Parallel-structure mechanisms with four degrees of freedom and four kinematic chains are discussed. The synthesis of these manipulators were performed using a device of closed screw groups. This approach allows avoiding complex equations of synthesis and analysis of singularities. Kinematic chains may impose equal constraints or different constraints, and each may contain a drive. The main result of this article is the synthesis of a new parallel-structure mechanism and a screw analysis of constraints imposed by the kinematic chains.