This article addresses parallel manipulators with fewer than six degrees of freedom, whose employ may prove valuable in those applications in which a higher mobility is uncalled-for. In particular, a family of 3-dof manipulators containing only revolute joints or at the most revolute and prismatic ones is studied. Design and assembly conditions sufficient to provide the travelling platform with a pure translational motion are determined and two sub-families that fulfill the imposed constraint are found: one is already known in the literature, whilst the other is original. The new architecture does not exhibit rotation singularities, i.e. configurations in which the platform gains rotational degrees of freedom. A geometric interpretation of the translation singularities is provided.