Parallel Kinematic Research Articles

Modeling and analysis of 2-axis reconfigurable parallel mechanism MOMA with translatory actuated joints

This paper presents modeling and analysis of a 2-axis reconfigurable parallel mechanism. In this paper, generalized model for solving of inverse and direct kinematic problems is presented. Generalized equations that represent the solution of the kinematic problems of parallel kinematic mechanism applicable to any configuration of 2-axis reconfigurable parallel mechanism are derived. Some of characteristic configurations of 2-axis parallel mechanism are shown as examples. For the selected configurations the workspaces are determined and the possible singular positions of these configurations are analized.

Optimization and comparison between two 6-DoF parallel kinematic machines for HIL simulations in wind tunnel

Parallel Robots are for sure the best choice for those applications in which a high accuracy and a high stiffness are required. As a matter of fact the closed-loop kinematic chains that characterize these machines guarantee a very low sensitivity of the end-effector position to the various sources of error. However the working volume of parallel kinematic machines is in general limited with respect to their dimensions. Moreover the reduced mobility range of the passive joints represents a critical aspect that cannot be underestimated. For these reasons PKMs should be optimized for the application they are meant.Given the specifications of the workspace that the machine should be able to cover, it’s necessary to identify an architecture that is suitable for this specific task. This paper describes the optimization process and the comparison between two candidates, the Hexaslide and the Gough-Stewart platform, in order to find out which one is the best choice for a task that requires to reproduce the hydrodynamic effect of sea waves at the bottom of scale models of off-shore wind turbines and boats during HIL simulations in the wind tunnel of the Politecnico di Milano.

Substructuring and Control Strategies for Hardware-in-the-Loop Simulations of Multiaxial Suspension Test Rigs

Abstract: Hardware-in-the-Loop (HiL) simulation is a powerful tool for testing and developing mechatronic systems under realistic conditions. The real components under consideration are coupled appropriately with a real-time computer which simulates mathematical models of the remainder of the system in parallel. For mechatronic systems like vehicle axles the realization of HiL simulations with spatial excitation can be a challenging task, as in general manipulator and specimen possess a complex contact situation. In this context, the following paper presents substructuring techniques and control strategies applied to a highly dynamic vehicle axle test rig with a parallel kinematic machine used as the excitation unit. Simulation results are provided to underline the effectiveness of the presented approaches.

An innovative machine for Fused Deposition Modeling of metals and advanced ceramics

The design of a new additive manufacturing (AM) system based on extrusion and 3D deposition of a mixture of metal (or advanced ceramic) powder and polymeric binder is described in this paper. The proposed system is totally innovative in terms of combination of deposited work material, extrusion system (head and nozzle), and deposition work table, which is based on a 5-axes parallel kinematics machine (PKM). The extrusion head and nozzle have been designed in order to be able to extrude high viscosity mixtures with low polymeric content. The 5-axes PKM is aimed at obtaining a good surface quality of the deposited work and reducing the need for supports during deposition. After the deposition, the material is de-binded and sintered to nearly the density of the solid material as-cast. The design and kinematics of the machine and especially the PKM table is described in this paper, the main design issues are discussed and some preliminary extrusion and sintering results are presented.

Inverse Kinematics for Upper Limb Compound Movement Estimation in Exoskeleton-Assisted Rehabilitation

Robot-Assisted Rehabilitation (RAR) is relevant for treating patients affected by nervous system injuries (e.g., stroke and spinal cord injury). The accurate estimation of the joint angles of the patient limbs in RAR is critical to assess the patient improvement. The economical prevalent method to estimate the patient posture in Exoskeleton-based RAR is to approximate the limb joint angles with the ones of the Exoskeleton. This approximation is rough since their kinematic structures differ. Motion capture systems (MOCAPs) can improve the estimations, at the expenses of a considerable overload of the therapy setup. Alternatively, the Extended Inverse Kinematics Posture Estimation (EIKPE) computational method models the limb and Exoskeleton as differing parallel kinematic chains. EIKPE has been tested with single DOF movements of the wrist and elbow joints. This paper presents the assessment of EIKPE with elbow-shoulder compound movements (i.e., object prehension). Ground-truth for estimation assessment is obtained from an optical MOCAP (not intended for the treatment stage). The assessment shows EIKPE rendering a good numerical approximation of the actual posture during the compound movement execution, especially for the shoulder joint angles. This work opens the horizon for clinical studies with patient groups, Exoskeleton models, and movements types.

Feasibility Study of an Extrusion-based Direct Metal Additive Manufacturing Technique

A new extrusion-based additive manufacturing technique is described in this paper together with the main components of the machine capable of carrying out the process. Innovative characteristics of the machine are the fixed extrusion head and the workpiece moving thanks to a 5-axis parallel kinematics handling system, allowing the capability of inclining the part during the material deposition and consequently avoiding support structures. The extrusion head and nozzle have been designed in order to be able to extrude high viscosity mixtures with low polymeric content. Preliminary tests prove that a good final density can be obtained after de-binding and sintering and that it is possible to achieve a good bonding of extruded and deposited wires in case of AISI 630 stainless steel.

Research on kinematics and singularity of a 3-RRR planar hybrid mechanism

This paper studies the kinematics and singularity of a 3-RRR planar hybrid mechanism, which consists of serial and parallel kinematic chains. The configuration characteristics of the 3-RRR planar hybrid mechanism are analysed. The kinematics of the 3-RRR planar hybrid mechanism is solved by applying chaos particle swarm optimisation. The forward position and the inverse position are formulated. Moreover, three kinds of singularities are analysed. The assembly configurations of forward singularity, inverse singularity are obtained, respectively. The results play an important role in practical application for the 3-RRR hybrid mechanism.

パラレルメカニズムを用いた高速・高精度3次元座標計測システム（第28報）

パラレルメカニズムを用いた高速・高精度3次元座標計測システム（第28報）

Error Analysis and Adaptive-Robust Control of a 6-DoF Parallel Robot with Ball-Screw Drive Actuators

Parallel kinematic machines (PKMs) are commonly used for tasks that require high precision and stiffness. In this sense, the rigidity of the drive system of the robot, which is composed of actuators and transmissions, plays a fundamental role. In this paper, ball-screw drive actuators are considered and a 6-degree of freedom (DoF) parallel robot with prismatic actuated joints is used as application case. A mathematical model of the ball-screw drive is proposed considering the most influencing sources of nonlinearity: sliding-dependent flexibility, backlash, and friction. Using this model, the most critical poses of the robot with respect to the kinematic mapping of the error from the joint- to the task-space are systematically investigated to obtain the workspace positional and rotational resolution, apart from control issues. Finally, a nonlinear adaptive-robust control algorithm for trajectory tracking, based on the minimization of the tracking error, is described and simulated.

Kinetostatic modeling and analysis of an exechon parallel kinematic machine(PKM) module

As a newly invented parallel kinematic machine(PKM), Exechon has found its potential application in machining and assembling industries due to high rigidity and high dynamics. To guarantee the overall performance, the loading conditions and deflections of the key components must be revealed to provide basic mechanic data for component design. For this purpose, a kinetostatic model is proposed with substructure synthesis technique. The Exechon is divided into a platform subsystem, a fixed base subsystem and three limb subsystems according to its structure. By modeling the limb assemblage as a spatial beam constrained by two sets of lumped virtual springs representing the compliances of revolute joint, universal joint and spherical joint, the equilibrium equations of limb subsystems are derived with finite element method(FEM). The equilibrium equations of the platform are derived with Newton’s 2nd law. By introducing deformation compatibility conditions between the platform and limb, the governing equilibrium equations of the system are derived to formulate an analytical expression for system’s deflections. The platform’s elastic displacements and joint reactions caused by the gravity are investigated to show a strong position-dependency and axis-symmetry due to its kinematic and structure features. The proposed kinetostatic model is a trade-off between the accuracy of FEM and concision of analytical method, thus can predict the kinetostatics throughout the workspace in a quick and succinct manner. The proposed modeling methodology and kinetostatic analysis can be further expanded to other PKMs with necessary modifications, providing useful information for kinematic calibration as well as component strength calculations.

Positioning uncertainty of the Tricept type parallel kinematic structure

The paper discusses theoretical aspects that arised during determination of theoretical positioning accuracy of parallel kinematic structures (PKS) with special regard to the Tricept type PKS. Apart from the conventional serial structures that employ translate or rotational movement (or their combination) of individual driving axes, parallel structures comprise a set of telescopic driving rods that are joined together via solid platform. Due to this fact, the mathematical model describing relationship between the driving actions of telescopic rods and resulting coordinates of the desired effector's endpoint is rather complex. To determine the theoretically achievable positioning accuracy of the endpoint, authors investigated theoretical influence of geometrical imperfections of the machine design and employed the law of uncertainties propagation. Their aim was to investigate theoretically achievable positioning accuracy of the machine prior to the final design solutions thus helping the designer to optimize the machine's design.

Five-axis interpolation of continuous short linear trajectories for 3[PP]S-XY hybrid mechanism by dual Bezier blending

A novel five-axis real-time interpolation algorithm for 3[PP]S-XY hybrid mechanism is proposed in this paper. In the algorithm, the five-axis tool path for controlling this hybrid mechanism is separated into two sub-paths. One sub-path describes the movement of 3[PP]S parallel kinematic mechanism module, and the other one describes the movement of XY platform. A pair of cubic Bezier curves is employed to smooth the corners in those two sub-paths. Based on the homogenous Jacobian matrix of 3[PP]S mechanism, a relationship between the position errors of every driving joint in hybrid mechanism and the position deviation of the tool tip center point at the moving platform is established. This relationship is used to estimate the approximation error for the corners smoothing according to the accuracy requirement of tool tip center in interpolation. Due to the high computational efficiency of this corner smoothing method, it is integrated into the look-ahead module of computer numerical control (CNC) system to perform online tool path smoothing. By performing the speed planning based on a floating window scheme, a jerk limited S-shape speed profile can be generated efficiently. On this basis, a realtime look-ahead scheme, which is comprised of path-smoothing and feedrate scheduling, is developed to acquire a speed profile with smooth acceleration. A monotonic cubic spline is employed for synchronization between those two smoothed sub-paths in tool path interpolation. This interpolation algorithm has been integrated into our own developed CNC system to control a 3PRS-XY experimental instrument (P, R and S standing for prismatic, revolute and spherical, respectively). A club shaped trajectory is adopted to verify the smoothness and efficiency of the five-axis interpolator for hybrid mechanism control.

Extended Model-Based Feedforward Compensation in ℒ1 Adaptive Control for Mechanical Manipulators: Design and Experiments

This paper deals with a new control scheme for Parallel Kinematic Manipulators (PKMs) based on the L1 adaptive control theory. The original L1 adaptive controller is extended by including an adaptive loop based on the dynamics of the PKM. The additional model-based term is in charge of the compensation of the modeled nonlinear dynamics in the aim of improving the tracking performance. Moreover, the proposed controller is enhanced to reduce the internal forces, which may appear in the case of Redundantly Actuated PKMs (RA-PKMs). The generated control inputs are first regulated through a projection mechanism that reduces the antagonistic internal forces, before being applied to the manipulator. To validate the proposed controller and to show its effectiveness, real-time experiments are conducted on a new four degrees-of-freedom (4-DOFs) RA-PKM developed in our laboratory.

Design and test of a parallel kinematic solar tracker

This article proposes a parallel kinematic solar tracker designed for driving high-concentration photovoltaic modules. This kind of module produces energy only if they are oriented with misalignment errors lower than 0.4°. Generally, a parallel kinematic structure provides high stiffness and precision in positioning, so these features make this mechanism fit for the purpose. This article describes the work carried out to design a suitable parallel machine: an already existing architecture was chosen, and the geometrical parameters of the system were defined in order to obtain a workspace consistent with the requirements for sun tracking. Besides, an analysis of the singularities of the system was carried out. The method used for the singularity analysis revealed the existence of singularities which had not been previously identified for this kind of mechanism. From the analysis of the mechanism developed, very low nominal energy consumption and elevated stiffness were found. A small-scale prototype of the system was constructed for the first time. A control algorithm was also developed, implemented, and tested. Finally, experimental tests were carried out in order to verify the capability of the system of ensuring precise pointing. The tests have been considered passed as the system showed an orientation error lower than 0.4° during sun tracking.

Static Stiffness Modeling of Parallel Kinematics Machine Tool Joints

Static Stiffness Modeling of Parallel Kinematics Machine Tool Joints

An Emulator-Based Prediction of Dynamic Stiffness for Redundant Parallel Kinematic Mechanisms

The accuracy of a parallel kinematic mechanism (PKM) is directly related to its dynamic stiffness, which in turn is configuration dependent. For PKMs with kinematic redundancy, configurations with higher stiffness can be chosen during motion-trajectory planning for optimal performance. Herein, dynamic stiffness refers to the deformation of the mechanism structure, subject to dynamic loads of changing frequency. The stiffness-optimization problem has two computational constraints: (i) calculation of the dynamic stiffness of any considered PKM configuration, at a given task-space location, and (ii) searching for the PKM configuration with the highest stiffness at this location. Due to the lack of available analytical models, herein, the former subproblem is addressed via a novel effective emulator to provide a computationally efficient approximation of the high-dimensional dynamic-stiffness function suitable for optimization. The proposed method for emulator development identifies the mechanism's structural modes in order to breakdown the high-dimensional stiffness function into multiple functions of lower dimension. Despite their computational efficiency, however, emulators approximating high-dimensional functions are often difficult to develop and implement due to the large amount of data required to train the emulator. Reducing the dimensionality of the approximation function would, thus, result in a smaller training data set. In turn, the smaller training data set can be obtained accurately via finite-element analysis (FEA). Moving least-squares (MLS) approximation is proposed herein to compute the low-dimensional functions for stiffness approximation. Via extensive simulations, some of which are described herein, it is demonstrated that the proposed emulator can predict the dynamic stiffness of a PKM at any given configuration with high accuracy and low computational expense, making it quite suitable for most high-precision applications. For example, our results show that the proposed methodology can choose configurations along given trajectories within a few percentage points of the optimal ones.

Trajectory planning of parallel kinematic manipulators for the maximum dynamic load-carrying capacity

The objective of this paper is to identify the trajectory that accomplishes the assigned motion with the maximum dynamic load-carrying capacity (DLCC) which is subject to constraints imposed by the kinematics and dynamics of a manipulator structure. In this study, the possible trajectories of the manipulator are modeled using a parametric path representation, the optimal trajectory is then obtained using a two-loop of optimization process, in which the inner-loop optimization process based on the Simplex-type linear programming method is used to determine the dynamic loading at each discrete point along the presumed trajectory and then to formulate the DLCC; the outer-loop optimization process based on the particle swarm optimization algorithm is to solve the controlled points by maximizing the formulated DLCC. The numerical results confirm the feasibility of the optimized trajectories and demonstrate the effectiveness of the proposed algorithm for the maximum dynamic load-carrying trajectory planning of a parallel kinematic manipulator.

Applications of Neural Networks for Exactness of Treatment on Machine-Tools with Parallel Kinematics

In this paper authors conducted analysis of management features on machine-tools with numerical control using neural network for achieving exactness. Applications of Hopfield networks are discussed in the paper along with application of neuron computers that offer decision making of tasks ticker-coil.

Inverse dynamics of a 3-DOF translational parallel kinematic machine

In this paper, kinematics and dynamics modeling of a typical 3-Degree of freedom (DOF) translational Parallel kinematic machine (PKM) is carried out. The kinematic structure of PKM consists of three limbs, connecting the base and the tool platform. Each limb consists of an arm and a forearm with joints Prismatic-revolute-revolute-revolute (PRRR). The arrangement of joints are in such a way that the tool platform will have pure translational motion along the Cartesian axes. Inverse kinematic relations that are necessary to find the slider positions and joint angles for a given position of tool platform are derived. The dynamics model is then derived based on Natural orhogonal complement (NOC). The inverse dynamics equations presented are used to compute actuator forces. The actuator forces using NOC are validated with those obtained based on Lagrangian method. The effect of slider, arm, and forearm inertia on the actuator forces is studied to know whether to neglect the arm and forearm inertias while computing the actuator forces for PKM. Finally, an attempt is made to find the optimal location of a circular trajectory using Genetic algorithms (GA) with minimization of Grand total actuator force (GTAF) as objective function.

Design and Development of a High-Speed and High-Rotation Robot With Four Identical Arms and a Single Platform

In this paper, a novel parallel kinematic mechanism (PKM) with Schönflies motion has been proposed under the guidance of a graphical type synthesis method. This PKM is composed of four identical arms and a single platform and has high rotational capability. The single-platform structure used in the proposed PKM can reduce structural complexity, increase dynamic response. In addition, the composite parallelogram structure in each arm brings in better limb stiffness. Based on the proposed concept, optimal design is carried out to make the PKM realize its high rotational potential. In this process, an input transmission index (ITI) and an output transmission index (OTI) (the two indices can be used to numerically evaluate motion and force transmission performance of PKMs, respectively) are taken as the performance evaluation criteria. On this basis, some other indices are defined and the corresponding performance atlases are also plotted to investigate the potential workspace. Consequently, dimensional parameters of the discussed PKM are derived on the precondition that the rotational capability should reach at least ±90 deg, and the workspace has also been identified. Based on these foundations, a parallel robot X4 has been developed which can realize high-speed pick-and-place manipulation in industrial lines.