The subject of this paper is about the synthesis of the design parameters of a parallel manipulator with three RPS legs while considering the prescribed operation modes at the design stage. The synthesis is based on the Eu-ler parametrization and the results of primary decomposition. The design parameters and the coordinates of one RPS leg are initially defined to formulate the constraint equation associated with this leg. Seven classes of RPS legs are identified and the geometric properties of each class are highlighted. By selecting three different or identical classes of the RPS leg, a new 3-RPS parallel manipulator is proposed without specific values of the design parameters. The primary decomposition is computed over a set of three constraint equations. One or more Euler parameter(s) in the results of primary decomposition is(are) constrained to be equal to zero, which leads to particular types of operation modes. The methodology also provides new architectures of the 3-RPS parallel manipulators based on a classification of the RPS legs, that satisfy the prescribed operation mode.