Int J Adv Manuf Technol DOI 10.1007/s00170-015-7611-3 ORIGINAL ARTICLE Some investigations into the optimal dimensional synthesis of parallel robots Ridha Kelaiaia 1 · Abdelouahab Zaatri 2 · Olivier Company 3 · Lotfi Chikh 4 Received: 3 January 2015 / Accepted: 19 July 2015 © Springer-Verlag London 2015 Abstract In this paper, we will perform a comparison between two approaches of dimensional synthesis of par- allel robots. The first one concerns the single-objective optimization approach; in this case, the dimensional syn- thesis is expressed by taking into account only one per- formance criterion but enables to get a final solution if it exists. The second one concerns the multi-objective optimization approach; it enables to simultaneously take into account several performance criteria. However, this  Ridha Kelaiaia r.kelaiaia@univ-skikda.dz Abdelouahab Zaatri zaatri@hotmail.com Olivier Company company@lirmm.fr Lotfi Chikh chikhlotfi@hotmail.com 1 Laboratoire de G´ enie M´ ecanique et Mat´ eriaux, Universit´ e 20 aoˆ ut 1955-Skikda, PB N ◦ 26 Route Elhadaik, Skikda 21000, Algeria 2 Laboratory of Advanced Technologies, University of Constantine1, Constantine, Algeria 3 The Montpellier Laboratory of Informatics Robotics and Microelectronics, UMR 5506 CNRS-UM2 161 Rue Ada 34392 Montpellier Cedex 5, France 4 Fatronik France Tecnalia, Cap Omega Rond-point B. Franklin, 34960, Montpellier, France approach appears to provide a set of solutions instead of a single expected final solution which should directly enable to carry out the structural synthesis. In fact, the search of a single final solution is postponed to a further step where the designers have to impose and/or restrict certain param- eters. And we will establish if it is really necessary to make a multi-objective optimization approach or if a single- objective is sufficient to reach the objectives set in the specifications (user requirements). A discussion is proposed concerning the arising questions related to each approach and leading to the optimal dimensional synthesis. The PAR2 robot with two degree-of-freedom is used to exemplify the analysis and the comparison of the two approaches. The pro- posed comparison can be applied to any classes of parallel robots. Keywords Dimensional synthesis · Single-objective optimization · Multi-objective optimization · Criteria of performance · SQP · Genetic algorithm NSGA-II · PAR2 robot 1 Introduction For nowadays technology and industry, the topic of optimiz- ing the performances of parallel robots is of a paramount importance. However, these performances strongly and essentially depend on the parallel robot dimensions and they are sometimes antagonistic. This means that if one increases the velocity which is essential to improve the production pace, it may deteriorate the precision which ensures the quality of the final product. Conversely, any attempt to improve the precision may result in a slower velocity and may be only satisfied in some part of the workspace.