This paper presents novel 2DOF and 3DOF closed-chain orientational manipulators, whose end-effector motion is actuated in a decoupled and homokinetic way by frame-located motors via holonomic transmissions based on constant-velocity couplings. The functioning of these couplings is investigated and the conditions applying for homokinetic transmission to be preserved during simultaneous motor drive are revealed and implemented. As a result, decoupled and configuration-independent relations between the motor rates and the time-derivatives of the variables describing the end-effector orientation are achieved. The attainment of analogous relations between the motor speeds and the components of the end-effector angular velocity is conversely proven to be unfeasible. The problem of singularities is furthermore examined, showing that input-output homokinesis is not a sufficient condition for a globally uniform kinetostatic behavior of the mechanism, which may, indeed, possibly reach uncertainty singular configurations. The connecting chains of the most typical constant-velocity couplings are analyzed, in order to obtain analytical expressions for the functions on which such singularities depend. The influence of design parameters is accordingly inspected. The results are valuable for the type and dimension synthesis of closed-chain wrists free from direct kinematic singularities, and characterized by simple kinematics and regular input-output kinetostatic relations.