Parallel Kinematic Machine Research Articles

A New 4-DOF Fully Parallel Robot With Decoupled Rotation for Five-Axis Micromachining Applications

We present a novel 4-DOF (degrees of freedom) parallel robot designed for five-axis micromachining applications. Two of its five telescoping legs operate simultaneously, thus acting as an extensible parallelogram linkage, and in conjunction with two other legs control the position of the tooltip. The fifth leg controls the tilt of the end-effector (a spindle), while a turntable fixed at the base of the robot controls the swivel of the workpiece. The robot is capable of tilting its end-effector up to 90 deg, for any tooltip position. In this paper, we study the mobility of the new parallel kinematic machine (PKM), describe its inverse and direct kinematic models, then study its singularities, and analyze its workspace. Finally, we propose a potential mechanical design for this PKM utilizing telescopic actuators as well as the procedure for optimizing it. In addition, we discuss the possibility of using constant-length legs and base-mounted linear actuators in order to increase the volume of the workspace.

Optimization design for a compact redundant hybrid parallel kinematic machine

Abstract Designing a machine tool that simultaneously satisfies the requirements of high rigidity, large dexterous workspace and small footprint is challenging. This paper proposed a redundant hybrid manipulator as a machine tool with these features. The design attempted to integrate the advantages of a PKM (parallel kinematic mechanism), SKM (serial kinematic mechanism) and redundancy mechanism. The geometric parameters of the manipulator were elaborately tuned to overcome intrinsic and extrinsic singularities with an optimal machining plane. High-accuracy and complex-shape machine results have been experimentally verified. The advantage is the ability to shorten the required strokes of the linear actuators effectively. This change not only improves the performance in terms of rigidity, accuracy and dynamics of the entire mechanism but also reduces the cost of the materials and the performance ratio. The second is to decrease the overall machinery-footprint-to-workspace ratio and lower the manufacturing cost via occupied floor space reduction and layout flexibility of the production line.

Reconfigurability Analysis of a Class of Parallel Kinematics Machines

A novel parallel kinematics machine (PKM) stemming from the 3-SRU (spherical-revolute-universal) under-actuated joints topology is presented in this paper. The concept here proposed takes advantage of a reconfigurable universal joint obtained by locking, one at a time, different rotations of a spherical pair. Such local reconfiguration causes a slight, yet crucial, modification of the robot legs mobility which is enough to provide the end-effector with different kinds of motion. In particular, the kinematic chain is converted to two different 3-URU architectures (universal-spherical-universal) able to provide the moving platform with essentially different mobilities. The paper is dedicated at formally demonstrating the motion capabilities offered by such parallel architectures. To this aim, the first part of the paper describes the mechanical structures and formalizes the kinematic problem through appropriate sets of polynomial equations. Then, an analysis of the equations is proposed to uniquely identify the mobilities of the moving platform. At last, a concept design is proposed for the reconfigurable spherical platform.

A Visual Servoing Strategy Under Limited Frame Rates for Planar Parallel Kinematic Machines

In this manuscript, an affordable alternative to control parallel kinematic machines is proposed based in a high-authority/low-authority control strategy. The high-authority loop is implemented using a model-based Cartesian control strategy. This feedback loop exploits a Pose-Based Visual Servo (PBVS) using an eye-to-hand limited frame rate camera. The low-authority loop is implemented using an independent space joint space control strategy. This proposal is experimentally compared with the Cartesian space computed torque control and with the independent joint space control strategies. The experimental campaign is carried out for tracking-trajectory problems using a planar 3R RR parallel manipulator. The experimental results demonstrate that the proposal can achieve results that are more accurate without increasing the manipulator’s energy consumption when compared to the use of the independent joint space control strategy. For a predefined square trajectory, a reduction of 4.9% and 24.5% was achieved in the root mean square error of the linear and angular positions, respectively.

Elastodynamic Optimization of a 5-DoF Parallel Kinematic Machine Considering Parameter Uncertainty

Geometric errors, vibration, and elastic deformation are the main causes for inaccuracy of parallel kinematic machines (PKMs). Instead of tackling these inaccuracies after the prototype has been built, this paper proposes a design optimization method to minimize vibration and deformation considering the effects of geometric errors before constructing the PKM. In this paper, geometric errors are described as parameter uncertainty because they are unknown in design stage. A five degree-of-freedom (DoF) PKM is taken to exemplify this method. Elastodynamic model is first formulated by a step-by-step strategy. On this basis, dynamic performances, including natural frequency, elastic deformation, and maximum stress, are analyzed. These analytical results are verified by finite-element simulation and experiment. Then, the necessity of concerning parameter uncertainty in optimization is addressed. Next, parameter uncertainty is added to the formulation of objectives and constraints by Monte Carlo simulation and response surface method. Finally, elastodynamic optimization of the 5-DoF PKM is implemented to rebuild a prototype which is robust to geometric errors and has minimal vibration and deformation. The proposed method can also be applied to accuracy improvement of any machines in practical applications.

An experimental investigation of control parameters in five-axis hybrid parallel kinematic machine in milling of aluminium 6061-T3

Surface roughness is an important factor in predicting performance of any machining operation. The experiment has been performed in milling a V-shaped pocket on aluminium 6061-T3 by Exechon parallel kinematic machine using carbide tool. Three different segmented surfaces are selected on V-block and the effect of control parameters were investigated over it. In this research, Taguchi method is used to identify the optimal combination of spindle speed, feed, and depth of cut. To analyse the effect of the control parameters for fine surface finish, Taguchi L9 orthogonal array, signal-to-noise (S/N) ratio and analysis of variance (ANOVA) are employed. Control parameters such as high spindle speed, low feed rate and low depth of cut plays a decisive role in the result of surface roughness. Also, the obtained results from PKM were compared to that of CNC machining, and the surface topologies were examined under optical and scanning electron microscope.

Effect of machining parameters over surface roughness in contour milling of aluminium 2024-T351 using 5-axis parallel kinematic machine

Surface roughness is reduced by optimising the machining parameters. This research analyses the effect of machining parameters on surface quality of aluminium 2024 T351 in milling of semi-circular pocket with carbide tool on 5-axis hybrid parallel kinematic machine (HPKM). Three different segmented surfaces were selected on semi-circular pocket and investigated the influence of machining parameters. The selected parameters are spindle speed, feed rate and depth of cut. Investigation of this study results in the optimum parameters that could produce good surface finish. The effect of these cutting parameters is evaluated using L9 Taguchi orthogonal array, s/n ratio, analysis of variance (ANOVA). Based on the result analysis, good surface finish can be obtained at high cutting speed, low feed rate, and low depth of cut. Also, the maximum influence of feed rate among the selected surface segments was ascertained.

Self-Configuration Machining capability of a 4-DOF parallel kinematic machine tool with nonsingular workspace for Intelligent Manufacturing Systems

Abstract Machining accuracy is affected by varying kinematic properties and singularities of parallel mechanisms inside their workspace. In this research an asymmetrical four degree of freedom parallel kinematic machine tool with rotational capability around one of its horizontal axis, developed for milling processes is investigated for its machining capability. Surface roughness of Al5083 alloy is analysed after machining on various domains of available workspace. Linear interpolation was used in creating tool paths to avoid kinematic non linearity of parallel mechanisms and experiments are conducted using Response Surface Methodology (RSM) and gathered data is modelled by linear regression. Surface roughness results demonstrated the high machining performance of the mechanism inside available workspace.

An experimental investigation of control parameters in five-axis hybrid parallel kinematic machine in milling of aluminium 6061-T3

An experimental investigation of control parameters in five-axis hybrid parallel kinematic machine in milling of aluminium 6061-T3

A smooth and undistorted toolpath interpolation method for 5-DoF parallel kinematic machines

Abstract Comparing with classical serial machining center, Parallel Kinematic Machines (PKMs) are displaying superiority in coupling rotational motion control, for which the tilt-and-torsion (T&T) angle was developed as a powerful research tool. However, this rotation modality is not widely used in manufacturing scenarios due to the lack of associated interpolation algorithm, which therefore impedes the application of PKMs. In this work, a modified spline method is designed to interpolate 5-axis PKM toolpath described by T&T angle. Quintic splines are constructed in both positional and orientational trajectories for smoothness requirement, and the interpolation quality is further reinforced by anti-distortion strategy and coordinating reparameterization spline. Simulation based on actual toolpath and machine model prove that the proposed algorithm realizes the smoothness of acceleration in all toolpath components, decreases the shock to the system, and reduces the surface error after cutting. The results indicate that the interpolation method in this paper can provide new algorithm for PKMs with T&T angle and promote their development in the industrial manufacturing and production.

Conceptual design and kinetostatic analysis of a modular parallel kinematic machine-based hybrid machine tool for large aeronautic components

Abstract Precision manufacturing and intelligent assembly in the aeronautic industry pose new challenges for the design of Flexible Manufacturing Systems (FMSs). To address these issues, a modular Parallel Kinematic Machine (PKM)-based hybrid machine tool is proposed. The 5-axis hybrid machine tool is conceptually designed by integrating 3-Degree-Of-Freedom (DOF) over-constrained PKMs with a 2-DOF serial mechanism including a unique double-circumferential guideway. By integrating accessory devices, the proposed machine provides a promising alternative solution to building a novel FMS for the flexible manufacturing requirements of larger arc-shaped aeronautic components. A kinematic model is established to conduct an inverse kinematic analysis to predict the reachable workspace by using a ‘sliced partition’ searching algorithm. To evaluate the kinetostatic performance of the hybrid machine tool, a modified kinetostatic model is established by including the compliances of all joints and limb structures. The prediction accuracy of the proposed kinetostatic model is validated by numerical simulations. Two kinetostatic performance indexes, the average reaction index and the average displacement index, are formulated and applied to reveal the gravity-caused joint reactions and elastic displacement of the hybrid machine tool, respectively. The analyses show that the kinetostatic performances of the machine are heavily affected by gravity; thus, gravity must be considered during the early design stage. Notably, with minor revisions, the proposed kinetostatic model and performance indexes can be applied to other hybrid mechanical systems to efficiently evaluate their kinetostatic performances.

Dynamic Performance Evaluation of a Redundantly Actuated and Over-constrained Parallel Manipulator

This paper presents a redundantly actuated and over-constrained 2RPU-2SPR parallel manipulator with two rotational and one translational coupling degrees of freedom. The kinematics analysis is firstly carried out and the mapping relationship of the velocity, acceleration and the independent parameters between the actuator joint and the moving platform are deduced by using the vector dot product and cross product operation. By employing d’Alembert’s principle and the principle of virtual work, the dynamics equilibrium equation is derived, and the simplified dynamics mathematical model of the parallel manipulator is further derived. Simultaneously, the generalized inertia matrix which can characterize the acceleration performance between joint space and operation space is further separated, and the performance indices including the dynamics dexterity, inertia coupling characteristics, energy transmission efficiency and driving force/torque balance are introduced. The analysis results show that the proposed redundantly actuated and over-constrained 2RPU-2SPR parallel manipulator in comparison with the existing non-redundant one has better dynamic comprehensive performance, which can be demonstrated practically by the successful application of the parallel kinematic machine head module of the hybrid machine tool.

Kinematics Analysis of a Class of Spherical PKMs by Projective Angles

This paper presents the kinematics analysis of a class of spherical PKMs Parallel Kinematics Machines exploiting a novel approach. The analysis takes advantage of the properties of the projective angles, which are a set of angular conventions of which their properties have only recently been presented. Direct, inverse kinematics and singular configurations are discussed. The analysis, which results in the solution of easy equations, is developed at position, velocity and acceleration level.

Elastodynamic-model-based stiffness analysis of a 6-RSS PKM

An elastodynamic model for a 6-RSS parallel kinematic machine (PKM) is established by combining the virtual joint method (VJM) and the finite element method (FEM). According to the proposed elastodynamic model, stiffness matrix of the system is derived, based on which static stiffness of the system is analyzed. In order to validate the proposed model, finite element analysis is conducted. Results show that the proposed model is relatively accurate and can be used to evaluate rigidity of the 6-RSS PKM. Two stiffness indices are proposed for the convenience of analysis. Stiffness distributions as well as parametric analysis are conducted to offer significant guidance on the trajectory planning and structural optimization at the early design stage.

Stiffness Characteristics Analysis of a Novel 3- DOF Parallel Kinematic Machine Tool

Stiffness Characteristics Analysis of a Novel 3- DOF Parallel Kinematic Machine Tool

Error modeling and sensitivity analysis of a novel 5-degree-of-freedom parallel kinematic machine tool

5-Degree-of-freedom parallel kinematic machine tools are always attractive in manufacturing industry due to the ability of five-axis machining with high stiffness/mass ratio and flexibility. In this article, error modeling and sensitivity analysis of a novel 5-degree-of-freedom parallel kinematic machine tool are discussed for its accuracy issues. An error modeling method based on screw theory is applied to each limb, and then the error model of the parallel kinematic machine tool is established and the error mapping Jacobian matrix of 53 geometric errors is derived. Considering that geometric errors exert both impacts on value and direction of the end-effector’s pose error, a set of sensitivity indices and an easy routine for sensitivity analysis are proposed according to the error mapping Jacobian matrix. On this basis, 10 vital errors and 10 trivial errors are identified over the prescribed workspace. To validate the effects of sensitivity analysis, several numerical simulations of accuracy design are conducted, and three-dimensional model assemblies with relevant geometric errors are established as well. The simulations exhibit maximal −0.10% and 0.34% improvements of the position and orientation errors, respectively, after modifying 10 trivial errors, while minimal 65.56% and 55.17% improvements of the position and orientation errors, respectively, after modifying 10 vital errors. Besides the assembly reveals an output pose error of (0.0134 mm, 0.0020 rad) with only trivial errors, while (2.0338 mm, 0.0048 rad) with only vital errors. In consequence, both results of simulations and assemblies validate the correctness of the sensitivity analysis. Moreover, this procedure can be extended to any other parallel kinematic mechanisms easily.

A Finite and Instantaneous Screw Based Approach for Topology Design and Kinematic Analysis of 5-Axis Parallel Kinematic Machines

Unifying the models for topology design and kinematic analysis has long been a desire for the research of parallel kinematic machines (PKMs). This requires that analytical description, formulation and operation for both finite and instantaneous motions are performed by the same mathematical tool. Based upon finite and instantaneous screw theory, a unified and systematic approach for topology design and kinematic analysis of PKMs is proposed in this paper. Using the derivative mapping between finite and instantaneous screws built in the authors’ previous work, the finite and instantaneous motions of PKMs are analytically described by the simple and non-redundant screws in quasi-vector and vector forms. And topological and parametric models of PKMs are algebraically formulated and related. These related topological and parametric models are ready to do type synthesis and kinematic analysis of PKMs under the unified framework of screw theory. In order to show the validity of the proposed approach, a kind of two-translational and three-rotational (2T3R) 5-axis PKMs is taken as example. Numerous new structures of the 2T3R PKMs are synthesized as the results of topology design, and their Jacobian matrix is obtained easily for parameter optimization and performance evaluation. Some of the synthesized PKMs have outstanding capabilities in terms of large workspaces and flexible orientations, and have great potential for industrial applications of machining and manufacture. Among them, METROM PKM is a typical example which has attracted a lot of attention from global companies and already been developed as commercial products. The approach is a general and unified approach that can be used in the innovative design of different kinds of PKMs.

Full-mobility 3-CCC parallel-kinematics machines: Forward kinematics, singularity, workspace and dexterity analyses

The 3-CCC class of parallel-kinematics machines (PKMs) bears many interesting features, as found in a previous paper on its optimum design. In this paper, its forward-kinematics (FK), singularity, workspace and dexterity analyses are studied. FK reveals that the rotation and translation of the moving platform (MP) are decoupled at the displacement level; moreover, a simple formulation is derived for the orientation subproblem that admits up to eight solutions, which is minimal; a quartic resolvent polynomial for the FK is then derived. All solutions thus can be found simultaneously in closed-form, while the computational cost is reduced; this brings robustness, especially when the robot operates near a singular configuration. Next, the translation problem is solved from a linear-equation system. These features, rare in six-dof PKMs, greatly simplify its simulation and control. Next, the singularity in question is shown to be determined solely by the orientation of the MP, thereby simplifying dramatically its evaluation and representation. Furthermore, the robot is shown to bear position and orientation workspaces of reasonable size, together with high dexterity. These features make the proposed PKM class quite promising in a variety of applications.

The design for isotropy of a class of six-dof parallel-kinematics machines

The design for isotropy of a large class of six-dof parallel-kinematics machines (PKMs) whose six actuated wrenches intersect pairwise, is the subject of this paper. A PKM is called isotropic when it can achieve one or more postures under which the condition number of its Jacobian matrices becomes unity, thereby offering a high positioning accuracy. Based on a symbolic expression of the inverse of the forward Jacobian matrix, we analyze the isotropy condition for this class of PKMs. It is shown that isotropy can be achieved only when the moving platform (MP) bears an equilateral-triangular shape; however, the operation point need not be the centroid of this triangle. Moreover, for a MP with an acute-triangular shape, there exist postures that we call quasi-isotropic, under which the condition number is close to unity, while the six rows of the Jacobian matrix are mutually orthogonal. This greatly enriches the list of candidates for the MP shape and the location of the operation point, required, e.g., when a gripper or another tool is attached to the MP triangle.

An approach for elastodynamic modeling of hybrid robots based on substructure synthesis technique

Parallel kinematic machines exhibit strong pose-dependent static and dynamic behaviors, which makes accurate and rapid compliance analysis over the entire workspace an important issue in the design optimization. This paper presents a general approach for elastodynamic modeling of parallel kinematic machines using substructure synthesis technique. Firstly, the whole system is decomposed into two groups of substructures, i.e. component substructures and joint substructures. Then, the degrees of freedom of component substructures are reduced using modal reduction technique, and joint substructures are modeled by virtual springs with contact stiffness between adjacent component substructures. Finally, two threads are merged at junction surfaces to offer the equations of motion of the system as a whole, allowing the static and dynamic performances to be rapidly predicted with sufficient accuracy. The dynamic model of a 5-DOF hybrid robot is developed using the proposed method and the computational results show that rigidity and lower mode natural frequencies over the workspace match well with those obtained by the full finite element analysis.