The use of robots to perform tasks traditionally assigned to people leads to an improvement in the quality of their implementation, a reduction in the costs and risks associated with them. A typical example of this is the task of monitoring and examining hard-to-reach areas. The introduction of robots to solve such problems could bring a significant economic and social effect, allowing the automation of a number of complex, time-consuming and potentially dangerous tasks, such as the compilation and updating of maps and three-dimensional models of emergency sites, the collection of data on the state of the environment in areas, exposed to biological or radiation contamination, continuous monitoring of the state of the environment and sampling of air and soil. The paper considers one of the possible designs of such robots: a wheeled jumping robot, which consists of an acceleration module for jumping(used to for overcome obstacles), and a wheel platform, which allows the robot to use wheeled locomotion when moving over the surfaces with small irregularities. The advantages of such a combined system include higher maneuverability and higher speeds of movement, as well as a wider functionality in terms of the range of terrains suitable for movement. For this robot, a design scheme has been developed and two critical positions of the device are identified, which allows to formulate conditions that impose limitations on the geometric parameters of the body, the acceleration module and the wheels, and their mutual arrangement, in order to ensure operation of the robot in two modes: wheeled and jumping. The results of modeling are presented in the form of permissible ranges for the length and height of the body, as well as the maximum length of the acceleration module from the radius of the wheels and the location of their installation point, taking into account the capability of the acceleration module to do a complete rotation within the robot’s frame .