Stiffness Estimation and Experiments for the Exechon Parallel Self-Reconfiguring Fixture Mechanism

2012 ◽  
Author(s):  
Xiong Li ◽  
Dimiter Zlatanov ◽  
Matteo Zoppi ◽  
Rezia Molfino
Keyword(s):  
Screw Theory ◽  
Virtual Work ◽  
Element Analysis ◽  
Stiffness Analysis ◽  
Stiffness Modeling ◽  
Successful Series ◽  
Stiffness Model ◽  
Stiffness Map ◽  
Fixture System ◽  
Typical Configuration

The Exechon X150, a new smaller member of a successful series of parallel kinematic machines, has been recently developed as a component of a mobile self-reconfigurable fixture system within an inter-European project. This paper is the first to address the stiffness analysis of the parallel mechanism on which the design is based. The stiffness modeling method uses reciprocal screw theory as well as the virtual work principle, resulting in a simpler formulation and more convenient than ones obtained with traditional stiffness-modeling methods. Based on this model, the stiffness map within the workspace is obtained. The stiffness of the mechanism at a typical configuration is carried out. The complete finite element analysis and simulation used to verify the effectiveness of the stiffness model. Using geometric spatial decomposition, numerical examples of the mechanism at three typical configurations are presented.

A Method for Compliance Modeling of Five Degree-of-Freedom Overconstrained Parallel Robotic Mechanisms With 3T2R Output Motion

2016 ◽  
Vol 9 (1) ◽  
Author(s):  
Wen-ao Cao ◽  
Huafeng Ding ◽  
Donghao Yang
Keyword(s):  
Screw Theory ◽  
Parallel Manipulators ◽  
Static Equilibrium ◽  
Equilibrium Equations ◽  
Element Analysis ◽  
Compliance Matrix ◽  
Fea Model ◽  
Stiffness Model ◽  
Compliance Modeling ◽  
The One

This paper presents an approach to compliance modeling of three-translation and two-rotation (3T2R) overconstrained parallel manipulators, especially for those with multilink and multijoint limbs. The expressions of applied wrenches (forces/torques) exerted on joints are solved with few static equilibrium equations based on screw theory. A systematic method is proposed for deriving the stiffness model of a limb with considering the couplings between the stiffness along the constrained wrench and the one along the actuated wrench based on strain energy analysis. The compliance model of a 3T2R overconstrained parallel mechanism is established based on stiffness models of limbs and the static equilibrium equation of the moving platform. Comparisons show that the compliance matrix obtained from the method is close to the one obtained from a finite-element analysis (FEA) model. The proposed method has the characteristics of involving low computational efforts and considering stiffness couplings of each limb.

Static Stiffness Analysis of a Novel Parallel Manipulator

2012 ◽  
Vol 522 ◽  
pp. 703-707
Author(s):  
Yun Feng Li ◽  
Chang Feng Li ◽  
Dong Sheng Qu ◽  
Ling Zou
Keyword(s):  
Parallel Manipulator ◽  
Virtual Work ◽  
Elastic Model ◽  
Static Stiffness ◽  
Single Chain ◽  
Stiffness Analysis ◽  
Stiffness Properties ◽  
Maximum Stiffness ◽  
Stiffness Model ◽  
Spatial Architecture

One novel 6-DOF parallel manipulator with hooke hinges is presented to provide precision positioning in this paper. The geometric parameters and spatial architecture of kinematic pairs will influence the system stiffness directly, which impact indirectly the characteristics such as supporting capacity, driving burden and so on. The elastic model of the single chain based on the stiffness equation is presented and the stiffness model of the whole structure is constructed via the principle of virtual work. The static stiffness properties of the manipulator are discussed and the problem of finding the minimum and maximum stiffness and the directions in which they occur for a manipulator in a given posture is addressed. An example is given and the results show that static stiffness properties can be used to guide the optimal design of the structure.

Stiffness modelling and comparison of the 5-UPS/PRPU parallel machine tool with its non-redundant counterpart

2016 ◽  
Vol 231 (9) ◽  
pp. 1646-1657 ◽  
Author(s):  
Xin Zhou ◽  
Yundou Xu ◽  
Jiantao Yao ◽  
Kuijing Zheng ◽  
Yongsheng Zhao
Keyword(s):  
Machine Tool ◽  
Stiffness Matrix ◽  
Parallel Mechanism ◽  
Screw Theory ◽  
Virtual Work ◽  
Matrix Decomposition ◽  
Parallel Machine ◽  
Stiffness Model ◽  
Redundantly Actuated ◽  
Parallel Machine Tool

This article presents a derivation of the stiffness matrix of a general redundantly actuated parallel mechanism based on the overall Jacobian. The Jacobian of the constraints and actuations is derived using reciprocal screw theory. Based on the mapping relationship between constraint, actuated and external forces combined with the principle of virtual work, a compatibility equation for the deformation of all of the limbs is achieved, and the stiffness model of the general redundantly actuated parallel mechanism is derived. The 5-UPS/PRPU redundantly actuated parallel machine tool is used to illustrate this method. The parallel machine tool comprehensively reveals the effect of the elastic deformation of active–passive joints and some basic transmission parts. The stiffness model is further validated by experimental data. Moreover, the global stiffness matrix of the general redundantly actuated parallel mechanism can be separated into two parts via matrix decomposition. The first part is the stiffness matrix of the corresponding non-redundant parallel mechanism, and the second part is the stiffness matrix of the redundantly actuated limbs (actuators). The redundantly actuated 5-UPS/PRPU parallel machine tool is also investigated for further analysis. The different stiffness characteristics of the machine tool and its corresponding non-redundant 5-UPS/PRPU parallel machine tool are compared. Actuation redundancy is found to improve the stiffness performance of the machine tool efficiently.

Stiffness Modeling and Analysis of Passive Four-Bar Parallelogram in Fully Compliant Parallel Positioning Stage

2011 ◽  
Vol 1 (1) ◽  
pp. 61-78 ◽  
Author(s):  
X. Jia ◽  
Y. Tian ◽  
D. Zhang ◽  
J. Liu
Keyword(s):  
Finite Element Analysis ◽  
Parallel Mechanism ◽  
Element Analysis ◽  
Modeling And Analysis ◽  
Stiffness Modeling ◽  
Stiffness Model ◽  
The Finite Element Analysis ◽  
Positioning Stage ◽  
Compliant Parallel Mechanism ◽  
Stiffness Variation

In order to investigate the influence of the stiffness of the compliant prismatic pair, a planar four-bar parallelogram, in a fully compliant parallel mechanism, the stiffness model of the passive compliant prismatic pair in a compliant parallel positioning stage is established using the compliant matrix method and matrix transformation. The influences of the constraints and the compliance of the connecting rods on the flexibility characteristics of the prismatic pair are studied based on the developed model. The relative geometric parameters are changed to show the rules of the stiffness variation and to obtain the demands for simplification in the stiffness modeling of the prismatic pair. Furthermore, the finite element analysis has been conducted to validate the analytical model.

Analytical Elastostatic Stiffness Modeling of Overconstrained Parallel Manipulators Using Geometric Algebra and Strain Energy

2019 ◽  
Vol 11 (3) ◽  
Author(s):  
Qinchuan Li ◽  
Lingmin Xu ◽  
Qiaohong Chen ◽  
Xinxue Chai
Keyword(s):  
Geometric Algebra ◽  
Strain Energy ◽  
Linear Equations ◽  
Parallel Manipulators ◽  
Equilibrium Equations ◽  
Element Analysis ◽  
Outer Product ◽  
Stiffness Analysis ◽  
Stiffness Modeling ◽  
Stiffness Matrices

A general method for the analytical elastostatic stiffness modeling of overconstrained parallel manipulators (PMs) using geometric algebra and strain energy is proposed. First, an analytical solution of the constraint and actuation wrenches exerted on the moving platform is obtained using the outer product and dual operation of geometric algebra, which avoids solving complex symbolic linear equations. Second, considering the compliances of the limbs, an analytical elastostatic model is established using the strain energy to obtain the stiffness matrices of the limbs. Finally, the deformation compatibility equations are added into equilibrium equations to obtain the overall stiffness matrix of the PM, which has a concise expression and a clear physical meaning. The proposed method is applied to the Tex3 overconstrained PM and the Tex4 overconstrained PM with redundant actuation to prove its validity. Comparable results between the theoretical analysis and the finite-element analysis (FEA) show that the former could be used as an effective alternative to the FEA method in the predesign stage. This new approach is universally applicable to the elastostatic stiffness analysis of overconstrained PMs.

Stiffness Modeling and Analysis of Passive Four-Bar Parallelogram in Fully Compliant Parallel Positioning Stage

2013 ◽  
pp. 59-75
Author(s):  
X. Jia ◽  
Y. Tian ◽  
D. Zhang ◽  
J. Liu
Keyword(s):  
Finite Element Analysis ◽  
Parallel Mechanism ◽  
Element Analysis ◽  
Modeling And Analysis ◽  
Stiffness Modeling ◽  
Stiffness Model ◽  
The Finite Element Analysis ◽  
Positioning Stage ◽  
Compliant Parallel Mechanism ◽  
Stiffness Variation

In order to investigate the influence of the stiffness of the compliant prismatic pair, a planar four-bar parallelogram, in a fully compliant parallel mechanism, the stiffness model of the passive compliant prismatic pair in a compliant parallel positioning stage is established using the compliant matrix method and matrix transformation. The influences of the constraints and the compliance of the connecting rods on the flexibility characteristics of the prismatic pair are studied based on the developed model. The relative geometric parameters are changed to show the rules of the stiffness variation and to obtain the demands for simplification in the stiffness modeling of the prismatic pair. Furthermore, the finite element analysis has been conducted to validate the analytical model.

scholarly journals Elastostatic Stiffness Analysis for the US/UPS Parallel Manipulators

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Weizhong Zhang ◽  
Wei Ye ◽  
Chao Yang
Keyword(s):  
Strain Energy ◽  
Screw Theory ◽  
Virtual Work ◽  
Element Model ◽  
Parallel Manipulators ◽  
Modeling Method ◽  
Stiffness Analysis ◽  
Design And Optimization ◽  
Stiffness Matrices ◽  
The Us

The virtual joint method (VJM) cannot calculate the strain energy stored in each rod. In order to solve the problem, a modeling method of the elastostatic stiffness was investigated for the UP/UPS parallel manipulators (PMs), taking the example of the 6-SPS PM. The modeling method was based on screw theory, Castigliano’s theorem, and strain energy (where U, P, and S, respectively, denote universal, prismatic, and spherical joints). First, the actuator and constraint wrenches of the mechanism were obtained by screw theory. Second, compact limb stiffness matrices were obtained in terms of strain energy and Castigliano’s second theorem. Finally, analytic expressions for the overall stiffness matrix of the mechanism and the amplitudes of the actuator force were obtained by adopting the virtual work principle and the balance equation for the mobile platform. All relative errors between the results of the analytical model and the finite element model are below 2%, which validates the effectiveness of the elastostatic stiffness model. The virtual work index was adopted to evaluate the stiffness performance of the mechanism, and the results show that the stiffness is not only related to position and orientation but also closely related to the directions of external loads. It is also demonstrated that the method has general adaptability for the stiffness analysis for the US/UPS PMs, laying the foundation for further reasonable dynamic design and optimization of such manipulators.

Optimal Design of Bi- and Multi-Stable Compliant Cellular Structures

2018 ◽  
Author(s):  
Quantian Luo ◽  
Liyong Tong
Keyword(s):  
Optimal Design ◽  
Virtual Work ◽  
Reaction Force ◽  
Nonlinear Finite Element ◽  
Cellular Structures ◽  
Stress And Strain ◽  
Principle Of Virtual Work ◽  
Stable States ◽  
Threshold Method ◽  
Element Analysis

This paper presents optimal design for nonlinear compliant cellular structures with bi- and multi-stable states via topology optimization. Based on the principle of virtual work, formulations for displacements and forces are derived and expressed in terms of stress and strain in all load steps in nonlinear finite element analysis. Optimization for compliant structures with bi-stable states is then formulated as: 1) to maximize the displacement under specified force larger than its critical one; and 2) to minimize the reaction force for the prescribed displacement larger than its critical one. Algorithms are developed using the present formulations and the moving iso-surface threshold method. Optimal design for a unit cell with bi-stable states is studied first, and then designs of multi-stable compliant cellular structures are discussed.

scholarly journals Conceptual design and comparative stiffness analysis of an Exechon-like parallel kinematic machine with lockable spherical joints

2017 ◽  
Vol 14 (4) ◽  
pp. 172988141772413
Author(s):  
Teng-fei Tang ◽  
Jun Zhang
Keyword(s):  
Conceptual Design ◽  
Prediction Accuracy ◽  
Parallel Kinematic Machine ◽  
Stiffness Analysis ◽  
Parallel Kinematic Machines ◽  
Stiffness Model ◽  
Dynamic Analyses ◽  
Parallel Kinematic ◽  
Kinetostatic Model ◽  
Limb Structure

This article proposes two types of lockable spherical joints which can perform three different motion patters by locking or unlocking corresponding rotational axes. Based on the proposed lockable spherical joints, a general reconfigurable limb structure with two passive joints is designed with which the conceptual designs of two types of Exechon-like parallel kinematic machines are completed. To evaluate the stiffness of the proposed Exechon-like parallel kinematic machines, an expanded kinetostatic model is established by including the compliances of all joints and limb structures. The prediction accuracy of the expanded stiffness model is validated by numerical simulations. The comparative stiffness analyses prove that the Exe-Variant parallel kinematic machine claims competitive rigidity performance to the Exechon parallel kinematic machine. The present work can provide useful information for further investigations on structural enhancement, rigidity improvement, and dynamic analyses of other Exechon-like parallel kinematic machines.

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