The paper addresses the geometric synthesis of Orthoglide-type mechanism, a family of 3-DOF parallel manipulators for rapid machining applications, which combine advantages of both serial mechanisms and parallel kinematic architectures. These manipulators possess quasi-isotropic kinematic performances and are made up of three actuated fixed prismatic joints, which are mutually orthogonal and connected to a mobile platform via three parallelogram chains. The platform moves in the Cartesian space with fixed orientation, similar to conventional XYZ-machine. Three strategies have been proposed to define the Orthoglide geometric parameters (manipulator link lengths and actuated joint limits) as functions of a cubic workspace size and dextrous properties expressed by bounds on the velocity transmission factors, manipulability or the Jacobian condition number. Low inertia and intrinsic stiffness have been set as additional design goals expressed by the minimal link length requirement. For each design strategy, analytical expressions for computing the Orthoglide parameters are proposed. It is showed that the proposed strategies yield Pareto-optimal solutions, which differ by the kinematic performances outside the prescribed Cartesian cube (but within the workspace bounded by the actuated joint limits). The proposed technique is illustrated with numerical examples for the Orthoglide prototype design.
Deep Dive into Design Strategies for the Geometric Synthesis of Orthoglide-type Mechanisms.
The paper addresses the geometric synthesis of Orthoglide-type mechanism, a family of 3-DOF parallel manipulators for rapid machining applications, which combine advantages of both serial mechanisms and parallel kinematic architectures. These manipulators possess quasi-isotropic kinematic performances and are made up of three actuated fixed prismatic joints, which are mutually orthogonal and connected to a mobile platform via three parallelogram chains. The platform moves in the Cartesian space with fixed orientation, similar to conventional XYZ-machine. Three strategies have been proposed to define the Orthoglide geometric parameters (manipulator link lengths and actuated joint limits) as functions of a cubic workspace size and dextrous properties expressed by bounds on the velocity transmission factors, manipulability or the Jacobian condition number. Low inertia and intrinsic stiffness have been set as additional design goals expressed by the minimal link length requirement. For eac
Parallel kinematic machines (PKM) are commonly claimed to offer several advantages over their serial counterparts, such as high structural rigidity, better payload-to-weight ratio, high dynamic capacities and high accuracy [1][2][3]. Thus, they are prudently considered as promising alternatives for high-speed machining and have gained essential attention of a number of companies and researchers. Since the first prototype presented in 1994 during the IMTS in Chicago by Gidding&Lewis (the VARIAX), many other parallel manipulators have appeared. However, most of the existing PKM still suffer from two major drawbacks, namely, a complex workspace and highly non-linear input/output relations [4,5].
For most PKM, the Jacobian matrix, which relates the joint rates to the output velocities, is 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 disadvantage for machining applications [6,7], which require regular workspace shape and acceptable kinetostatic performances throughout. In milling applications, for instance, the machining conditions must remain constant along the whole tool path [8].
Nevertheless, in many research papers, this criterion is not taken into account in the algorithmic methods used for the optimization of the workspace volume [9,10].
In contrast, for the conventional XYZ-machines, the tool motion in any direction is linearly related to the motions of the actuated axes. Also, the performances are constant throughout the Cartesian parallelepiped workspace. The only drawback is inherent to the serial arrangement of the links, which causes poor dynamic performances. So, in recent years, several new parallel kinematic structures have been proposed. In particular, a 3-dof translational mechanism with gliding foot points was found in three separate works to be fully isotropic throughout the Cartesian workspace [11][12][13]. Although this manipulator behaves like the conventional Cartesian mechanism, its legs are rather bulky to assure stiffness. The latter motivates further research in PKM architecture that seeks for compromise solutions, which admit a partial isotropy in favour of other manipulator features.
One of such compromise solutions is the Orthoglide proposed by Wenger and Chablat [14], which was derived from a Delta-type architecture with three fixed linear joints and three articulated parallelograms. As follows from the previous works, this manipulator possesses good (almost isotropic) kinetostatic performances and also has some technological advantages, such as (i) symmetrical design; (ii) quasi-isotropic workspace; and (iii) low inertia effects [15]. In a previous Pashkevich, Wenger, Chablat Design Strategies for the Geometric Synthesis of Orthoglide-type Mechanisms 28/08/07 2 work, the Orthoglide was optimised with respect to the Jacobian matrix conditioning and transmission factor limits throughout a prescribed Cartesian workspace [16]. This paper further contributes to the Orthoglide kinematic synthesis and focuses on the comparison of different design strategies and inherited criteria. It proposes a systematic design procedure to define the manipulator geometric parameters (the actuated joint limits and the link lengths) as function of the prescribed cubic workspace size and performances measure bounds. The reminder of the paper is organized as follows. Section 2 briefly describes the Orthoglide kinematics and defines the design goals. Section 3 investigates the manipulator performances through the workspace. Section 4 deals with the design of the dextrous workspace with bounded manipulability, condition number and velocity transmission factors. Section 5 focuses on defining the largest cube inscribed in the dextrous workspace. Section 6 illustrates the proposed design strategies by numerical examples and also contains some discussions. And, finally, Section 7 summarises the main contributions of the paper.
The kinematic architecture of the Orthoglide is shown in Fig. 1. It consists of three identical parallel chains that may be formally described as PRP a R, where P, R and P a denote the prismatic, revolute, and parallelogram joints respectively. The mechanism input is made up of three actuated orthogonal prismatic joints. The output machinery (with a tool mounting flange) is connected to the prismatic joints through a set of three parallelograms, so that it is restricted for translational movements only. Because of its symmetrical structure, the Orthoglide can be presented in a simplified model, which consists of three bar links connected by spherical joints to the tool centre point at one side and to the corresponding prismatic joints at another side (Fig. 2a).
Thus, if the origin of a reference frame is located at the intersection of the prismatic joint axes and , see Fig. 2b.
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