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The application of the quaternionic elements for motion representation not only guarantees an orthonormal transformation but also results in the smallest variance and minimizes the acceleration peaks. The use of a unit quaternion avoids these phenomena, but there are dimensional limitations that make it impossible to translate the representation. This work presents a methodology for using dual quaternions in the analysis of robot kinematics using the Davies method, which avoids kinematic singularities and ensures the optimal torque profiles.<\/jats:p>","DOI":"10.1017\/s0263574714001982","type":"journal-article","created":{"date-parts":[[2014,7,24]],"date-time":"2014-07-24T10:08:15Z","timestamp":1406196495000},"page":"942-956","source":"Crossref","is-referenced-by-count":12,"title":["A new approach to singularity-free inverse kinematics using dual-quaternionic error chains in the Davies method"],"prefix":"10.1017","volume":"34","author":[{"given":"Andre Schneider","family":"de Oliveira","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Edson Roberto","family":"De Pieri","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ubirajara Franco","family":"Moreno","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Daniel","family":"Martins","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,7,24]]},"reference":[{"key":"S0263574714001982_ref23","first-page":"373","article-title":"Dual quaternions in spatial kinematics in an algebraic sense","volume":"32","author":"Akyar","year":"2008","journal-title":"Turk. 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