Analysis and dimensional synthesis of the DELTA robot for a prescribed workspace M.A. Laribi a,b , L. Romdhane a, * , S. Zeghloul b a Laboratoire de Ge´nie Me´ canique, LAB-MA-05, Ecole Nationale d’Inge´nieurs de Monastir, Monastir 5019, Tunisia b Laboratoire de Me´canique des Solides, CNRS UMR 6610, Bd Pierre et Marie Curie, BP 30179, 86962 Futuroscope Chasseneuil cedex, France Received 23 September 2005; accepted 14 June 2006 Available online 10 October 2006 Abstract This paper deals with an optimal dimensional synthesis method of the DELTA parallel robot for a prescribed work- space. The objective function is based on the mathematical concept of the power of a point with respect to bounding con- straint surfaces. A genetic algorithm based method was used to solve this problem. The proposed method is simple and was shown to be effective in finding the dimensions of the DELTA robot having the smallest workspace containing a prespec- ified region in space. These dimensions were also determined in the case where the user defines a safety region, to avoid points in the prescribed workspace being on the boundary of the DELTA robot’s actual workspace. Ó 2006 Elsevier Ltd. All rights reserved. Keywords: DELTA parallel robot; Synthesis; Genetic algorithm; Workspace; Power of a point; Safety region 1. Introduction The Stewart platform mechanism is a fully parallel mechanism. In the general sense, each of these mecha- nisms consists of two platforms that are connected by six prismatic joints acting in parallel. One of the plat- forms is defined as the moving platform. It has six degrees of freedom relative to the other fixed platform, which is the ‘‘base’’. The analysis of this type of mechanisms has been the focus of much recent research. Stewart presented his platform in 1965 [20]. Since then, several authors [5,6] have proposed a large variety of designs. The interest in parallel manipulators (PM’s) arises from the fact that they exhibit high stiffness in nearly all configurations and a high dynamic performance. Recently, there has been a growing tendency to focus on par- allel manipulators with 3-translational degree of freedom (dof) [1,4,10,11,17,18,23,24]. In this case, the mobile platform can only translate, along the three cartesian axes, with respect to the base. The DELTA robot is one of the most famous translational parallel manipulators [4,25,21]. 0094-114X/$ - see front matter Ó 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.mechmachtheory.2006.06.012 * Corresponding author. Tel.: +216 73500244; fax: +216 73500514. E-mail address: lotfi.romdhane@enim.rnu.tn (L. Romdhane). Mechanism and Machine Theory 42 (2007) 859–870 www.elsevier.com/locate/mechmt Mechanism and Machine Theory