A modified elasto-dynamic model based static stiffness evaluation for a 3-PRS PKM

2015 ◽  
Vol 230 (3) ◽  
pp. 353-366 ◽  
Author(s):  
Yan-Qin Zhao ◽  
Jun Zhang ◽  
Ling-Yan Ruan ◽  
Hai-Wei Luo ◽  
Xiao-Liu Yu
Keyword(s):  
Dynamic Model ◽  
Stiffness Matrix ◽  
Performance Enhancement ◽  
Element Formulation ◽  
Parallel Kinematic Machine ◽  
Design Variables ◽  
Parallel Kinematic ◽  
And Performance ◽  
Global Stiffness Matrix ◽  
Spring Constants

This paper proposes a modified elasto-dynamic model for a three-prismatic revolute spherical parallel kinematic machine, in which the flexibility of the prismatic revolute spherical limb structures are accounted in and modeled as a hollowed spatial beam with nonuniform cross section. The governing equations are derived through substructure synthesis and finite element formulation. The stiffness matrix of the platform is then extracted from global stiffness matrix and its characteristics at typical configurations are calculated to reveal complicated coupling effects of diagonal and nondiagonal elements of the stiffness matrix. The concept of principle stiffness and coupled stiffness are proposed and their distributions over the workspace are predicted with numerical simulations in a quick manner. Then the stiffness of the platform is physically interpreted as a kinematically unconstrained rigid body suspended by six screw springs with equivalent spring constants and pitches through eigenscrew decomposition. The distributions of screw spring constants over the workspace are then plotted to demonstrate a duality property. At last, the effects of some design variables such as structural and dimensional parameters on system rigidity performance are investigated with the purpose of providing useful information for the structural design and performance enhancement of the parallel kinematic machine.

Hybrid-model-based stiffness analysis of a three-revolute-prismatic-spherical parallel kinematic machine

2016 ◽  
Vol 231 (14) ◽  
pp. 2561-2576 ◽  
Author(s):  
Jun Zhang ◽  
Yan Q Zhao ◽  
Hai W Luo
Keyword(s):  
High Speed ◽  
Experimental Tests ◽  
Design Parameters ◽  
Parallel Kinematic Machine ◽  
Modeling Methodology ◽  
Parallel Kinematic ◽  
Stiffness Characteristics ◽  
And Performance ◽  
High Dynamics ◽  
Spring Constants

A three-revolute-prismatic-spherical parallel kinematic machine is proposed as an alternative solution for high-speed machining tool due to its high rigidity and high dynamics. Considering the parallel kinematic machine module as a typical compliant parallel mechanism, whose three limb assemblages have bending, extending and torsional deflections, this article proposes a hybrid modeling methodology to establish an analytical stiffness model for the three-revolute-prismatic-spherical device. The developed analytical model is further used to evaluate the stiffness mapping of the three-revolute-prismatic-spherical module over a given work plane which is then validated by experimental tests. The simulations and experiments indicate that the present hybrid methodology can predict the three-revolute-prismatic-spherical parallel kinematic machine’s stiffness in a quick and accurate manner. The solution for eigenvalue problem of the stiffness matrix leads to the stiffness characteristics of the parallel module including eigenstiffnesses and the corresponding eigenscrews as well as the equivalent screw spring constants. Based on the eigenscrew decomposition, the parallel kinematic machine is physically interpreted as a rigid platform suspending by six screw springs. The minimum, maximum and average of the screw spring constants are chosen as indices to assess the three-revolute-prismatic-spherical parallel kinematic machine’s stiffness performance. The distributions of the proposed indices throughout the workspace reveal a strong dependency on the mechanism’s configurations. At the final stage, the effects of some design parameters on system stiffness characteristics are investigated with the purpose of providing useful information for the conceptual design and performance improvement of the parallel kinematic machine.

An Algorithm to Study the Elastodynamics of Parallel Kinematic Machines With Lower Kinematic Pairs

2012 ◽  
Vol 5 (1) ◽  
Author(s):  
Alessandro Cammarata ◽  
Davide Condorelli ◽  
Rosario Sinatra
Keyword(s):  
Stiffness Matrix ◽  
Rigid Bodies ◽  
Parallel Kinematic Machine ◽  
Element Analysis ◽  
Stiffness Matrices ◽  
The Matrix ◽  
Parallel Kinematic ◽  
Global Stiffness Matrix ◽  
Local Stiffness

In this paper, an algorithm to help designers to integrate the elastodynamics analysis along with the inverse positioning and orienting problems of a parallel kinematic machine (PKM) into a single package is conceived. The proposed algorithm applies concepts from the matrix structural analysis (MSA) and finite element analysis (FEA) to determine the generalized stiffness matrix and the linearized elastodynamics equations of a PKM with only lower kinematic pairs. A PKM is modeled as a system of flexible links and rigid bodies connected by means of joints. Three cases are analyzed to consider the combinations between flexible and rigid bodies in order to find the local stiffness matrices. The latter are combined to obtain the limb matrices and, then, the global stiffness matrix of the whole robotic system. The same nodes coming from the links discretization are considered to include joint masses/inertias into the model. Finally, a case study is proposed to show some feasible applications and to compare results to commercial software for validation.

scholarly journals Hybrid Modelling; Mixed Rigid and Flexible Systems

1997 ◽  
Author(s):  
Ibrahim Esat ◽  
K. Banisoleiman
Keyword(s):  
Stiffness Matrix ◽  
Finite Size ◽  
Rigid Bodies ◽  
Element Formulation ◽  
Flexible Systems ◽  
Body System ◽  
Oscillatory Behaviour ◽  
Hybrid Modelling ◽  
Global Stiffness Matrix ◽  
Multi Body

The paper presents the Euler Newton formulation of oscillatory behaviour of a multi-body system interconnected by discrete stiffness elements. The dynamical system is treated as geometrically and materially linear, where assembly of the global stiffness matrix may be achieved. The formulation is extended to incorporate flexible shafting systems. It is assumed that flexible shafts are connected to rigid bodies of finite size and the connection is assumed to be built-in or pin jointed. Flexible shafting system is formulated using beam finite element formulation.

Translator Dynamics and Performance Comparison on One and Two Cylinder Free Piston Engines

2018 ◽  
Author(s):  
Mehar Bade ◽  
Nigel N. Clark ◽  
Parviz Famouri ◽  
PriyaankaDevi Guggilapu
Keyword(s):  
Permanent Magnets ◽  
Electrical Power ◽  
Performance Comparison ◽  
Spring Constant ◽  
Design Parameters ◽  
Free Piston ◽  
Design Variables ◽  
Sinusoidal Motion ◽  
And Performance ◽  
Spring Constants

Free Piston Linear Engines and Alternators (FPLEA) may be designed following several different baseline configurations. Common designs include a translator that carries permanent magnets, with either one piston attached to one end of the translator, or a piston at each end of the translator. The single cylinder engine requires a reversing force from a spring so that it can operate whereas the dual cylinder version can operate without a spring, but inclusion of a stiff springs would serve to raise operating frequency. Higher spring constants drive higher frequencies and also reduce the variability of the FPLEA compression ratio. The major component choices include the use of one or two cylinders, a spring constant, a bore and a stroke, and volumetric heat release. For design, the alternator is a component with translating mass that depends by design on the frequency, stroke and electrical power. The alternator demand must be matched to the engine power or the operating condition will change for the next cycle. Though there are many different FPLEA configurations, the performance comparisons of several baseline configurations have not been completely explored. A MATLAB®/Simulink numerical model with translator rod dynamics and in-cylinder thermodynamics is employed to predict the overall performance and efficiency of diesel-fueled FPLEA. This allowed comparisons of different FPLEA configurations for a variety of design variables. First, a two-cylinder FPLEA design is considered where the spring constant is varied, changing the frequency of operation and the motion of the translator. The simulation results show that without springs the motion is far from sinusoidal, and low in frequency and power, whereas the presence of stiff springs in the system strongly dictates nearly sinusoidal motion and high power at high frequency. Further, Fourier coefficients are used to characterize the motion of springs for different configurations. Effects of other parameters such as stroke and bore are also examined. Comparison is also performed for competing designs with the same power, but with one or two cylinders. The results provide a basis for selecting major design parameters before proceeding with a detailed design.

The dynamic modeling, redundant-force optimization, and dynamic performance analyses of a parallel kinematic machine with actuation redundancy

Robotica ◽  
2014 ◽  
Vol 33 (2) ◽  
pp. 241-263 ◽  
Author(s):  
Yao Jiang ◽  
Tiemin Li ◽  
Liping Wang
Keyword(s):  
Dynamic Model ◽  
Dynamic Performance ◽  
Euler Method ◽  
Parallel Kinematic Machine ◽  
Constraint Forces ◽  
Inverse Dynamic ◽  
Actuation Redundancy ◽  
Position Errors ◽  
Parallel Kinematic ◽  
Performance Analyses

SUMMARYThis paper discusses a planar 2-DOF (degrees of freedom) parallel kinematic machine with actuation redundancy. Its inverse dynamic model is constructed by utilizing the Newton–Euler method based on the kinematic analysis. However, the dynamic model cannot be solved directly because the number of equations is less than the number of unknowns, which is due to the redundant force. In order to solve this problem, the relationship between the deformations of the links and the position errors of the moving platform are further explored. Then a novel method, which aims at minimizing the position errors of the machine, is proposed to optimize the redundant force. It also enables to solve the dynamic model. Finally, the dynamic performance analyses of this machine and its non-redundant counterpart are provided by numerical examples. Besides, another optimization method proposed for minimizing the constraint forces is also applied for comparison. The results show the effectiveness of the novel methods in improving the position precision of the machine.

Multi-Objective Optimization of Stiffness and Workspace for a Parallel Kinematic Machine

2012 ◽  
Author(s):  
Zhongzhe Chi ◽  
Dan Zhang
Keyword(s):  
Genetic Algorithms ◽  
Machine Tool ◽  
Parallel Manipulator ◽  
Multi Objective Optimization ◽  
Parallel Kinematic Machine ◽  
Multi Objective ◽  
Parallel Kinematic Manipulator ◽  
Design Variables ◽  
Parallel Kinematic

This paper presents optimizations of a parallel kinematic manipulator used for a machine tool in terms of its workspace and stiffness. The system stiffness and workspace of the parallel manipulator are conducted in the paper. In order to locate the maximum system stiffness and workspace, single and multi objective optimizations are performed in terms of rotation angles in x and y axes and translation displacement in z axis with Genetic Algorithms. By optimizing the design variables including geometric dimensions of the manipulator, the system stiffness and workspace of the proposed parallel kinematic manipulator has been greatly improved.

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.

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