{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,6]],"date-time":"2026-01-06T13:27:51Z","timestamp":1767706071282,"version":"build-2065373602"},"reference-count":29,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2018,9,15]],"date-time":"2018-09-15T00:00:00Z","timestamp":1536969600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100007109","name":"Universit\u00e0 degli Studi di Ferrara","doi-asserted-by":"publisher","award":["FAR 2017"],"award-info":[{"award-number":["FAR 2017"]}],"id":[{"id":"10.13039\/501100007109","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003593","name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico","doi-asserted-by":"publisher","award":["232250\/2014-6"],"award-info":[{"award-number":["232250\/2014-6"]}],"id":[{"id":"10.13039\/501100003593","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Robotics"],"abstract":"<jats:p>Rigid-body displacements obtained by combining spatial translations and rotations around axes whose direction is fixed in the space are named Shoenflies\u2019 motions. They constitute a 4-dimensional (4-D) subgroup, named Shoenflies\u2019 subgroup, of the 6-D displacement group. Since the set of rotation-axis\u2019 directions is a bi-dimensional space, the set of Shoenflies\u2019 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\u2019 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 (CImin) that evaluates the worst local performance in the useful workspace. The results of this optimization procedure are the geometric parameters\u2019 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.<\/jats:p>","DOI":"10.3390\/robotics7030055","type":"journal-article","created":{"date-parts":[[2018,9,17]],"date-time":"2018-09-17T10:42:20Z","timestamp":1537180940000},"page":"55","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Performance-Based Design of the CRS-RRC Schoenflies-Motion Generator"],"prefix":"10.3390","volume":"7","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3925-3016","authenticated-orcid":false,"given":"Raffaele","family":"Di Gregorio","sequence":"first","affiliation":[{"name":"Department of Engineering, University of Ferrara, 44100 Ferrara, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mattia","family":"Cattai","sequence":"additional","affiliation":[{"name":"Department of Engineering, University of Ferrara, 44100 Ferrara, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1858-541X","authenticated-orcid":false,"given":"Henrique","family":"Simas","sequence":"additional","affiliation":[{"name":"Raul Guenther laboratory of Applied Robotics, Department of Mechanical Engineering, Federal University of Santa Catarina, Florian\u00f3polis, SC 88040-900, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,9,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"719","DOI":"10.1016\/S0094-114X(98)00051-2","article-title":"The Lie group of rigid body displacements, a fundamental tool for mechanism design","volume":"34","year":"1999","journal-title":"Mech. 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