seven-link statically defined spatial  mechanism  with  an  additional  movable  link,  a  tumbling  machine  crank,  in  which  the  working capacity performs a complex spatial movement, is proposed. Carried out 3D modeling of the machine in the CAD  system  SolidWorks  2016.  Analytical  studies  of  the  main  geometric  parameters  of  the  developed tumbling machine were carried out.  Scientific novelty. A relationship has been established between various geometric parameters of the synthesized seven-link statically determined spatial hinge mechanism, in particular, between the center-to-center length of the intermediate connecting rod (working capacity) and the length of the crank, which makes it  possible  to  calculate  the  necessary  ratios  of  the  lengths  of  the  links  of  the  mechanism  to  ensure  the functioning of the machine without jamming its spatial mechanism. Practical significance. A new design of a machine for processing parts has been developed, based on  a  seven-link  statically  determined  spatial  hinge  mechanism  with  an  additional  movable  crank  link. Mathematical dependences are obtained for calculating its basic design and geometric parameters. These dependencies can be used in the corresponding design bureaus of machine-building enterprises at the design stage of tumbling equipment with a complex spatial movement of working containers.

An approach is proposed to carry out multivariate calculations of the magnetic field distribution in the working gaps of a plate polygradient matrix of an electromagnetic separator, based on a combination of the advantages of two- and three-dimensional computer modeling. Two-dimensional geometric models of computational domains are developed, which differ in the geometric dimensions of the plate matrix elements and working air gaps. To determine the vector magnetic potential at the boundaries of two-dimensional computational domains, a computational 3D experiment is carried out. For this, three variants of the electromagnetic separator are selected, which differ in the size of the working air gaps of the polygradient matrices. For them, three-dimensional computer models are built, the spatial distribution of the magnetic field in the working intervals of the electromagnetic separator matrix and the obtained numerical values of the vector magnetic potential at the boundaries of the computational domains are investigated. The determination of the values of the vector magnetic potential for all other models is carried out by interpolation. The obtained values of the vector magnetic potential are used to set the boundary conditions in a computational 2D experiment. An approach to the choice of a rational version of a lamellar matrix is substantiated, which provides a solution to the problem according to the criterion of the effective area of the working area. Using the method of simple enumeration, a variant of the structure of a polygradient matrix with rational geometric parameters is selected. The productivity of the electromagnetic separator with rational geometric parameters of the matrix increased by 3–5 % with the same efficiency of extraction of ferromagnetic inclusions in comparison with the basic version of the device