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Rigid-body displacements obtained by combining spatial translations and rotations around axes whose direction is fixed in the space are named Shoenflies’ motions. They constitute a 4-dimensional (4-D) subgroup, named Shoenflies’ subgroup, of the 6-D displacement group. Since the set of rotation-axis’ directions is a bi-dimensional space, the set of Shoenflies’ subgroups is a bi-dimensional space, too. Many industrial manipulations (e.g., pick-and-place on a conveyor belt) require displacements that belong to only one Schoenflies’ subgroup and can be accomplished by particular 4-degrees-of-freedom (4-DOF) manipulators (Shoenflies-motion generators (SMGs)). The first author has recently proposed a novel parallel SMG of type CRS-RRC1. Such SMG features a single-loop architecture with actuators on the base and a simple decoupled kinematics. Here, firstly, an organic review of the previous results on this SMG is presented; then, its design is addressed by considering its kinetostatic performances. The adopted design procedure optimizes two objective functions, one (global conditioning index (GCI)) that measures the global performance and the other (CI_min) that evaluates the worst local performance in the useful workspace. The results of this optimization procedure are the geometric parameters’ values that make the studied SMG have performances comparable with those of commercial SMGs. In addition, a realistic 3D model that solves all the manufacturing doubts with simple and cheap solutions is presented. Full article