Schoenflies-motion generators (SMGs) are 4-degrees-of-freedom (dof) manipulators whose end effector can perform translations along three independent directions and rotations around one fixed direction (Schoenflies motions). Such motions constitute the 4-dimensional (4-D) Schoenflies subgroup of the 6-D displacement group. The most known SMGs are the serial robots named SCARA. Pick-and-place tasks are typical industrial applications that can be accomplished by SMGs. Over the SCARA, lower-mobility parallel manipulators (PMs) have been proposed as SMGs. Here, a novel type of SMG with parallel architecture is presented together with its kinematics analysis. The proposed SMG has a single-loop not-overconstrained architecture, actuators on or near the base and decoupled kinematics.