Solution of the problems of synthesis of spatial five-bar hinged mechanisms with two degrees of freedom task considering the angle of transmission and definition of conditions of existence of cranks is given in the paper. A possibility of movement of the designed mechanism without seizure that is depended on shape and sizes of the mechanism links is envisaged. At solution of the problem of synthesis first are determined sizes of the mechanism couples considering the angle of transmission and then are determined the limits of variation of the angle of transmission depending on sizes of the mechanism links. The conditions are ascertained which must be met by sizes of the spatial five-bar mechanism links so that the two links adjoining to the frame are crank (theorem on existence of cranks in the spatial five-bar mechanism).
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