The article describes the method of simple kinematic connections, which allows to organize at the matrix level the solution of problems of spherical trigonometry and angular orientation, which is reduced to the decomposition of the original matrix description of the problem into a system of simple matrices, the sequential solution of which individually or in combinations, allows to produce unambiguous results in the absence of restrictions in the original data. The mathematical apparatus of homogeneous transformations makes it possible to calculate the values of angular reversals in all intermediate joints, from the first to the n-1st, uniquely determining their required spatial orientation, as well as the spatial orientation of the end section of the switchgear.