The article describes the application of optimization algorithms for solving the problem of determining the workspace of a relative mechanism device, which includes a planar 3-RPS mechanism and a tripod module. Approximation sets of individual modules are used to approximate its workspace in the moving coordinate system. The considered method of approximating a solution set of nonlinear inequalities based on the concept of the non-uniform coverings, describes constraints on the robot geometric parameters. The exterior and interior approximations of the 3-RPS mechanism are obtained. Similarly, an approximation of the restrictions for the tripod module in the moving platform coordinate system is obtained. The constraints with a given accuracy are transferred to the coordinate system of the output using a three-dimensional binary array approximating the workspace. The workspace of the relative mechanism device was obtained on the basis of these results, taking into account the relative manipulation of modules and restrictions on the workpiece geometric parameters. Moving coordinate system is located in the center of the planar 3-RPS mechanism platform. © 2020, Springer Nature Switzerland AG.