This paper addresses the architecture optimization of a 3-DOF translational parallel mechanism designed for machining applications. The design optimization is conducted on the basis of a prescribed Cartesian workspace with prescribed kinetostatic performances. The resulting machine, the Orthoglide, features three fixed parallel linear joints which are mounted orthogonally and a mobile platform which moves in the Cartesian x-y-z space with fixed orientation. The interesting features of the Orthoglide are a regular Cartesian workspace shape, uniform performances in all directions and good compactness. A small-scale prototype of the Orthoglide under development is presented at the end of this paper.
P ARALLEL kinematic machines (PKM) are commonly claimed to offer several advantages over their serial counterparts, like high structural rigidity, high dynamic capacities and high accuracy [1], [2]. Thus, PKM are interesting alternative designs for high-speed machining applications. This is why parallel kinematic machine-tools attract the interest of more and more researchers and companies. Since the first prototype presented in 1994 during the IMTS in Chicago by Gidding&Lewis (the VARIAX), many other prototypes have appeared.
However, the existing PKM suffer from two major drawbacks, namely, a complex workspace and highly non linear input/output relations. For most PKM, the Jacobian matrix which relates the joint rates to the output velocities is not constant and not isotropic. Consequently, the performances e.g. maximum speeds, forces, accuracy and rigidity) vary considerably for different points in the Cartesian workspace and for different directions at one given point. This is a serious drawback for machining applications [1], [3], [4]. To be of interest for machining applications, a PKM should preserve good workspace properties, that is, regular shape and acceptable kinetostatic performances throughout. In milling applications, the machining conditions must remain constant along the whole tool path [5]. In many research papers, this criterion is not taken into account in the algorithmic methods used for the optimization of the workspace volume [6], [7].
Most industrial 3-axis machine-tools have a serial kinematic architecture with orthogonal linear joint axes along the x, y Damien Chablat and Philippe Wenger are with the Institut de Recherche en Communications et Cybernétique de Nantes (IRCCyN), 1, rue de la Noë, 44321 Nantes, France, email: Philippe.Wenger@irccyn.ec-nantes.fr and z directions. Thus, the motion of the tool in any of these directions is linearly related to the motion of one of the three actuated axes. Also, the performances are constant throughout the Cartesian workspace, which is a parallelepiped. The main drawback is inherent to the serial arrangement of the links, namely, poor dynamic performances. The purpose of this paper is to design a translational 3-axis PKM with the advantages of serial machine tools but without their drawbacks. Starting from a Delta-type architecture with three fixed linear joints and three articulated parallelograms, an optimization procedure is conducted in which two criteria are used successively, (i) the conditioning of the Jacobian matrix of the PKM [8], [9], [10], [11] and (ii) the manipulability ellipsoid [12]. The first criterion leads to an isotropic architecture that features a configuration where the tool forces and velocities are equal in all directions. The second criterion makes it possible to define the actuated joint limits and the link lengths with respect to a desired Cartesian workspace size and prescribed limits on the transmission factors. The resulting PKM, the Orthoglide, has a Cartesian workspace shape that is close to a cube whose sides are parallel to the planes xy, yz and xz respectively. A systematic design procedure is proposed to define the geometric parameters as function of the size of a prescribed cubic Cartesian workspace and bounded velocity and force transmission factors throughout.
Next section presents the existing PKM. The design parameters and the kinematics of the mechanism to be optimized are reported in Section 3. Section 4 is devoted to the design procedure of the Orthoglide and the presentation of the prototype.
Most existing PKM can be classified into two main families. The PKM of the first family have fixed foot points and variable length struts. These PKM are generally called “hexapods” when they have 6 degrees of freedom. Hexapods have a Stewart-Gough parallel kinematic architecture. Many prototypes and commercial hexapod PKM already exist like the VARIAX (Gidding&Lewis), the CMW300 (Compagnie Mécanique des Vosges), the TORNADO 2000 (Hexel), the MIKROMAT 6X (Mikromat/IWU), the hexapod OKUMA (Okuma), the hexapod G500 (GEODETIC). In this first family, we find also hybrid architectures with a 2-axis wrist mounted in series to a 3-DOF “tripod” positioning structure (e.g. the TRICEPT from Neos-Robotics [13]). Since many machining tasks require only 3 translational degrees of freedom, several 3-axis translational PKM have been proposed. There are several ways to design such mechanisms [20], [14], [15], [16]. In the first family, we find the Tsai mechanism and its variants. In these mechanisms, the mobile platform is connected to the base by three extensible limbs with a special arrangement of the universal joints that restrains completely the orientation of the mobile platform [18], [19].
The PKM of the second family have fixed length struts with moveable foot points gliding on fixed linear joints. In this category we find the HEXAGLIDE (ETH Zürich) which features six parallel (also in the geometrical sense) and
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