Optimization of H4 Parallel Manipulator Using Genetic Algorithm

Parallel manipulators have the advantages of high stiffness and low inertia compared to serial ones (Merlet, 2006). Most pick-and-place operations, including picking, packing and palletizing tasks; require four-degree-of-freedom (DOF), i.e. three translations and one rotation around a vertical axis (Company et al, 2003). A new family of 4-DOF parallel manipulator being called H4 that could be useful for high-speed, pick-and-place applications is proposed by Pierrot and Company (Pierrot & Company, 1999). This manipulator offers 3-DOF in translation and 1-DOF in rotation about a given axis. The H4 manipulator is useful for highspeed handling in robotics and milling in machine tool industry since it is a fully-parallel mechanism with no passive chain which can provide high performance in terms of speed and acceleration (Wu et al, 2006). Its prototype, built in the Robotics Department of LIRMM, can reach 10g accelerations and velocities higher than 5 m/s (Robotics Department of LIRMM). Pierrot et al. proved the efficiency of H4 serving as a high-speed pick-and-place robot (Pierrot et al, 2006). Corradini et al. evaluated the 4-DOFs parallel manipulator stiffness by two methods and compared the results (Coradini & Fauroux, 2003). Renaud et al. presented the kinematic calibration of a H4 robot using a vision-based measuring device (Renaud et al, 2003). Tantawiroon et al. designed and analyzed a new family of H4 parallel robots (Tantawiroon & Sangveraphunsiri, 2003). Poignet et al. estimated dynamic parameters of H4 with interval analysis (Poignet et al, 2003). Parallel manipulators suffer from smaller workspaces relative to their serial counterparts; therefore, many researchers addressed the optimization of their workspaces (Boudreau & Gosselin, 1999; Laribi et al, 2007). But optimization for such a purpose might lead to a manipulator with poor dexterity. To alleviate this drawback some others considered both performance indices and volume of workspace, simultaneously (Li & Xu, 2006; Xu & Li, 2006; Lara et al, 2010). This chapter deals with an optimal design of H4 parallel manipulator aimed at milling and Rapid-Prototyping applications with three degrees of freedom in translation and one in rotation. The forward and inverse kinematics of the manipulator are solved. The forward kinematics analysis of H4 leads to a univariate polynomial of degree eight. The workspace of the manipulator is parameterized using several design parameters. Some geometric constraints are considered in the problem, as well. Because of nonlinear discontinuous behaviour of the