Parallel Kinematic Machine Tool Research Articles

Gain scheduled task space control of multi DOF machine tools with non-linear parallel kinematics

Machine tools with multiple degrees of freedom and parallel kinematics offer tremendous opportunities for new kind of processes but at the same time also a lot of control challenges. They are subject to uncertainties in the form of kinematic errors, elasticities and thermal deflections. Their kinematic non-linearity requires the application of model-based control concepts whose full effectiveness can only be unlocked through controls in the task space. In particular, kinematic singularities occur in forming machines such as presses, which make closed-loop control at corresponding operating points considerably more difficult. In this paper, we use the example of a servo-driven press with three ram degrees of freedom to show how parallel kinematic machine tools can be controlled via inverse differential kinematics models in task space and to what extent the controls can benefit from scheduled gain factors. The results are validated both simulatively and experimentally. In the experimental tests, three-dimensional tool paths are traced that can be used to carry out orbital forging processes. Furthermore, the example of a punch hole rolling process demonstrates that the ram pose is controlled more accurately, which also has positive effects on the resulting workpiece geometry. The performance of the developed gain scheduling task space control is compared with that of a robust and non-robust control with static gains.

Spatial hybrid/parallel force control of a hexapod machine tool using structure-integrated force sensors and a commercial numerical control

Structure-integrated force measurement in hexapod structures or kinematics offers great potential for spatial process force control in six degrees of freedom. Although force control has been studied for many years, research questions remain unanswered, especially when regarding parallel kinematic machine tools with numerical control and integrated sensors. This contribution summarizes the technology of structure-integrated force sensing in hexapod machine tools and develops two approaches to use the measured signals for direct hybrid/parallel force control. For different use-cases, such as teach-in or synchronous force/position control with variable task frame, different approaches of set-point specification and injection of manipulated values are studied from a practical point of view. As a result of the work, the feasibility of the force control with structure-integrated sensors on a commercial CNC can be confirmed through appropriate experiments. Furthermore, the realized G-Code integration represents a practical solution for programming force-controlled machine tools in an easy and concise way from the NC programme.

Geometric modeling with small defects of over-constrained Parallel Kinematic Machine

In the case of over-constrained mechanisms, the system can only be assembled or move under strict geometric conditions. A crucial step is to identify these conditions from the geometric model. Classically, the geometric model of a robot is computed from the Denavit–Hartenberg formalism. However, when imperfect mechanisms are studied, this formalism does not introduce exhaustively small geometric defects. In this article, a formalism based on kinematic joint invariants is preferred to describe the geometric behavior. The efficiency of this formalism is demonstrated for the accuracy improvement of a serial robot. A stationarity analysis of the geometric model is then performed to determine the geometric constraints induced by the over-constrained systems and to reduce the number of geometric parameters initially introduced. The methodology is first illustrated on an over-constrained slider–rod–crank system. Then, it is applied to the over-constrained mechanism of the Tripteor X7, a Parallel Kinematic Machine-tool. The benefit of our methodology is validated by a comparison of the geometric model obtained with a CAD model and a previous geometric model proposed in the literature. Finally, the identification of the parameters of the defined geometric model is conducted in order to quantify the potential accuracy benefit.

Dynamic stability of a paralle kinematic machine

Machine tool chatter causes machining instability, surface roughness, and tool wear in metal cutting processes. A stability lobe diagram based on the theory of regenerative vibration is an effective tool to predict and control the chatter. This paper presents the advances in the mechanical design of a parallel kinematic machine tool. The features that make it ideal for machining tasks, and that make unique in its own way, are highlighted. In addition, the description of the progress of this work will be focused on the analysis of the stability limitation for machining systems to derive the stability lobe diagram with modal analysis of the spindle. A vibratory model is developed by adding cutting forces and including analytical equations for the depth of cut and for the cutting speeds, both depending on the frequency of vibration. A step-by-step procedure provides a stability lobe diagram. The results show that it is relatively easy to provide a relationship between depth of cut and spindle speed. In turn, it makes it easy to compare machining processes under different cutting parameters and conditions.

Machining capability of a 2-D of parallel kinematic machine tool and conventional CNC milling machine

Machining performance of an optimally designed prototype of a 2 degree of freedom PKM (parallel kinematic machine) is optimized in this work. The effect of machining parameters upon the surface quality of machined components is studied. Pocket milling operations are performed at various feed, speeds, and depth of cut on PKM and conventional CNC milling machine. The surface roughness of the machined component is measured, and the results are compared. Taguchi approach is used to design the experiment and analysis of variance is employed to obtain the optimal cutting conditions. The depth of cut is noticed as the most significant parameter that affect the surface roughness. The first version of the PKM prototype shows machining performance similar to the conventional CNC machine. The study establishes the machining capability of PKM and offers scope for developing dynamically superior substitute over the CNC machine tool.

Influence of Tool Posture and Position on Stability in Milling with Parallel Kinematic Machine Tool

This paper investigated the machining stability influenced by tool posture and position in ball-end milling with parallel kinematic machine tool (PKM). Initially, the geometric structure was identified, and the machinery stiffness was measured by impulse respond method at several positions with four tool postures. Then, the milling tests were conducted on flat work surface using a ball-end mills. Cutting force and acceleration signals of milling tests were measured by three-axis dynamometer and accelerometer. Furthermore, these signals were analyzed by using Fast-Fourier transform and Hilbert–Huang transform (HHT). The results showed that the length of arm change with tool posture, where the machinery stiffness decreased with the total length of arms for any tool position. The experimental results also demonstrated the machining stability varied with tool posture; the trend of stability corresponds with the machinery stiffness. The vibration analysis by HHT presented the increasing of power level in the time–frequency plot when the length of arm increase during milling process. Therefore, the geometric influence must be considered to support process planning on the PKM.

A novel six-legged walking machine tool for in-situ operations

The manufacture and maintenance of large parts in ships, trains, aircrafts, and so on create an increasing demand for mobile machine tools to perform in-situ operations. However, few mobile robots can accommodate the complex environment of industrial plants while performing machining tasks. This study proposes a novel six-legged walking machine tool consisting of a legged mobile robot and a portable parallel kinematic machine tool. The kinematic model of the entire system is presented, and the workspace of different components, including a leg, the body, and the head, is analyzed. A hierarchical motion planning scheme is proposed to take advantage of the large workspace of the legged mobile platform and the high precision of the parallel machine tool. The repeatability of the head motion, body motion, and walking distance is evaluated through experiments, which is 0.11, 1.0, and 3.4 mm, respectively. Finally, an application scenario is shown in which the walking machine tool steps successfully over a 250 mm-high obstacle and drills a hole in an aluminum plate. The experiments prove the rationality of the hierarchical motion planning scheme and demonstrate the extensive potential of the walking machine tool for in-situ operations on large parts.

Special Issue on Machine Accuracy Evaluation

The accuracy of a three-dimensional (3D) positioning system can ultimately be evaluated via measurement of a 3D vector between command and actual end-effector positions at arbitrary points over the entire workspace. This is a simple, yet challenging, metrological problem. The motion accuracy of a machine tool is traditionally evaluated on an axis-to-axis basis, with every error motion of every axis being independently measured as part of a one-dimensional measurement process in a different setup. Toward the ultimate goal of 3D position measurement over the entire workspace, research efforts have offered several new, practical measurement technologies. This special issue covers the technical and academic efforts regarding the evaluation of machine tool accuracy. The papers in this special issue clarify the latest research frontiers regarding machine tool accuracy from a metrological viewpoint. In the first paper, by Montavon et al., error calibration technologies and their management are reviewed within the Internet of production concept. Long-term accuracy monitoring and management are clearly among the most crucial technical challenges faced regarding machine tools, and the work by Xing et al. is related to them. Ibaraki et al. presented machining tests to evaluate the thermal distortion of a machine tool. Peukert et al. studied the dynamic interaction between machine tools and their foundations. Various 3D measurement schemes for determining machine error motions have been investigated by many researchers, and some have been implemented in industrial applications. Kenno et al. and Florussen et al. investigated 3D measurement using the R-test for five-axis machines. Miller et al. studied simultaneous measurement of six-degree-of-freedom error motions of a linear axis. Nagao et al. presented an error calibration method for a parallel kinematic machine tool. The editors appreciate the contributions of all the authors, as well as the work of the reviewers. We are confident that this special issue will further encourage research and engineering work for improving the accuracy and performance of machine tools.

Parametric vibration analysis and validation for a novel portable hexapod machine tool attached to surfaces with unequal stiffness

The Free-Leg Hexapod (Free-Hex) machine tool is an advancement from the conventional Stewart platform, which has the fixed base platform removed to enable the limbs to be attached to a wider range of surfaces (e.g. non-flat and curved). However, in some scenarios (e.g. in-situ repair of industrial installations), the limbs of the Free-Hex need to be attached to the surfaces with unequal stiffness, which brings the challenge of predicting the dynamics of the system for conducting machining operations under dynamically stable conditions. In this paper, after introducing the attachment stiffness (i.e. feet attached to the environment with different materials) in the conventional dynamic model of the parallel manipulator, the dynamic behavior of the Free-Hex machine tools devoted to the in-situ operation environments was studied. Then, the experimental validation was conducted to prove the dynamic model developed in this paper. It was found that the errors of the proposed model are under 6% (i.e. 5.1% at symmetrical limb configuration and 5.8% at the arbitrary configuration) when the limbs are attached to the surfaces with unequal stiffness. Further, by applying the validated model, the dynamic performance of the Free-Hex with a wider range of attachment stiffness was analyzed. Overall, it was found that the attachment stiffness has a remarkable influence on the natural frequencies of the machine tool (e.g. the frequency of mode 4 at the symmetrical configuration is increased by 36.8% when the attachment stiffness of one limb changes from 0 to 1e+12 N/m). Thus, the work discussed in this paper can be utilized to avoid the dynamically unstable configurations of parallel kinematic machine tools (e.g. Free-Hex) when mounting on the surface with unequal stiffness in the in-situ operation environments.

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.

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.

Gravity compensation of a 6-UPS parallel kinematics machine tool through elastically balanced constant-force generators

Gravity compensation of a 6-UPS parallel kinematics machine tool through elastically balanced constant-force generators

Development of a 3-axis parallel kinematic machine for milling wood material – Part 1: Design

A 3-axis parallel kinematic machine tool and advanced control system with programming in G-code for the milling of wood material are described in detail. This parallel kinematic machine is based on a 3-PSS (prismatic link, spherical link, and spherical link) parallel mechanism. A programming system and control based on a real-time PC windows platform and Mach3 software system was implemented for this tool. Finally, a model application of a programming system developed for a three-degree-of-freedom linear delta parallel machine was presented, and the workability for milling wood material (medium-density fibreboard) was shown.

Cinemática paralela en la máquina-herramienta: Investigación, desarrollo y tendencias futuras

Desde su presentación a la sociedad a mediados de los 90’s, las Máquinas Herramientas de Cinemática Paralela (MHCP), han suscitado grandes expectativas por el papel que pueden jugar en la industria. Han pasado más de veinte años desde esa fecha (1994) y pese a que estas arquitecturas han entregado prestaciones nunca antes vistas en términos de capacidad dinámica, precisión y rigidez, su impacto en el mercado, no ha sido el esperado. ¿Qué pudo haber fallado? ¿Hace falta más desarrollo? ¿Es cuestión de mercado?. Este artículo, intenta resolver estos interrogantes, partiendo de los inicios de la cinemática paralela, sus fortalezas y debilidades, analiza su situación actual y prevé sus desarrollos futuros haciendo especial énfasis en las fresadoras de 3 ejes.

Kinematic calibration of a 3-P(Pa)S parallel-type spindle head considering the thermal error

Calibration is considered to be the most effective way to improve the accuracy of parallel kinematic machine tools (PKMTs). However, ordinary calibrations only considered the time-invariant errors (manufacturing error), neglecting some time-variant errors, a significant one of which is thermal error. Therefore, in this paper, the influence of thermal error was considered in the calibration of a 3-P(Pa)S parallel-type spindle head. First, a new kinematic model of the spindle head was proposed, which is closer to the real physical model, so the thermal error of the spindle head can be considered in the model. Second, the structural parameters of the spindle head were expressed as the sum of the ideal parameters, the manufacturing errors, and the thermal errors. Third, the pose (position and orientation) of the end effector and the temperature of the spindle head were measured. The positions of the temperature sensors were selected using the global temperature sensitivity index (GTSI), which is derived from the global sensitivity index (GSI). Thus, by setting a standard temperature, the thermal error of the structural parameter can be obtained. Fourth, the influence of the thermal error was inputted into the identification equation for calibration, so the results are the structural parameters at the standard temperature (20 °C). To solve the ill-conditioning problem, a Regularization method was used in the identification. Finally, the calibration was verified on a 3-P(Pa)S-XY machine tool. The RTCP test, performed immediately after the measurement, shows that the maximum position error after the calibration is 0.019mm at the tilt angle of 30° and 0.037mm at 20°. In addition, the RTCP test after a temperature change shows that the calibration considering the thermal error can improve the average position accuracy from 0.025mm to 0.015mm. The calibration method in this paper is expected to be applicable for other machine tools.

Dominant types of errors at parallel kinematics machine tools

Dominant types of errors at parallel kinematics machine tools

Machining with the WalkingHex: A walking parallel kinematic machine tool for in situ operations

In situ repair/maintenance of industrial installations is challenging working scenario considering the variety of operations that are required to be performed against the clock. The paper reports on a unique walking hexapod (WalkingHex) machine tool which has a set of key abilities: (i) walks autonomously to the place of intervention; (ii) calibrates autonomously and references itself against features on the ground; (iii) performs machining operations. The essential design and theoretical aspects are presented to allow the understanding of main working principles of the WalkingHex while a selected set of experimental trails show its ability to generate accurate features.

A concept for actuating and controlling a leg of a novel walking parallel kinematic machine tool

The scope of this paper is to present a novel method of actuating the legs of a walking parallel kinematic machine tool (WalkingHex) such that the upper spherical joint can be actively driven while walking and remain a free, passive joint while performing machining operations. Different concepts for the number of Degrees of Freedom (DoF) and methods for actuating the chosen concept are presented, leading to a description of a three-wire actuated spherical joint arrangement. The inverse kinematics for the actuation mechanism is defined and a control methodology that accounts for the redundantly actuated nature of the mechanism is explored. It is demonstrated that a prototype of the system is capable of achieving a motion position accuracy within 5.64% RMS. Utilising the concept presented in this paper, it is possible to develop a walking robot that is capable of manoeuvring into location and performing precision machining or inspection operations.

Contour maps for developing optimal toolpath and workpiece setup in hexapod machine tools by considering the kinematics nonlinearity

Contrary to the conventional serial kinematics machine tools, the parallel kinematics machine tools exhibit nonlinear behavior which is a major source of the machining error. This causes even a linearly programmed path to be traversed along a nonlinear path. The resulting error, known here as the kinematic error, should be critically considered during the toolpath planning. The estimation of the maximum kinematic error using the concept of median osculating circle is introduced in this article. The proposed formulation demonstrates that the maximum kinematic error depends on the curvature of the actual trajectory. In order to estimate the curvature, constant curvature contour maps are introduced. These maps depend on the structural parameters of the machine and are recommended to be provided by the machine’s manufacturer. The constant curvature contour maps are illustrated to be an effective graphical tool for kinematic error estimation and thus successfully conducting the optimal planning of the toolpath and the workpiece setup. Consequently, it is recommended in this article that the constant curvature contour maps be employed in the format of a database by computer-aided manufacturing systems during toolpath planning and by interpolators during command generation or by a part programmer to optimally setup the workpiece or conduct the toolpath planning such that the least kinematic error occurs during the machining.