Parallel Kinematic Machine Research Articles

Enhanced Kalman filter methods for end pose measurement of parallel kinematic machine considering the error sensitivity

For robust accuracy, this paper proposes a parallel measurement method for parallel kinematic machine (PKM) combining indirect measurement using grating ruler with direct measurement using monocular vision. However, due to differing error sensitivity of two methods, the general Kalman filter (KF) cannot integrate them under the assumption of equal data weighting. Therefore, a novel Enhanced KF data fusion method designed to account for varying data sensitivities is developed.The paper first outlines the principles of parallel measurement approach for PKMs, followed by modeling the error sensitivities associated with each measurement source. Subsequently, an enhanced KF data fusion model is developed, treating these sensitivities as noise, and validated. Compared to the conventional KF method, the root mean squared (RMS) position error is significantly reduced from 0.569 mm to 0.293 mm. This enhanced KF method presents an innovative approach to multi-source data fusion, tailored to the error characteristics of different measurement sources.

Heavy-load Nonapod: A novel flexible redundant parallel kinematic machine for multi-DoF forming process

The high-performance multi-DoF forming process (MDFP) necessitates a 6-DoF forming machine tool with high normal and lateral stiffness to bear large normal and lateral forming force of millions of Newton (MN). However, the payload of parallel kinematic machine (PKM) is generally limited to thousands of Newton (kN), which restricts its application in MDFP. Therefore, this paper aims to develop a novel heavy load PKM with high stiffness for MDFP. To maximise the normal stiffness, a 6-PSS PKM with zero base angle and horizontal driver is proposed. Further, the inner force transfer model of 6-PSS PKM is established, indicating that the normal stiffness will be maximised when the link force approaches to be vertical. Consequently, a design criterion for maximising normal stiffness, i.e., the root mean square error (RMSE) for horizontal projection of all links should be minimised, is established. To maximise the lateral stiffness, general force balance equations of 6-PSS PKM are derived, indicating that lateral force can cause unintended negative force of links, significantly reducing the lateral stiffness. Thus, a novel auxiliary 3-SPS configuration is employed to provide additional force system to mitigate this negative force via hydraulic links. Correspondingly, a design criterion for maximising lateral stiffness, i.e., all link force should remain positive, is proposed. By combining aforementioned design criterion and kinetostatic models, a near-singular 6-PSS PKM with maximising normal stiffness is achieved, and dimension parameters of 3-SPS PKM with maximising lateral stiffness are optimised. On this basis, a novel flexible redundant 6-PSS/3-SPS PKM with both high normal and lateral stiffness is proposed, and a novel heavy load Nonapod with payload of 8 MN and payload-mass ratio of 40 is developed, showing good stiffness performance. The plastic deformation mechanisms of multi-DoF formed aviation bevel gear are revealed, and experimentally formed aviation bevel gear in the new Nonapod achieves good accuracy, microstructure and mechanical performance. This work provides a new methodology for synthesis of heavy load PKM with high normal and lateral stiffness, and has significant application prospect in PKM under heavy load working condition.

Multi-Objective Optimization of a Three Degree-of-Freedom Translational Parallel Kinematic Machine with Coplanar Rails

Several advancements in the field of parallel manipulators have taken place in recent days as they offer many advantages over serial manipulators in terms of accuracy, agility, stiffness, speed, etc. The Parallel Kinematic Machines (PKMs) with lower Degree of Freedom (DoF) joints are being explored for a variety of industrial applications and, in particular, machining applications as these offer more accuracy, high machining capability, and more stiffness. This research work focuses on the modeling, kinematics, workspace and dexterity analyses of a 3DoF Translational PKM having coplanar rails along the Cartesian axes: -X, +X, +Y. Actuation of sliders, independently along the respective rails, offer the tool platform pure translational motion. Fixed length links are used to connect the sliders and tool platform. The PKM under study is modeled in CATIA. Inverse kinematics and workspace analysis are carried out using the performance indices, namely, Workspace Volume Index (WVI) and Global Condition Index (GCI). Attempts are also made to find the optimal dimensions of the PKM through multi-objective optimization using Genetic Algorithms in MATLAB. The methodology presented is helpful to predict the PKM's performance capability while the results obtained are helpful for the development of a physical prototype necessary for further experimental investigations.

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.

Workspace, Singularity, and Dexterity Analyses of a Six-Degrees-of-Freedom SDelta Robot With an Orthogonal Base Platform

Abstract The SDelta is a three-limb, six-degrees-of-freedom parallel kinematics machine, a pertinent candidate for high-speed operations by virtue of its simple architecture. The original design of the SDelta includes a planar base and moving platforms. Here, we propose a novel architecture for an improved SDelta, the orthogonal SDelta (OSD), with a cube-shaped orthogonal base platform. Inverse and forward position models are reported, along with singularity and dexterity analyses. Moreover, design parameters and mechanical constraints leading to a singularity-free workspace are provided. An evaluation of the system translational workspace and orientational capability, upon consideration of volume and dexterity, is included. The SDelta as well as a generic 6SPS mechanism (C, P, and S denote, respectively, the cylindrical, prismatic, and spherical kinematic pairs, the actuated pair is represented underlined, as P) are designed with the same parameters, then the performance of the SDelta, the OSD, and the 6SPS mechanisms are being compared. The results show that the orientational capability of the OSD is better than those of the 6SPS and the SDelta. Furthermore, the OSD has an average condition number of 2.9 over its translational workspace and 1.69 over a predefined effective regular workspace, which make the OSD a good candidate for operations that need both a high orientational capability and high dexterity.

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.

Dynamics of a Parallel-Kinematics Machine With Six Pairs of Offset Joints

Abstract The authors propose a systematic formulation of the dynamics of the 6-P-RR-R-RR parallel-kinematics machine (PKM) with offset RR -joints. The kinematics of the same system is reported in an accompanying paper. Based on the kinematics model developed in the former, the dynamics model of the limb-chain is derived here using the Newton–Euler equations. Then, the constraint wrenches in the governing equations of the limb-chain are eliminated with the aid of the natural orthogonal complement. This is the twist-shaping matrix, which maps the joint-rate array of the limb-chain into the twist array of the PKM. Furthermore, the dynamics model of the whole PKM with offset joints is formulated. Moreover, the actuator forces are obtained. Finally, upon validation via simulation, the dynamics model is proven to be both precise and effective.

Experimental investigations and error analysis on 3-PRS parallel kinematic machine

Industrial robots play a predominant role in factory automation particularly in the area of machining like grinding, cutting, milling, drilling, polishing etc. In these applications serial manipulators could not provide rigidity and accuracy. This research focuses on the need for precise angular drilling applications. Generally, special fixtures are used to make angular hole in drilling machines. In this research, the 3-PRS (Prismatic – Revolute – Spherical) parallel mechanism is redesigned to execute angular drilling operations. The moving/mobile platform (MP) of the proposed manipulator is utilized as worktable. The experimental model is fabricated with lead screw and nut pair to obtain precise position of drill tool and to maintain high stiffness. By varying the geometric parameters, the positions of parallel kinematic machine (PKM) are analysed. Moreover, the orientation error and parallelism of the developed PKM are studied in detail using laser torch and height gauge. Further, the PKM positions are simulated through ADAMS software package and the same is compared with the real-time accelerometer values. From the experimental study, the deviations in orientation, parallelism and position of the PKM are found to be minimal and satisfactory.

A comparative study on structural analysis of 3-PRS Tri-Glide, 3-PRR and 3-PRS Tripod parallel kinematic machines for angular drilling applications

Parallel kinematic machines are a result of intensive research and development in the area of high speed machining (HSM). The high stiffness and low inertia characteristics of the parallel kinematic architecture make it suitable for high speed machine tool. This research aims to compare the structural characteristics of 3-DOF Tri-Glide and Tripod Parallel Kinematic Machines (PKMs) by varying the geometrical parameters of their links. Both solid and hollow tube structures are considered to evaluate the stiffness of the PKMs. Initially, mild steel is used for this comparative study. Later, mild steel is replaced by aluminium alloy due to its high strength to weight ratio. The 3PRS Tri-Glide, 3PRS and 3PRR Tripod models are modeled and analyzed using the Finite element software package ANSYS. Based on the structural analysis the results are compared and summarized.

A Novel Reconfigurable 3-DOF Parallel Kinematics Machine

Abstract This paper proposes a novel, reconfigurable parallel kinematics machine with three degrees of freedom that can be used for various three-axis manipulation tasks, including machining. By locking some joints, the proposed parallel kinematics machine (PKM) can be transformed into four topologies with eight configurations to attain certain kinematic properties while keeping the number of its degrees of freedom unchanged. Either the proximal or intermediate prismatic joints of the reconfigurable PKM can be actuated. Some of the configurations are orthogonal configurations having a large rectangular cuboid workspace, and some other configurations are non-orthogonal configurations which provide the capability to perform a machining task to a large workpiece in various positions with respect to the machine. Accordingly, the proposed machine can be transformed from an orthogonal machine to a non-orthogonal machine with the advantages of each. The mobility of the various topologies of the reconfigurable PKM is rigorously analyzed using the screw theory. The workspace is analyzed using a graphical approach and verified by a computational approach. The pose kinematics shows that the various topologies have unified kinematics. The differential kinematics shows that the singularities in the various configurations occur at the workspace boundary. Similarly, the stiffness analysis shows that the low-stiffness postures occur around the workspace boundary. Accordingly, a used workspace far from the workspace boundary easily avoids the singularities and the low stiffness.

Adaptive RISE Feedback Control for Robotized Machining With PKMs: Design and Real-Time Experiments

The development of high-precision tasks, such as machining, needs a positioning device for the cutting tool with the smallest possible error. Multiple design factors need to be considered to ensure a mechatronic device successfully performs such tasks. One of these factors may be attributed to the control scheme, which is responsible for controlling the position of the machine. In view of the importance of designing a good control scheme for a robotic system, in this article, we propose a new extension of the robust integral sign of the error (RISE) for the positioning device a parallel kinematic machine (PKM). This extension consists in including a nominal feedforward term based on the inverse dynamic model of the robot and replacing the RISE fixed feedback gains with adaptive ones. The RISE part of the proposed controller ensures semiglobal asymptotic stability. Moreover, it can accommodate sufficiently smooth bounded disturbances. The feedforward part cancels the nonlinearities of the system, improving the tracking performance of the controller. The adaptive feedback gains produce corrective actions when an increase in the tracking errors is due to the contact forces that occur during the machining process. A Lyapunov-based stability analysis is conducted to prove the semiglobal asymptotic stability of the proposed control solution. To show its effectiveness, real-time experiments are performed for two case studies; the first one is on a free motion trajectory and the second on machining experiments under three different forward speeds on SPIDER4, a redundantly actuated PKM.

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.

Comparative Study Using CAD Optimization Tools for the Workspace of a 6DOF Parallel Kinematics Machine

This paper deals with an up-to-date topic among robotic industrial applications that require a high degree of speed, rigidity, and orientation. Currently, when technology and software applications reach a high level of performance, in various robotic industrial applications that start from certain concepts, the implementation of efficient structures has proven to be challenging. New structures such as the parallel kinematic machine (PKM) category has proven its efficiency through its structure in terms of high inertia rigidity and high speeds during processes. This paper deals with the subject of PKM-type structures in terms of the optimal design workspace of such a structure. The calculation of the workspace is considered the premise from which it starts in terms of its implementation in a robotic production line. The entire process of calculating the workspace for a given PKM structure is carried out through modern CAD applications that have specific modules in place in this direction. CATIA V5 offers the possibility through the product engineering optimizer module, simulation and calculation of different scenarios aimed at identifying the volume of the workspace for a PKM structure. In the article, we demonstrate the relations between the robot workspace and the design parameters, a method that can also be applied for other parallel structures. The method is useful for robot designers in the optimization of parallel robots with regard to the workspace by using CAD tools. Previous research in the field refers of the usage of CAD tools only for visual representation and not for optimizing the workspace, while this study and test results show that CAD tools are suitable for analyzing and optimizing the robot workspace of the 6DOF parallel robot, due to its easiness in application and fast implementation time.

Kinematic error model of a 3-PUU parallel mechanism for translational motion

Accuracy of parallel kinematic machine (PKM) is affected by geometric parameters (GPs) and non-geometric parameters (NGPs). For GPs, the use kinematic error model (KEM) to calibrate these errors has been studied, but few of them have considered the influence of the linkage posture. In this paper, link-orientation-based joint error model (LOBJEM) and sensitivity analysis are presented. In LOBJEM, the original KEM, which is constant joint error model (CJEM), is derived first. The angle between each link and the Z axis is considered as the parameter to adjust the KEM to derive LOBJEM and it can cause the value of joint error to vary with the position of end effector. The calibration process includes measuring the positioning error by a laser interferometer, identifying the error terms using least square method and compensating by the numerical control code (NC-code). The error model and calibration process have been realized on the delta robot 3D printer. Compared with the CJEM, the residual error of LOBJEM was reduced from 75% to 60% of the original error. To estimate the positioning errors caused by NGPs, we constructed a backpropagation neural network model, which can reduce the final residual error to 25% of the original error.

Workspace and kinematic structure analysis of a 6-DOF Lambda parallel kinematic machine

This paper presents workspace and kinematic analysis of a parallel kinematic machine based on the Lambda mechanism. The considered parallel kinematic machine has six degrees of freedom (DOF), achievable with six actuated translation joints. The kinematic analysis includes the definition of every active part of the machine, as well as the definition of every active or passive joint used to connect machine parts. The mathematical model of the machine is created for the better understanding of the machine's operation. The proposed mathematical model of the machine includes inverse kinematic equations, whose solving presents the first step in workspace analysis. In this case, the offered parallel kinematic machine has six active-joint variables, and every active-joint variable is the result of one inverse kinematic equation. Verification of the inverse kinematic equations has been done analytically, using MatLab software and a CAD/CAM system. Workspace analysis, as one of the most important parameters of the parallel kinematic machine, presents the main topic of this paper. In this case two approaches to the workspace analysis are given. The first considered analysis is used to determine the achievable workspace of the machine, and the second analysis is used to determine the total orientation workspace of the machine. Polar coordinates are used to simplify the process of the workspace analysis.

Kinematic calibration of a symmetric parallel kinematic machine using sensitivity-based iterative planning

Since kinematic calibration will induce variations in the structural parameter values, the forward kinematics may have multiple or no solutions after calibration. This paper proposes a novel kinematic calibration method to obtain the optimal solution and high accuracy after calibration. We use the closed-loop vector to represent the clearance and the concomitant motion and convert the angular to a dimensionless variable to simplify the kinematic calibration model. Thus, we can calculate the global sensitivity index (GSI) of the symmetric parallel kinematic machine (sPKM). Then, we present a sensitivity-based iterative planning method to ensure iterative convergence and obtain the optimal solution. Due to the large difference in magnitude between the position and orientation errors, we adopt a segmental calibration approach to calibrate the two types of errors to improve the calibration accuracy. Finally, the Levenberg-Marquard(L-M) iterative algorithm is used to obtain the parameter errors. Simulations and experiments are performed on a 3-PPR sPKM. The results show that the proposed method prevents the kinematics with multiple solutions or without solutions after the calibration and reduces the position and orientation errors by 89.74% and 90.71%, respectively.

Elasto-Dynamic Modeling of an Over-Constrained Parallel Kinematic Machine Using a Beam Model

This article deals with the development of a simple model to evaluate the first natural frequencies of over-constrained parallel kinematic machines (PKMs). The simplest elasto-dynamic models are based on multi-body approaches. However, these approaches require an expression of the Jacobian matrices that may be difficult to obtain for complex PKMs. Therefore, this paper focuses on the determination of the global mass and stiffness matrices of an over-constrained PKM in stationary configurations without the use of Jacobian matrices. The PKM legs are modeled by beams. Because the legs are connected to a moving platform and the mechanism is over-constrained, constraint equations between the parameters that model the deformation of each leg are determined according to screw theory. The first natural frequencies and associated modes can then be determined. It should be noted that the proposed method can be easily used at the conceptual design stage of PKMs. The Tripteor X7 machine is used as an illustrative example and is characterized experimentally.

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.

Double-sided milling of thin-walled parts by dual collaborative parallel kinematic machines

Thin-walled parts with double-sided features are widely used in many industrial sectors but their machining is particularly time consuming and challenging. Collaborative machining is a new paradigm in the development of industrial 4.0. It can potentially revolutionize the existing thin-walled part machining methods, leading to higher productivity, flexibility and sustainability. For this end, this paper introduces a novel concept with dual parallel kinematic machines (PKMs) collaboratively performing synchronized and asynchronized cutting and support from both sides of a thin-walled part, without changeover/re-clamping of the workpiece. Compared to the conventional single-sided machining, this study shows that static and dynamic performances of the workpiece are significantly improved under the dual PKM collaborative operation. A case study of milling a thin-walled part with double-sided features was conducted by PKMs under three comparative strategies, namely, double-sided synchronized milling, alternative single-sided milling, and sequential single-sided milling. Experimental results show that the novel double-sided synchronized milling strategy by dual collaborative PKMs produced the best dimensional accuracy and satisfactory surface quality due to the improved static stiffness and dynamic performance, and balanced deflections. More importantly, a two-fold greater productivity has been achieved as the novel strategy doubles the material removal rate while eliminating the cumbersome in-process steps used in conventional single-sided machining.

Elastostatic Performance Evaluation of a Full-Mobility Parallel-Kinematics Machine with Flexible Links

Elastostatic Performance Evaluation of a Full-Mobility Parallel-Kinematics Machine with Flexible Links