Аннотация:The truss of a manipulator designed for dynamic loads is a flat, statically determinate structure with masses distributed over the console nodes. An algorithm is proposed for deriving the dependence of the first oscillation frequency of the structure on the number of panels in an analytical form. The operators of the Maple symbolic mathematics system and the induction method are used for two parameters of the truss: the number of panels in the console and the number of panels in the vertical support rack-truss. The coefficients of the desired formula are found as common terms of the sequences of coefficients obtained as a result of solving a series of problems with an increasing number of panels in the truss. The formula of Dunkerley is used. The solution has high accuracy. For comparison, the traditional numerical method of solving the problem is used.