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.

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 Analysis of a Spatial Parallel Mechanism With Flexible Moving Platform

2010 ◽  
Author(s):  
Amir Rezaei ◽  
Alireza Akbarzadeh ◽  
Javad Enferadi
Keyword(s):  
Inverse Kinematics ◽  
Strain Energy ◽  
Parallel Manipulators ◽  
Physical Structure ◽  
Fem Model ◽  
Lumped Model ◽  
Stiffness Analysis ◽  
Spatial Parallel Mechanism ◽  
Inverse Kinematics Problem ◽  
Moving Platform

In this paper, stiffness analysis of a 3-DOF spatial, 3-PSP type, parallel manipulator is investigated. Most previous stiffness analysis studies of parallel manipulators are performed using lumped model as well as assuming a rigid moving platform. In this paper, unlike traditional stiffness analysis, the moving platform is assumed to be flexible. Additionally, a continuous method is used for obtaining mathematical model of the manipulator stiffness matrix. This method is based on strain energy and Castigliano’s theorem [1]. For this purpose, first we solve inverse kinematics problem then We must find relationship between the applied external torques on the moving platform and the resultant joints forces. Next, strain energy moving platform is calculated. Strain energy of this element is calculated using force analysis and inverse kinematics problem. Finally, a FEM model is generated and used to simulate the physical structure. Simulation results are compared with the analytical model.

scholarly journals A Symbolic Formulation for Analytical Compliance Analysis and Synthesis of Flexure Mechanisms

2012 ◽  
Vol 134 (5) ◽  
Author(s):  
Hai-Jun Su ◽  
Hongliang Shi ◽  
JingJun Yu
Keyword(s):  
Sensitivity Analysis ◽  
Finite Element ◽  
Stiffness Matrix ◽  
Screw Theory ◽  
Element Model ◽  
Fe Model ◽  
Flexure Mechanism ◽  
Stiffness Matrices ◽  
Analysis And Synthesis ◽  
Flexure Joints

This paper presents a symbolic formulation for analytical compliance analysis and synthesis of flexure mechanisms with serial, parallel, or hybrid topologies. Our approach is based on the screw theory that characterizes flexure deformations with motion twists and loadings with force wrenches. In this work, we first derive a symbolic formulation of the compliance and stiffness matrices for commonly used flexure elements, flexure joints, and simple chains. Elements of these matrices are all explicit functions of flexure parameters. To analyze a general flexure mechanism, we subdivide it into multiple structural modules, which we identify as serial, parallel, or hybrid chains. We then analyze each module with the known flexure structures in the library. At last, we use a bottom-up approach to obtain the compliance/stiffness matrix for the overall mechanism. This is done by taking appropriate coordinate transformation of twists and wrenches in space. Four practical examples are provided to demonstrate the approach. A numerical example is employed to compare analytical compliance models against a finite element model. The results show that the errors are sufficiently small (2%, compared with finite element (FE) model), if the range of motion is limited to linear deformations. This work provides a systematical approach for compliance analysis and synthesis of general flexure mechanisms. The symbolic formulation enables subsequent design tasks, such as compliance synthesis or sensitivity analysis.

Jacobian-based stiffness analysis method for parallel manipulators with non-redundant legs

2015 ◽  
Vol 230 (3) ◽  
pp. 341-352 ◽  
Author(s):  
Antonius GL Hoevenaars ◽  
Patrice Lambert ◽  
Just L Herder
Keyword(s):  
Parallel Manipulator ◽  
Screw Theory ◽  
Parallel Manipulators ◽  
Structural Elements ◽  
Analysis Method ◽  
End Effector ◽  
Stiffness Analysis ◽  
Compliant Joints ◽  
Lower Mobility ◽  
Actuated Joints

Stiffness is an important element in the model of a parallel manipulator. A complete stiffness analysis includes the contributions of joints as well as structural elements. Parallel manipulators potentially include both actuated joints, passive compliant joints, and zero stiffness joints, while a leg may impose constraints on the end-effector in the case of lower mobility parallel manipulators. Additionally, parallel manipulators are often designed to interact with an environment, which means that an external wrench may be applied to the end-effector. This paper presents a Jacobian-based stiffness analysis method, based on screw theory, that effectively considers all above aspects and which also applies to parallel manipulators with non-redundant legs.

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.

scholarly journals Discrete element model for general polyhedra

2021 ◽  
Author(s):  
Alfredo Gay Neto ◽  
Peter Wriggers
Keyword(s):  
Frictional Contact ◽  
Virtual Work ◽  
Particle Surface ◽  
Element Model ◽  
Discrete Element ◽  
Discrete Element Model ◽  
Principle Of Virtual Work ◽  
Dynamics Model ◽  
Railway Ballast ◽  
Multibody Dynamics Model

AbstractWe present a version of the Discrete Element Method considering the particles as rigid polyhedra. The Principle of Virtual Work is employed as basis for a multibody dynamics model. Each particle surface is split into sub-regions, which are tracked for contact with other sub-regions of neighboring particles. Contact interactions are modeled pointwise, considering vertex-face, edge-edge, vertex-edge and vertex-vertex interactions. General polyhedra with triangular faces are considered as particles, permitting multiple pointwise interactions which are automatically detected along the model evolution. We propose a combined interface law composed of a penalty and a barrier approach, to fulfill the contact constraints. Numerical examples demonstrate that the model can handle normal and frictional contact effects in a robust manner. These include simulations of convex and non-convex particles, showing the potential of applicability to materials with complex shaped particles such as sand and railway ballast.

scholarly journals A numerical analysis of skin–PPE interaction to prevent facial tissue injury

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Rikeen D. Jobanputra ◽  
Jack Hayes ◽  
Sravani Royyuru ◽  
Marc A. Masen
Keyword(s):  
Strain Energy Density ◽  
Strain Energy ◽  
Tissue Injury ◽  
Soft Materials ◽  
Element Model ◽  
Healthcare Systems ◽  
Skin Injury ◽  
Energy Density Distribution ◽  
The World ◽  
The Face

AbstractThe use of close-fitting PPE is essential to prevent exposure to dispersed airborne matter, including the COVID-19 virus. The current pandemic has increased pressure on healthcare systems around the world, leading to medical professionals using high-grade PPE for prolonged durations, resulting in device-induced skin injuries. This study focuses on computationally improving the interaction between skin and PPE to reduce the likelihood of discomfort and tissue damage. A finite element model is developed to simulate the movement of PPE against the face during day-to-day tasks. Due to limited available data on skin characteristics and how these vary interpersonally between sexes, races and ages, the main objective of this study was to establish the effects and trends that mask modifications have on the resulting subsurface strain energy density distribution in the skin. These modifications include the material, geometric and interfacial properties. Overall, the results show that skin injury can be reduced by using softer mask materials, whilst friction against the skin should be minimised, e.g. through use of micro-textures, humidity control and topical creams. Furthermore, the contact area between the mask and skin should be maximised, whilst the use of soft materials with incompressible behaviour (e.g. many elastomers) should be avoided.

Structure Synthesis of 3-RRS Type Spatial Compliant Parallel Manipulator

2010 ◽  
Vol 44-47 ◽  
pp. 1375-1379
Author(s):  
Da Chang Zhu ◽  
Li Meng ◽  
Tao Jiang
Keyword(s):  
Parallel Manipulator ◽  
Compliant Mechanisms ◽  
Screw Theory ◽  
Weight Ratio ◽  
Parallel Manipulators ◽  
Robot System ◽  
New Approach ◽  
Structure Synthesis ◽  
Rigid Joints ◽  
Type 3

Parallel manipulators has been extensively studied by virtues or its high force-to-weight ratio and widely spread applications such as vehicle or flight simulator, a machine tool and the end effector of robot system. However, as each limb includes several rigid joints, assembling error is demanded strictly, especially in precision measurement and micro-electronics. On the other hand, compliant mechanisms take advantage of recoverable deformation to transfer or transform motion, force, or energy and the benefits of compliant mechanisms mainly come from the elimination of traditional rigid joints, but the traditional displacement method reduce the stiffness of spatial compliant parallel manipulators. In this paper, a new approach of structure synthesis of 3-DoF rotational compliant parallel manipulators is proposed. Based on screw theory, the structures of RRS type 3-DoF rotational spatial compliant parallel manipulator are developed. Experiments via ANSYS are conducted to give some validation of the theoretical analysis.

Sign in / Sign up

Export Citation Format

Share Document