Kinematic Design of a 6-DOF Parallel Manipulator with Decoupled Translation and Rotation

A new three-limb, six-degree-of-freedom (DOF) parallel manipulator (PM), termed a selectively actuated PM (SA-PM), is proposed. The end-effector of the manipulator can produce 3-DOF spherical motion, 3-DOF translation, 3-DOF hybrid motion, or complete 6-DOF spatial motion, depending on the types of the actuation (rotary or linear) chosen for the actuators. The manipulator architecture completely decouples translation and rotation of the end-effector for individual control. The structure synthesis of SA-PM is achieved using the line geometry. Singularity analysis shows that the SA-PM is an isotropic translation PM when all the actuators are in linear mode. Because of the decoupled motion structure, a decomposition method is applied for both the displacement analysis and dimension optimization. With the index of maximal workspace satisfying given global conditioning requirements, the geometrical parameters are optimized. As a result, the translational workspace is a cube, and the orientation workspace is nearly unlimited.

Conceptual Design and Workspace Analysis of an Exechon-inspired Parallel Kinematic Machine

Inspired by the commercial application of the Exechon machine, this paper proposed a novel parallel kinematic machine (PKM) named Exe-Variant. By exchanging the sequence of kinematic pairs in each limb of the Exechon machine, the Exe-Variant PKM claims an arrangement of 2UPR/1SPR topology and consists of two identical UPR limbs and one SPR limb. The inverse kinematics of the 2UPR/1SPR parallel mechanism was firstly analyzed based on which a conceptual design of the Exe-Variant was carried out. Then an algorithm of reachable workspace searching for the Exe-Variant and the Exchon was proposed. Finally, the workspaces of two example systems of the Exechon and the Exe-Variant with approximate dimensions were numerically simulated and compared. The comparison shows that the Exe-Variant possesses a competitive workspace with the Exechon machine, indicating it can be used as a promising reconfigurable module in a hybrid 5-DOF machine tool system.

Kinematic Analysis and Dimensional Synthesis of Exechon Parallel Kinematic Machine for Large Volume Machining

A parallel kinematic machine (PKM) topology can only give its best performance when its geometrical parameters are optimized. In this paper, dimensional synthesis of a newly developed PKM is presented for the first time. An optimization method is developed with the objective to maximize both workspace volume and global dexterity of the PKM. Results show that the method can effectively identify design parameter changes under different weighted objectives. The PKM with optimized dimensions has a large workspace to footprint ratio and a large well-conditioned workspace, hence justifies its suitability for large volume machining.

Elastodynamic Modeling and Analysis for an Exechon Parallel Kinematic Machine

As a newly invented parallel kinematic machine (PKM), Exechon has attracted intensive attention from both academic and industrial fields due to its conceptual high performance. Nevertheless, the dynamic behaviors of Exechon PKM have not been thoroughly investigated because of its structural and kinematic complexities. To identify the dynamic characteristics of Exechon PKM, an elastodynamic model is proposed with the substructure synthesis technique in this paper. The Exechon PKM is divided into a moving platform subsystem, a fixed base subsystem and three limb subsystems according to its structural features. Differential equations of motion for the limb subsystem are derived through finite element (FE) formulations by modeling the complex limb structure as a spatial beam with corresponding geometric cross sections. Meanwhile, revolute, universal, and spherical joints are simplified into virtual lumped springs associated with equivalent stiffnesses and mass at their geometric centers. Differential equations of motion for the moving platform are derived with Newton's second law after treating the platform as a rigid body due to its comparatively high rigidity. After introducing the deformation compatibility conditions between the platform and the limbs, governing differential equations of motion for Exechon PKM are derived. The solution to characteristic equations leads to natural frequencies and corresponding modal shapes of the PKM at any typical configuration. In order to predict the dynamic behaviors in a quick manner, an algorithm is proposed to numerically compute the distributions of natural frequencies throughout the workspace. Simulation results reveal that the lower natural frequencies are strongly position-dependent and distributed axial-symmetrically due to the structure symmetry of the limbs. At the last stage, a parametric analysis is carried out to identify the effects of structural, dimensional, and stiffness parameters on the system's dynamic characteristics with the purpose of providing useful information for optimal design and performance improvement of the Exechon PKM. The elastodynamic modeling methodology and dynamic analysis procedure can be well extended to other overconstrained PKMs with minor modifications.