This paper presents a new solution for an exoskeleton robotic system that is used for locomotor assistance in people with locomotor disabilities. As novel features of the present research, a novel structural solution of a plane-parallel kinematic chain, intended to be used as the leg of an exoskeleton robot, is proposed. A virtual prototype is made, on the basis of which kinematic and dynamic studies are carried out using ADAMS software for the dynamic analysis of multibody systems. The dynamic simulation of the exoskeleton is performed in two simulation situations: walking on a horizontal plane, as well as the simulation of motion assistance when climbing stairs. Following this analysis, it is noted that the robotic system achieves angular variations in the hip and knee joints similar to that of a human subject. As a result, the constructive solution is feasible, and the next stage of the study is to realize an experimental prototype by the rapid prototyping technique. The kinematic elements of the exoskeleton are designed to provide structural strength, to be easily manufactured by 3D printing and to be easy to assemble. For this purpose, the structural optimization is performed with the finite element method to eliminate stress concentrators. Finally, an experimental prototype of the exoskeleton robot is manufactured and assembled, whose motion is analyzed using ultrafast-camera-based video analysis.