Nonstationary Vibration of a Fully Flexible Parallel Kinematic Machine

2007 ◽  
Vol 129 (5) ◽  
pp. 623-630 ◽  
Author(s):  
Zili Zhou ◽  
Chris K. Mechefske ◽  
Fengfeng Xi
Keyword(s):  
Natural Frequencies ◽  
Kinematic Model ◽  
Inertial Force ◽  
Mode Shapes ◽  
Absolute Amount ◽  
Hard Material ◽  
Parallel Kinematic Machine ◽  
Damping Matrix ◽  
Nonstationary Vibration ◽  
Parallel Kinematic

This paper studies the problem of the nonstationary vibration of a fully flexible parallel kinematic machine (PKM) that has flexibilities both in links and in joints. In the stationary case, the PKM was treated as a varying structure and the natural frequencies and mode shapes changed with the changes in the PKM configuration, without consideration of the PKM nominal motion. In the nonstationary case as studied in this paper, the nominal motion is included to investigate how it would affect the natural frequencies and mode shapes. To do so, a nonstationary model is developed using the elasto-dynamics method. First, a kinematic model is built based on rigid links and ideal joints, which is used to solve the PKM nominal motion. Second, the kinetic model is developed considering the flexibilities in the links and joints. In this case, the vibration equations would contain the Coriolis and gyroscopic damping matrix and the tangential and normal stiffening matrix, which are the terms resulting from the nominal motion. The instantaneous eigensolutions are obtained from the nonstationary eigenequations. The results show that (i) the slider velocity affects the instantaneous natural frequencies more than the slider acceleration; and (ii) the nominal motion has an effect on the system eigencharacteristics (e.g., the nonstationary frequencies can be higher or lower than the stationary ones) but the effect is small in an absolute amount (within 2.1Hz in natural frequencies presented at set nominal motions of the studied PKM prototype). This is because the extra inertial force from the nominal motion is always much smaller than the stiffness force in the system bodies as long as the bodies are made of hard material. The method presented is more convenient to use for the multibody system with flexible joints than other methods.

scholarly journals Rapid Evaluation for Position-Dependent Dynamics of a 3-DOF PKM Module

2014 ◽  
Vol 6 ◽  
pp. 238928 ◽  
Author(s):  
Hai-wei Luo ◽  
Hui Wang ◽  
Jun Zhang ◽  
Qi Li
Keyword(s):  
Natural Frequencies ◽  
Mode Shapes ◽  
Parallel Kinematic Machine ◽  
Computationally Efficient ◽  
Element Analysis ◽  
Reduction Techniques ◽  
Modal Reduction ◽  
Governing Differential Equation ◽  
Parallel Kinematic ◽  
Analytical System

Based on the substructure synthesis and modal reduction technique, a computationally efficient elastodynamic model for a fully flexible 3-RPS parallel kinematic machine (PKM) tool is proposed, in which the frequency response function (FRF) at the end of the tool can be obtained at any given position throughout its workspace. In the proposed elastodynamic model, the whole system is divided into a moving platform subsystem and three identical RPS limb subsystems, in which all joint compliances are included. The spherical joint and the revolute joint are treated as lumped virtual springs with equal stiffness; the platform is treated as a rigid body and the RPS limbs are modelled with modal reduction techniques. With the compatibility conditions at interfaces between the limbs and the platform, an analytical system governing differential equation is derived. Based on the derived model, the position-dependent dynamic characteristics such as natural frequencies, mode shapes, and FRFs of the 3-RPS PKM are simulated. The simulation results indicate that the distributions of natural frequencies throughout the workspace are strongly dependant on mechanism's configurations and demonstrate an axial-symmetric tendency. The following finite element analysis and modal tests both validate the analytical results of natural frequencies, mode shapes, and the FRFs.

Characteristic Equation-Based Dynamic Analysis of a Three-Revolute Prismatic Spherical Parallel Kinematic Machine

2015 ◽  
Vol 10 (2) ◽  
Author(s):  
Jun Zhang ◽  
Jian S. Dai ◽  
Tian Huang
Keyword(s):  
Dynamic Model ◽  
Dynamic Characteristics ◽  
Natural Frequencies ◽  
Eigenvalue Decomposition ◽  
Mode Shapes ◽  
Design Parameters ◽  
Parallel Kinematic Machine ◽  
Characteristic Equations ◽  
Parallel Kinematic ◽  
Compliance Model

A three-revolute prismatic spherical (3-RPS) parallel kinematic machine (PKM) module is proposed as an alternative solution for high-speed machining (HSM) tool. Considering the PKM as a typical compliant parallel device, whose three limb assemblages have bending, extending, and torsional deflections, this paper applies screw theory to establish an analytical compliance model for the device. The developed compliance model is then combined with the energy method to deduce a comprehensive dynamic model of the 3-RPS module. The solution for the characteristic equations of the dynamic model leads to the modal properties of the PKM module. Based on the eigenvalue decomposition of the characteristic equations, a modal analysis is conducted. The natural frequencies and corresponding mode shapes at typical and nontypical configurations are analyzed and compared with finite element analysis (FEA) results. With an algorithm of workspace partitions combining with eigenvalue decompositions, the distributions of natural frequencies throughout the workspace are predicted to reveal a strong dependency of dynamic characteristics on mechanism's configurations. At the last stage, the effects of some design parameters on system dynamic characteristics are investigated with the purpose of providing useful information for the conceptual design and performance improvement for the PKM.

scholarly journals Kinematic Analysis and Trajectory Planning of the Orthoglide 5-Axis

2015 ◽  
Author(s):  
S. Caro ◽  
D. Chablat ◽  
P. Lemoine ◽  
P. Wenger
Keyword(s):  
Trajectory Planning ◽  
Kinematic Analysis ◽  
High Speed ◽  
Degrees Of Freedom ◽  
Kinematic Model ◽  
Inverse Kinematic ◽  
Hybrid Architecture ◽  
Parallel Kinematic Machine ◽  
Control Loop ◽  
Parallel Kinematic

The subject of this paper is about the kinematic analysis and the trajectory planning of the Orthoglide 5-axis. The Orthoglide 5-axis a five degrees of freedom parallel kinematic machine developed at IRCCyN and is made up of a hybrid architecture, namely, a three degrees of freedom translational parallel manipulator mounted in series with a two degrees of freedom parallel spherical wrist. The simpler the kinematic modeling of the Orthoglide 5-axis, the higher the maximum frequency of its control loop. Indeed, the control loop of a parallel kinematic machine should be computed with a high frequency, i.e., higher than 1.5 MHz, in order the manipulator to be able to reach high speed motions with a good accuracy. Accordingly, the direct and inverse kinematic models of the Orthoglide 5-axis, its inverse kinematic Jacobian matrix and the first derivative of the latter with respect to time are expressed in this paper. It appears that the kinematic model of the manipulator under study can be written in a quadratic form due to the hybrid architecture of the Orthoglide 5-axis. As illustrative examples, the profiles of the actuated joint angles (lengths), velocities and accelerations that are used in the control loop of the robot are traced for two test trajectories.

Design and Experimental Investigation of a New 2R1T Overconstrained Parallel Kinematic Machine With Actuation Redundancy

2019 ◽  
Vol 11 (3) ◽  
Author(s):  
Lingmin Xu ◽  
Xinxue Chai ◽  
Qinchuan Li ◽  
Liangan Zhang ◽  
Wei Ye
Keyword(s):  
Inverse Kinematics ◽  
High Speed ◽  
Degrees Of Freedom ◽  
Kinematic Model ◽  
Curved Surfaces ◽  
Parallel Kinematic Machine ◽  
Actuation Redundancy ◽  
Dimensional Parameters ◽  
Force Transmissibility ◽  
Parallel Kinematic

Two rotations and one translation (2R1T) parallel kinematic machines (PKMs) are suitable for the machining of complex curved surfaces, which requires high speed and precision. To further improve rigidity, precision, and avoid singularity, actuation redundancy, and overconstrained PKMs with fixed actuators and limited-degrees of freedom (DOF) limbs are preferred. However, there are few 2R1T PKMs with these features. This paper introduces a new 2R1T overconstrained PKM with actuation redundancy, which is called Tex4. The Tex4 PKM consists of four limited-DOF limbs; that is, two PUR limbs and two 2PRU limbs (where P denotes an actuated prismatic joint, U denotes a universal joint, and R denotes a revolute joint). The kinematic model of the proposed 2PUR-2PRU machine is presented along with the results of mobility, inverse kinematics, and velocity analysis. By considering the motion/force transmissibility, the dimensional parameters of the Tex4 PKM were optimized to obtain an improved satisfactory transmission workspace without singular configurations. Finally, a prototype based on the optimized parameters was fabricated, and its feasibility and accuracy were validated by motion and position error experiments. The Tex4 PKM has the advantages of high rigidity, simple kinematic model, and zero singularity in the workspace, which suggests that it has potential for use in the high-speed machining of curved surfaces.

Elastodynamic Modeling and Analysis for an Exechon Parallel Kinematic Machine

2015 ◽  
Vol 138 (3) ◽  
Author(s):  
Jun Zhang ◽  
Yan Q. Zhao ◽  
Yan Jin
Keyword(s):  
Differential Equations ◽  
Dynamic Characteristics ◽  
Natural Frequencies ◽  
Equations Of Motion ◽  
Structural Features ◽  
Parallel Kinematic Machine ◽  
Dynamic Behaviors ◽  
Elastodynamic Modeling ◽  
Parallel Kinematic ◽  
Moving Platform

As a newly invented parallel kinematic machine (PKM), Exechon has attracted intensive attention from both academic and industrial fields due to its conceptual high performance. Nevertheless, the dynamic behaviors of Exechon PKM have not been thoroughly investigated because of its structural and kinematic complexities. To identify the dynamic characteristics of Exechon PKM, an elastodynamic model is proposed with the substructure synthesis technique in this paper. The Exechon PKM is divided into a moving platform subsystem, a fixed base subsystem and three limb subsystems according to its structural features. Differential equations of motion for the limb subsystem are derived through finite element (FE) formulations by modeling the complex limb structure as a spatial beam with corresponding geometric cross sections. Meanwhile, revolute, universal, and spherical joints are simplified into virtual lumped springs associated with equivalent stiffnesses and mass at their geometric centers. Differential equations of motion for the moving platform are derived with Newton's second law after treating the platform as a rigid body due to its comparatively high rigidity. After introducing the deformation compatibility conditions between the platform and the limbs, governing differential equations of motion for Exechon PKM are derived. The solution to characteristic equations leads to natural frequencies and corresponding modal shapes of the PKM at any typical configuration. In order to predict the dynamic behaviors in a quick manner, an algorithm is proposed to numerically compute the distributions of natural frequencies throughout the workspace. Simulation results reveal that the lower natural frequencies are strongly position-dependent and distributed axial-symmetrically due to the structure symmetry of the limbs. At the last stage, a parametric analysis is carried out to identify the effects of structural, dimensional, and stiffness parameters on the system's dynamic characteristics with the purpose of providing useful information for optimal design and performance improvement of the Exechon PKM. The elastodynamic modeling methodology and dynamic analysis procedure can be well extended to other overconstrained PKMs with minor modifications.

Geometric and Kinematic Modelling of a New Parallel Kinematic Machine Tool: The Tripteor X7 Designed by PCI

2010 ◽  
Vol 112 ◽  
pp. 159-169 ◽  
Author(s):  
Sylvain Pateloup ◽  
Helene Chanal ◽  
Emmanuel Duc
Keyword(s):  
Machine Tools ◽  
Kinematic Model ◽  
Inverse Kinematic ◽  
Parallel Kinematic Machine ◽  
Joint Coordinates ◽  
Kinematic Behaviour ◽  
Kinematic Modelling ◽  
Kinematic Models ◽  
Automotive Part ◽  
Parallel Kinematic

Today, Parallel Kinematic Machine tools (PKMs) appear in automotive and aeronautic industry. These machines propose high kinematic performances allowing a higher productivity than Serial Kinematic Machine tools (SKMs). However, this kinematic behaviour is anisotropic and a particular study is then necessary to locate the part in a workspace where the kinematic performances are well exploited. The study presented in this article deals with the determination of geometric and kinematic models of a new PKM : the Tripteor X7 designed by PCI. The inverse kinematic model expresses the joint coordinates with regard to the cartesian coordinates. The kinematic model which takes into account velocity, acceleration and jerk limits axis, allows computing the displacement time between two tool positions. Finally, this model can be used to determine the workspace where Non Effective cutting Times (TNE) are minimum. The method is applied for an automotive part machining

On Performance Enhancement of Parallel Kinematic Machine

2005 ◽  
Author(s):  
Dan Zhang ◽  
Lihui Wang
Keyword(s):  
Remote Control ◽  
Degrees Of Freedom ◽  
Geometric Model ◽  
Kinematic Model ◽  
Parallel Kinematic Machine ◽  
Web Based ◽  
Remote Manipulation ◽  
Parallel Kinematic ◽  
Moving Platform ◽  
Three Degrees Of Freedom

This paper proposes a spatial three degrees of freedom parallel kinematic machine enhanced by a passive leg and a web-based remote control system. First, the geometric model of the three degrees of freedom parallel kinematic machine is addressed; in the mechanism, a fourth kinematic link — a passive link connecting the base center to the moving platform center — is introduced. This last link is used to constrain the motion of the tool (located in the moving platform) to only three degrees of freedom, as well as to enhance the global stiffness of the structure and distribute the torque from machining. With the kinematic model, a web-based remote control approach is then applied. The concept of the web-based remote manipulation approach is introduced and the principles behind the method are explored in detail. Finally, an example of remote manipulation is demonstrated to the proposed 3-DOF structure using web-based remote control concept before conclusions.

Homing Strategy for a Redundantly Actuated Parallel Kinematic Machine

2008 ◽  
Vol 130 (4) ◽  
Author(s):  
Jinsong Wang ◽  
Jun Wu ◽  
Liping Wang ◽  
Tiemin Li
Keyword(s):  
Control System ◽  
Kinematic Model ◽  
Degree Of Freedom ◽  
Numerical Control ◽  
The Other ◽  
Numerical Control System ◽  
Parallel Kinematic Machine ◽  
Redundantly Actuated ◽  
Parallel Kinematic ◽  
Singular Configuration

In the homing process of a regular parallel kinematic machine (PKM), all servoaxes are independently driven to return to their homing positions. However, in a redundantly actuated PKM, the redundant limb will interfere with other servoaxes. This paper concerns the homing of a redundant four degree of freedom PKM, and an assistant homing strategy is proposed for the machine to pass the singular configuration in the homing process. After the assistant homing is finished, the other four nonredundant axes are driven to return to their home positions independently. Based on the kinematic model and the length of the redundant limb, the condition that the redundant limb performs assistant homing is determined. The homing strategy is incorporated into the numerical control system of the studied PKM. The test shows that the homing strategy is effective, and it can also be useful for other kinds of redundantly actuated PKMs.

scholarly journals A novel, low-cost technique for modelless calibration of a 3-axis parallel kinematic machine

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Bence Tipary ◽  
Ferenc Gábor Erdős
Keyword(s):  
Measurement Technique ◽  
Low Cost ◽  
Kinematic Model ◽  
Calibration Method ◽  
Parallel Kinematic Machine ◽  
Positioning Accuracy ◽  
Content Type ◽  
Volumetric Errors ◽  
Axis Parallel ◽  
Parallel Kinematic

Purpose The purpose of this paper is to propose a novel measurement technique and a modelless calibration method for improving the positioning accuracy of a three-axis parallel kinematic machine (PKM). The aim is to present a low-cost calibration alternative, for small and medium-sized enterprises, as well as educational and research teams, with no expensive measuring devices at their disposal. Design/methodology/approach Using a chessboard pattern on a ground-truth plane, a digital indicator, a two-dimensional eye-in-hand camera and a laser pointer, positioning errors are explored in the machine workspace. With the help of these measurements, interpolation functions are set up per direction, resulting in an interpolation vector function to compensate the volumetric errors in the workspace. Findings Based on the proof-of-concept system for the linear-delta PKM, it is shown that using the proposed measurement technique and modelless calibration method, positioning accuracy is significantly improved using simple setups. Originality/value In the proposed method, a combination of low-cost devices is applied to improve the three-dimensional positioning accuracy of a PKM. By using the presented tools, the parametric kinematic model is not required; furthermore, the calibration setup is simple, there is no need for hand–eye calibration and special fixturing in the machine workspace.

scholarly journals Discussion of the Improved Methods for Analyzing a Cantilever Beam Carrying a Tip-Mass under Base Excitation

2014 ◽  
Vol 2014 ◽  
pp. 1-15 ◽  
Author(s):  
Wang Hongjin ◽  
Meng Qingfeng ◽  
Feng Wuwei
Keyword(s):  
Cantilever Beam ◽  
Analytical Methods ◽  
Natural Frequencies ◽  
Separation Of Variables ◽  
Inertial Force ◽  
Mode Shapes ◽  
Base Excitation ◽  
Inertial Moment ◽  
Tip Mass ◽  
Improved Methods

Two improved analytical methods of calculations for natural frequencies and mode shapes of a uniform cantilever beam carrying a tip-mass under base excitation are presented based on forced vibration theory and the method of separation of variables, respectively. The cantilever model is simplified in detail by replacing the tip-mass with an equivalent inertial force and inertial moment acting at the free end of the cantilever based on D’Alembert’s principle. The concentrated equivalent inertial force and inertial moment are further represented as distributed loads using Dirac Delta Function. In this case, some typical natural frequencies and mode shapes of the cantilever model are calculated by the improved and unimproved analytical methods. The comparing results show that, after improvement, these two methods are in extremely good agreement with each other even the offset distance between the gravity center of the tip-mass and the attachment point is large. As further verification, the transient and steady displacement responses of the cantilever system under a sine base excitation are presented in which two improved methods are separately utilized. Finally, an experimental cantilever system is fabricated and the theoretical displacement responses are validated by the experimental measurements successfully.

Sign in / Sign up

Export Citation Format

Share Document