Proceedings of the 11th World Congress in Mechanism and Machine Science August 18–21, 2003, Tianjin, China China Machinery Press, edited by Tian Huang Total and Partial Stationary Configurations for a 6-RUS Hunt-Type Parallel Manipulator Isidro Zabalza a,* , Jesús M. Pintor a , José J. Gil a , Javier Ros a and José M. Jiménez a,b º Mechanical, Energy and Materials Department, Public University of Navarra, Campus Arrosadia, 31006 Pamplona,Spain b Sports Training Technologies, S.L. Parque Empresarial Zuatzu, Edif. Easo, 2 nd floor, 20018 San Sebastián,Spain (*) Corresponding author, Fax: 34 948 169099, e-mail: izavi@unavarra.es Abstract: In this paper, the “stationary configurations” (SCs) of a 6-RUS parallel manipulator are analyzed and their use on industrial applications such as positioning mechanisms are discussed. This paper presents the SC concept from a geometric point of view and shows how they can be divided into two categories depending on whether the moving platform remains “practically fixed” under the simultaneous action of all the actuators or only a subset of them. The first category is denoted as “total stationary configurations” (TSCs) while the second group is called “partial stationary configurations” (PSCs). In this work it is calculated the number of TSCs and PSCs the parallel manipulator has. In addition, the spatial surfaces where the platform vertices must be positioned in order to draw the moving platform to either a TSC or a PSC are discussed. A computational method for determining the different TSCs is presented. Keywords: Stationary configurations, Parallel manipulators 1 Introduction Some planar and three-dimensional mechanisms show certain particular configurations in which the velocity of the output link of the kinematic chain vanishes independently of the velocity of the input link. As shown in Shigley and Uicker [1], the slider-crank mechanism and the crank-rocker configuration of the four-bar linkage are examples of such systems. In the slider-crank mechanism, two stationary configurations are reached when the crank and the connecting rod are aligned, similarly, in the crank- rocker mechanism, the stationary positions are obtained when the crank and the coupler are aligned. In this paper, those singular configurations are called “stationary configurations” (SCs). It must be noted that they are positions of the mechanical system in which the position of the output link is set with a very high precision. In those positions small perturbations in the position of the input element have significantly no effect on the position of the output link. It can be said that the output link’s position is “stationary” with regard to the position of the input element. Singular configurations in which the output element can move while the input element remains fixed can be found. In this paper, these configurations are called “uncertainty configurations” (UCs) and they are not object of this work. Since the introduction of the Stewart platform [2] (who mentioned the presence of “instability positions”) some authors as Hunt [3], Merlet [4], Gosselin and Angeles [5], Gosselin [6], Tahmasebi and Tsai [7], Zlatanov et al. [8], Basu and Ghosal [9], Karger and Husty [10] and Wohlhart [11] have addressed the problem of SCs and UCs in parallel manipulators with several degrees of freedom. For parallel manipulators with rotatory actuators, similar to the one object of this work, Pierrot et al. [12] tackled the problem of the singular configurations of the HEXA robot, Takeda et al. [13] determined the regions of the workspace where singular configurations of a parallel manipulator may be present, Benea [14] studied the singular configurations of the parallel manipulator 6-RUS. Zabalza [15] showed that the usual approach to singular configurations of the majority of researchers is to determine the UCs in order to eliminate them from the actual workspace of the parallel manipulator. Usually no special attention is paid to the existence of SCs or, in the better case, they are treated as if they were UCs. However, SCs may show important benefits in some industrial applications because these configurations are almost “stationary” with regard to the small perturbations that may appear in the actuators position. The benefits of working with SCs are shown in this paper. 2 SCs on 6-RUS Parallel Manipulator The 6-RUS parallel manipulator introduced by Hunt is depicted in figures 1 and 2. This parallel robot is composed of two triangular platforms, one of them fixed to the ground. On the fixed platform there are six rotating actuators (R) located on the edges of the triangle. These actuators are the input elements on which the motors are located. Each actuator is linked to the moving platform through a rod. In each rod, one tip is linked to the crank of an actuator through an universal joint (U) and the other tip is connected to the moving platform by means of a spherical joint (S), as depicted in figure 1. A couple of rods converge on each spherical joint of the moving platform. Figure 1 Hunt's 6-RUS parallel manipulator