Parallel Kinematic Mechanism Research Articles

Design and performance evaluation of a novel parallel kinematic micromanipulator

The targeted placement of selected carbon nanotubes is associated with low throughput rates. Hence, this paper presents a novel stage design for the fully automatic assembly of carbon nanotube field-effect transistors (CNTFETs) via mechanical dry transfer. It constitutes the core module of an assembly machine for the precise deployment of nanotubes onto a prefabricated wafer. The mechanical dry transfer approach allows high level of carbon nanotube selectivity with the aim of enabling a high-volume fabrication of ultra-clean devices. The previous production rate of such ultra-clean devices is less than one per hour, which offers a high potential for improvement. The stage consists of a parallel kinematic mechanism (PKM) with 3 degrees of freedom (X2Y2C1) carrying two additional stacked axes (Z1C2). The PKM is suspended on a vacuum preloaded aerostatic bearing, voice coil motors (VCM) and flexure hinges. Together with a combination of high precision and resolution touch probe measurement systems close to its tool center point (TCP), high accuracy and low settling time can be achieved. Based on realistic manufacturing tolerances, a sensitivity analysis of the mechanism’s pseudo rigid body model (PRBM) suggests a theoretical closed-loop error below 0.15μm over the entire XY workspace of 20mm×2.8mm. Measurements of positioning motions show that the settling time can be decreased by the compensation of friction resistances inside the internal bearings of the VCMs.

Positioning Error Estimation Models for Horizontal-Distributed Prismatic–Universal–Universal Parallel Mechanism

Abstract In this paper, two models were proposed to estimate the positioning error of a 3-translational prismatic–universal–universal parallel kinematic mechanism. The two models were a kinematic error model (KEM) and a backpropagation neural network (BPNN) model, respectively. The KEM was constructed by incorporating three translational joint errors into the ideal kinematic model to describe the errors that occur during machining or assembly. Additionally, a sensitivity analysis was presented for each error parameter. The BPNN model was constructed to establish the relationship between the position of the end effector, the posture of each link, and the positioning error of the end effector using a neural network approach. Moreover, a hybrid method was proposed to decrease the final estimated residual error. The average errors of the KEM and BPNN models were 35% and 15% of the original error, respectively. The hybrid model reduced the final average error to less than 10% of its original value.

Dynamic error prediction and link strain feedback control for a novel heavy load multi-DOF envelope forming machine

Thin walled and high rib components (TWHRC) are widely used for rocket cabins, aircraft wings, panels and frames in aerospace equipment as critical load bearing structures. This paper is aimed to develop a novel multi-DOF envelope forming machine (MEFM) with parallel kinematic mechanism (PKM) to realize efficient manufacturing of TWHRC with high performance. Since the heavy load MEFM with PKM has many total differences with the light load PKM, such as dynamic error and precision control, this paper conducts research on dynamic error prediction modelling and precision control method for this novel heavy load MEFM.Firstly, the configuration of MEFM is developed and the kinematic model of MEFM is established. Then, a RFC (rigid-flexible coupling) and RFE (rigid finite element) coupling dynamic model of MEFM is established considering time-variation of kinematic configuration caused by large deformation of all the kinematic elements. Based on the dynamic model, the dynamic deformation and error of MEFM are predicted and their generation mechanisms are revealed. It is found that the linear compression deformation of two-force links is the largest among all the kinematic elements, and it is the most sensitive to the heavy forming load and the most insensitive to the installation error of strain gauges, thus suiting for the feedback of large deformation of MEFM. Based on the above findings, a novel link strain feedback and dynamic error compensation control method is proposed. Finally, experiments under different control methods are conducted, showing that the motion precision of envelope tool and forming precision of formed components under the proposed control method are remarkably improved compared with that under the traditional control method (The geometric deviation of formed components under the proposed control method is remarkably reduced to −18 ∼ 32um from −64 ∼ 54um under the traditional control method). The experimental results verify that the proposed dynamic error prediction model and link strain feedback control method for heavy load MEFM are reasonable.

Design and Motion Principle Analysis of new parallel mechanisms with fewer active inputs than the degrees of freedom

AbstractIn this paper, two new parallel mechanisms (PMs) with fewer active inputs than the degrees of freedom (DOFs)are proposed: (i) an nSPS (n = 7, 8, 9) six‐DOF PM with n‐6 active inputs and six lockable joints. and (ii) a 3RPS‐SPS 3‐DOF PM with one active input and three lockable joints. Compared with the traditional PMs, the difference is that the proposed PMs can achieve the same mobility by using a minimal number of active joints. Moreover, the load‐carrying capacity is also improved compared with the original standard mechanisms, since the new PMs become statically redundant when all the branches are locked. For this purpose, a sequential motion control principle is introduced that requires both inverse and forward kinematics of PMs. Kinematic modeling, dimensional optimization, and structural design are carried out for the 7SPS and 3RPS‐SPS mechanisms, and the two prototypes are constructed for experimental validation. Both simulation and experiment results have shown that the proposed hybrid PM can achieve the original mobility while significantly reducing the number of actuators.

Kinematic Analysis of Six-Legged Robot

Nowadays, robots are applied in many fields which means flexibility in robot movement is always in high demand. A walking robot is a form of a mobile robot that is gentle to the environment, and it is possible to move through various settings while selecting landing points. In this study, a systematic approach for dealing with a controlling algorithm is proposed for the six-legged walking robot. A mathematical model is applied for studying the kinematics and gaits of the six-legged robots based on parallel and serial kinematic mechanism theory. The kinematic analysis is based on classical kinematic theory, which uses a formulation that is helpful in computer algorithms. The experiment results show that the effectiveness of robot design and control algorithms are responsive to different movements.

Elastodynamic modeling and structural error compensation for a 5-DOF parallel mechanism with subclosed loops

In order to reduce the adverse effects of structural errors on a novel 5-degrees of freedom (DOF) parallel kinematic mechanism (PKM) with subclosed loops, studies on the elastodynamic modeling and structural error compensation are conducted in this paper. First, considering that introduction of subclosed loops significantly increased the complexity and difficulty of elastodynamic modeling, an equivalent unit modeling method for the branch chain with subclosed loop is proposed based on force analysis and deformation compatibility condition. Then, elastodynamic model of the whole 5-DOF PKM is established with the matrix structural analysis based method. Second, by defining a six-dimensional error (three translational errors and three rotational errors) for each node, structural error model of the PKM is constructed based on closed-loop vector method. To consider the coupling effects of static and dynamic structural errors, the dynamic structural errors derived by above elastodynamic model would be substituted into the structural error model along with given static structural errors. Finally, structural error compensation optimization model is established and structural errors are compensated by adjusting the driven parameters based on the improved particle swarm optimization (PSO) algorithm. Numerical simulations are conducted to verify the proposed elastodynamic modeling and structural error compensation methods. After compensation, the position errors along x, y, and z directions are respectively decreased by 68.036%, 81.409%, and 90.625%, and the angle errors around x and y directions are respectively decreased by 91.426% and 62.042%.

Kinematic error model and non-uniform calibration method for heavy load multi-DOF envelope forming press

Multi-DOF envelope forming is a new continuous and local plastic forming process for manufacturing high performance complex components with thin wall and high rib used in the aerospace industry. To achieve the new process, this paper develops a new heavy load multi-DOF envelope forming press with parallel kinematic mechanism (PKM), which can achieve the multi-DOF motion of envelope die. However, owing to the large scale and heavy load characteristics of the press, the kinematic error (fabrication and installation error) of the press is relatively large, resulting in the increased motion error of envelope die. Therefore, it is necessary to establish a reasonable kinematic error model and a calibration method to provide an essential basis for the precision design and control of the new press. Firstly, the kinematic error model, in which the 114 kinematic errors and multi-DOF motion error of envelope die are unitedly expressed and calculated based on the small displacement screw theory, and error Jacobian matrix for the press are established. Then the kinematic error mechanism for the press is disclosed. It is found that the motion error of envelope die is mainly attributed to 10 positional errors among 114 kinematic errors. Moreover, all the six error components of motion error of envelope die are time-varying with position changing of envelope die, and the position distributions of the maximum six error components are non-uniform during one motion period of envelope die. Based on the above results, a new non-uniform kinematic error calibration method for the press is proposed. Finally, the kinematic error calibration experiments are conducted. It is shown that the prediction accuracy of motion error of envelope die with the proposed non-uniform kinematic error calibration method is significantly improved from 89.06% to 99.67% compared with the traditional uniform kinematic error calibration method, which verifies that the established kinematic error model and non-uniform calibration method for heavy load multi-DOF envelope forming press are reliable.

A rapid prediction method for the stiffness and the machining accuracy evaluation of a parallel kinematic mechanism

A rapid prediction method for the stiffness and the machining accuracy evaluation of a parallel kinematic mechanism

Design of a 2RRU-RRS Parallel Kinematic Mechanism for an Inner-Cavity Machining Hybrid Robot

Abstract This article presents a hybrid robot for machining the inner cavity of large-scale workpiece, and it is composed of three parts: a mobile device with 1T degree-of-freedom (DoF), a serial module with 1R1T DoFs, and a 2RRU-RRS parallel kinematic mechanism (PKM) with 2R1T DoFs. The 2RRU-RRS PKM has some advantages with a folding structure, only one S joint, two certain rotational axes, and all the fixed actuators. In this article, the conceptual design, theoretical kinematic and dynamic modeling, performance evaluation, and optimization of the parallel system are investigated. A 3D printing model is built to demonstrate the application potential. This article plays an exemplary role in the design of inner-cavity machining hybrid robots.

Geometric Error Calibration of XYZ-3RPS Hybrid Kinematic Machine via Binocular Vision

Abstract To improve the motion accuracy of an XYZ-3RPS hybrid kinematic machine (HKM), a geometric error calibration method via binocular vision measurement is studied. First, to separately calibrate the series kinematic mechanisms (SKMs) and parallel kinematic mechanisms (PKMs), the geometric error identification equations (GEIEs) of the XYZ SKM and 3RPS PKM are derived, respectively. By analyzing the different influence principles of the geometric errors on the position and attitude of the 3RPS PKM, a constraint function is added to the GEIE of the PKM to improve the calculation accuracy. Moreover, the geometric error compensation strategy is based on the structural characteristics of the XYZ-3RPS HKM. In addition, based on the principle of binocular vision measurement, two calibration plates, called dynamic and static calibration plates, are designed as markers to define the coordinate systems, enabling the acquisition of full positions and attitudes. Furthermore, a marker transformation method and an in-situ adjustment method are designed to determine the positions and attitudes of the HKM required for calibration such that the marker is always at the center of the field of view of the camera to improve measurement accuracy. Finally, the effectiveness of the calibration method is verified through prototype experiments.

Quasi-Coordinates-Based Closed-Form Dynamic Modeling and Analysis for a 2R1T PKM with a Rigid–Flexible Structure

This work derives a closed-form dynamic model for a two rotational and one translational degrees-of-freedom (2R1T) parallel kinematic mechanism (PKM) with a hybrid rigid–flexible structure for force-control applications. Based on the three-prismatic-prismatic-spherical (3PPS) kinematic configuration of the 2R1T PKM and its zero-torsion motion characteristics, a symbolic formulation approach is proposed to establish closed-form kinematic models for both forward and inverse kinematics analysis. As the moving platform pose of the 2R1T 3PPS PKM can be readily determined by the three active prismatic joint variables and the three passive prismatic joint variables, these six joint variables are selected as the quasi-coordinates so as to systematically develop the closed-form dynamic model with a Lagrangian formulation, in which the stiffness and deformation of the three flexure-based passive prismatic joints are uniformly taken into consideration. Through eliminating the three passive prismatic joint variables based on the principle of virtual work and the relationships between the active and passive prismatic joint variables, a closed-form dynamic model for the 2R1T 3PPS PKM with a rigid–flexible structure is finally obtained. The correctness of the closed-form dynamic model was validated with the commercial dynamic simulation software. Utilizing the closed-form dynamic model, the effects of different flexure stiffness in driving directions on the required active joint force were investigated, which indicated that little flexure stiffness in driving directions is desired.

Singularity analysis of 3-DOF planar parallel continuum robots with constant curvature links.

This paper presents the singularity analysis of 3-DOF planar parallel continuum robots (PCR) with three identical legs. Each of the legs contains two passive conventional rigid 1-DOF joints and one actuated planar continuum link, which bends with a constant curvature. All possible PCR architectures featuring such legs are enumerated and the kinematic velocity equations are provided for each of them. Afterwards, a singularity analysis is conducted based on the obtained Jacobian matrices, providing a geometrical understanding of singularity occurences. It is shown that while loci and occurrences of type II singularities are mostly analogous to conventional parallel kinematic mechanisms (PKM), type I singularity occurences for the PCR studied in this work are quite different from conventional PKM and less geometrically intuitive. The study provided in this paper can promote further investigations on planar parallel continuum robots, such as structural design and control.

パラレルメカニズムを用いた小形三次元座標測定機

パラレルメカニズムを用いた小形三次元座標測定機

THE NEW IMPLEMENTATION METHODS MANAGEMENT MECHANICAL CUTTING AND VIBRO PROCESS

The problem of ensuring the required quality and operation of the properties of machine parts is becoming increasingly important in mechanical engineering. However, to date, no generalized theoretical relationships between surface quality parameters, machining accuracy, performance properties of parts and parameters of machining processes, which allow to solve the problem of technological support of the specified performance properties of parts. The control of the surface formation process with the required properties is carried out mainly by using partial experimental dependences and tables of processing modes. The complexity of the problem is that when machining parts it is necessary to establish such processing conditions that would provide a set of requirements for tool wear, machining accuracy, surface quality characteristics, productivity and more. Working machines of special and general purpose, their separate knots and mechanisms are constantly improved, thus increase of a technical level of machines is carried out by introduction of new technical decisions, use of modern technologies and scientific developments. The experience of development and operation of mechanisms of parallel kinematics confirms their high efficiency and prospects of this direction of mechanical engineering. Due to the design features of the layout, the mechanisms of parallel kinematics have closed kinematic chains that form spatial structures. As a rule, these structures are based on triangular rod systems. They have high rigidity characteristics, provide high speeds and acceleration of working bodies. Accordingly, these capabilities can significantly increase the static and dynamic accuracy of positioning mechanisms. The lack of theoretical foundations for the development of mechanisms, in particular high-precision mechanisms, hinders the widespread introduction of parallel kinematics mechanisms. Improving accuracy requires a comprehensive study of kinematics and work processes, taking place in their main nodes. Therefore, studies aimed at improving the parameters of static and dynamic accuracy of spatial mechanisms of parallel kinematics are relevant.

An efficient combined local and global search strategy for optimization of parallel kinematic mechanisms with joint limits and collision constraints

The optimization of parallel kinematic manipulators (PKM) involve several constraints that are difficult to formalize, thus making optimal synthesis problem highly challenging. The presence of passive joint limits as well as the singularities and self-collisions lead to a complicated relation between the input and output parameters. In this article, a novel optimization methodology is proposed by combining a local search, Nelder–Mead algorithm, with global search methodologies such as low discrepancy distribution for faster and more efficient exploration of the optimization space. The effect of the dimension of the optimization problem and the different constraints are discussed to highlight the complexities of closed-loop kinematic chain optimization. The work also presents the approaches used to consider constraints for passive joint boundaries as well as singularities to avoid internal collisions in such mechanisms. The proposed algorithm can also optimize the length of the prismatic actuators and the constraints can be added in modular fashion, allowing to understand the impact of given criteria on the final result. The application of the presented approach is used to optimize two PKMs of different degrees of freedom.

Optimization and Control of a Planar Three Degrees of Freedom Manipulator with Cable Actuation

The paper analyzes a planar three degrees of freedom manipulator with cable actuation. Such a system can be understood as a special type of hybrid parallel kinematic mechanism composed of the rigid serial chain and the additional auxiliary cable system. The advantage of the auxiliary cable mechanism is the ability to reconfigure the whole system. The fulfillment of sufficient prestressing is the constraint of the optimization process. Computed Torque Control with a cable force distribution algorithm is implemented. The control algorithm performance is examined on different trajectories, including non-smooth motion requests, and its robustness is tested by randomly generated errors of the model parameters in regulators. The results demonstrate that the optimized structure is capable of controlling the manipulator motion and keeping the cable prestressing within the given limits.

Design Optimization of 3-DOF Redundant Planar Parallel Kinematic Mechanism Based Finishing Cut Stage for Improving Surface Roughness of FDM 3D Printed Sculptures

This paper describes the optimal design of a 3-DOF redundant planar parallel kinematic mechanism (PKM) based finishing cut stage to improve the surface roughness of FDM 3D printed sculptures. First, to obtain task-optimized and singularity minimum workspace of the redundant PKM, a weighted grid map based design optimization was applied for a task-optimized workspace without considering the redundancy. For the singularity minimum workspace, the isotropy and manipulability of the end effector of the PKM were carefully modeled under the previously obtained redundancy for optimality. It was confirmed that the workspace size increased by 81.4%, and the internal singularity significantly decreased. To estimate the maximum rated torque and torsional stiffness of all active joints and prevent an undesired end effector displacement of more than 200 μμm, a kinematic stiffness model composed of active and passive kinematic stiffness was derived from the virtual work theorem, and the displacement characteristic at the end effector was examined by applying the reaction force for the PLA surface finishing as an external force acting at the end effector. It was confirmed that the displacement of the end effector of a 1-DOF redundant PKM was not only less than 200 μμm but also decreased from 40.9% to 67.4% compared to a nonredundant actuation.

Design of an Ankle Rehab Robot With a Compliant Parallel Kinematic Mechanism

Abstract In this article, we present the design of a novel ankle rehabilitation robot (ARR), called the Flex-ARR, that employs a compliant parallel kinematic mechanism (PKM) with decoupled degrees-of-freedom. While multiple ARRs have been developed and commercialized, their clinical adoption has been limited primarily because they do not emulate the natural motion of the ankle. Based on a review of existing ARRs and their limitations, this article defines functional requirements and design specifications for an optimal ARR. These are then used to develop a design strategy followed by conceptual and detailed design of a novel ARR. The proposed Flex-ARR is designed to collocate the biological center of rotation of the ankle with that of the robot's center of rotation to allow natural ankle motion. The strategic use of a compliant PKM in the Flex-ARR not only absorbs any residual misalignment between these two centers but also helps inherently accommodate variations in user foot sizes with minimal adjustments. Detailed design includes the ARR structure with adjustable features, compliant PKM optimization, sensor and actuator selection, and an alignment tool.

Design and testing of a soft parallel robot based on pneumatic artificial muscles for wrist rehabilitation

Wrist rehabilitation is needed to help post-stroke and post-surgery patients recover from wrist fracture or injury. Traditional rehabilitation training is conducted by a therapist in a hospital, which hinders timely treatment due to the corresponding time and space constraints. This paper presents the design and implementation of a soft parallel robot for automated wrist rehabilitation. The presented wrist rehabilitation robot integrates the advantages of both soft robot and parallel robot structures. Unlike traditional rigid-body based rehabilitation robots, this soft parallel robot exhibits a compact structure, which is highly secure, adaptable, and flexible and thus a low-cost solution for personalized treatment. The proposed soft wrist-rehabilitation robot is driven by six evenly distributed linear actuators using pneumatic artificial muscles and one central linear electric motor. The introduced parallel-kinematic mechanism design enables the enhancement of the output stiffness of the soft robot for practical use. An electromyography sensor is adopted to provide feedback signals for evaluating the rehabilitation training process. A kinematic model of the designed robot is derived, and a prototype is fabricated for experimental testing. The results demonstrate that the developed soft rehabilitation robot can assist the wrist to realize all the required training motions, including abduction-adduction, flexion-extension, and supination-pronation. The compact and lightweight structure of this novel robot makes it convenient to use, and suitable rehabilitation training modes can be chosen for tailored rehabilitation at home or in a hospital.

A Planar Parallel Device for Neurorehabilitation

The patient population needing physical rehabilitation in the upper extremity is constantly increasing. Robotic devices have the potential to address this problem, however most of the rehabilitation robots are technically advanced and mainly designed for clinical use. This paper presents the development of an affordable device for upper-limb neurorehabilitation designed for home use. The device is based on a 2-DOF five-bar parallel kinematic mechanism. The prototype has been designed so that it can be bound on one side of a table with a clamp. A kinematic optimization was performed on the length of the links of the manipulator in order to provide the optimum kinematic behaviour within the desired workspace. The mechanical structure was developed, and a 3D-printed prototype was assembled. The prototype embeds two single-point load cells to measure the force exchanged with the patient. Rehabilitation-specific control algorithms are described and tested. Finally, an experimental procedure is performed in order to validate the accuracy of the position measurements. The assessment confirms an acceptable level of performance with respect to the requirements of the application under analysis.