Decoupling of the Cartesian Stiffness Matrix: A Case Study on Accelerometer Design

2011 ◽  
Author(s):  
Ting Zou ◽  
Jorge Angeles
Keyword(s):  
Mechanical Properties ◽  
Finite Element Analysis ◽  
Stiffness Matrix ◽  
Screw Theory ◽  
Rotational Stiffness ◽  
Element Analysis ◽  
Cartesian Stiffness Matrix ◽  
Stiffness Matrices ◽  
Cartesian Stiffness

The 6 × 6 Cartesian stiffness matrix obtained through finite element analysis for structures designed with material and geometric symmetries may lead to unexpected coupling that stems from discretization error. Hence, decoupling of the Cartesian stiffness matrix becomes essential for design and analysis. This paper reports a numerical method for decoupling the Cartesian stiffness matrix, based on screw theory. With the aid of this method, the translational and rotational stiffness matrices can be analyzed independently. The mechanical properties of the decoupled stiffness submatrices are investigated via their associated eigenvalue analyses. The decoupling technique is applied to the design of two accelerometer layouts, uniaxial and biaxial, with what the authors term simplicial architectures. The decoupled stiffness matrices reveal acceptable compliance along the sensitive axes and high off-axis stiffness.

Stiffness analysis and comparison of a Biglide parallel grinder with alternative spatial modular parallelograms

Robotica ◽  
2016 ◽  
Vol 35 (6) ◽  
pp. 1310-1326 ◽  
Author(s):  
Guanglei Wu ◽  
Ping Zou
Keyword(s):  
Eigenvalue Problem ◽  
Stiffness Matrix ◽  
Rotational Stiffness ◽  
Stiffness Analysis ◽  
Stiffness Modeling ◽  
Cartesian Stiffness Matrix ◽  
Modeling Analysis ◽  
Cartesian Stiffness

SUMMARYThis paper deals with the stiffness modeling, analysis and comparison of a Biglide parallel grinder with two alternative modular parallelograms. It turns out that the Cartesian stiffness matrix of the manipulator has the property that it can be decoupled into two homogeneous matrices, corresponding to the translational and rotational aspects, through which the principal stiffnesses and the associated directions are identified by means of the eigenvalue problem, allowing the evaluation of the translational and rotational stiffness of the manipulator either at a given pose or the overall workspace. The stiffness comparison of the two alternative Biglide machines reveals the (dis)advantages of the two different spatial modular parallelograms.

A Geometrical Approach to the Study of the Cartesian Stiffness Matrix

1998 ◽  
Vol 124 (1) ◽  
pp. 30-38 ◽  
Author(s):  
Milosˇ Zˇefran ◽  
Vijay Kumar
Keyword(s):  
Rigid Body ◽  
Stiffness Matrix ◽  
Affine Connection ◽  
Geometrical Approach ◽  
Cartesian Stiffness Matrix ◽  
Stiffness Matrices ◽  
Symmetric Connection ◽  
Asymmetric Connection ◽  
Definition Of ◽  
Cartesian Stiffness

The stiffness of a rigid body subject to conservative forces and moments is described by a tensor, whose components are best described by a 6×6 Cartesian stiffness matrix. We derive an expression that is independent of the parameterization of the motion of the rigid body using methods of differential geometry. The components of the tensor with respect to a basis of twists are given by evaluating the tensor on a pair of basis twists. We show that this tensor depends on the choice of an affine connection on the Lie group, SE3. In addition, we show that the definition of the Cartesian stiffness matrix used in the literature [1,2] implicitly assumes an asymmetric connection and this results in an asymmetric stiffness matrix in a general loaded configuration. We prove that by choosing a symmetric connection we always obtain a symmetric Cartesian stiffness matrix. Finally, we derive stiffness matrices for different connections and illustrate the calculations using numerical examples.

scholarly journals A self-adjusting stiffness center design for large stroke compliant XY nanomanipulators

2018 ◽  
Vol 9 (1) ◽  
pp. 41-50 ◽  
Author(s):  
Zhiqing Liu ◽  
Zhen Zhang ◽  
Peng Yan
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Geometric Parameters ◽  
Rotational Stiffness ◽  
Element Analysis ◽  
Redundant Constraint ◽  
Alternative Approach ◽  
Motion Stage ◽  
The Moment

Abstract. In the present paper, it is proposed a self-adjusting stiffness center (SASC) design for large stroke XY beam flexure-based mechanisms. An important feature of the SASC lies in it restricts the in-plane parasitic rotation by reducing the moment of force instead of increasing the rotational stiffness widely utilized in the literature. Specifically, it is shown that by leveraging on the varied stiffness of the parallelogram flexure, the stiffness center can be made stationary by appropriately setting the relevant geometric parameters, so that the parasitic rotation can be restricted. Furthermore, it is presented a millimeter stroke XY nanomanipulator with the SASC-based redundant constraint in a case study. Numerous finite element analysis (FEA) results demonstrate that the proposed design is not only capable of achieving 1.5 × 1.5 mm2 working range in a compact desktop size, but significantly reduces the in-plane moment applied to the motion stage. The proposed SASC-based design provides an alternative approach to reduce the parasitic rotation of large stroke XY beam flexure-based mechanisms.

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.

Stiffness Matrix of Compliant Parallel Mehanisms

2008 ◽  
Author(s):  
Cyril Quennouelle ◽  
Cle´ment Gosselin
Keyword(s):  
Stiffness Matrix ◽  
Compliant Mechanisms ◽  
Positive Definiteness ◽  
Large Displacements ◽  
Numerical Example ◽  
Cartesian Stiffness Matrix ◽  
Stiffness Matrices ◽  
Definition Of ◽  
Cartesian Stiffness

Starting from the definition of a stiffness matrix, the authors present the Cartesian stiffness matrix of parallel compliant mechanisms. The proposed formulation is more general than any other stiffness matrix found in the literature since it can take into account the stiffness of the passive joints and remains valid for large displacements. Then, the validity, the conservative property, the positive definiteness and the relation with other stiffness matrices of this matrix are discussed theoretically. Finally, a numerical example is given in order to illustrate the correctness of this matrix.

Finite Element Analysis of Reinforced Concrete Beams with Exterior FRP Shell

2011 ◽  
Vol 243-249 ◽  
pp. 1461-1465
Author(s):  
Chuan Min Zhang ◽  
Chao He Chen ◽  
Ye Fan Chen
Keyword(s):  
Mechanical Properties ◽  
Finite Element Analysis ◽  
Finite Element ◽  
Reinforced Concrete ◽  
Concrete Beams ◽  
Reinforced Concrete Beams ◽  
Test Results ◽  
Contact Interface ◽  
Accurate Calculation ◽  
Element Analysis

The paper makes an analysis of the reinforced concrete beams with exterior FRP Shell in Finite Element, and compares it with the test results. The results show that, by means of this model, mechanical properties of reinforced concrete beams with exterior FRP shell can be predicted better. However, the larger the load, the larger deviation between calculated values and test values. Hence, if more accurate calculation is required, issues of contact interface between the reinforced concrete beams and the FRP shell should be taken into consideration.

ANSYS Simply Supported Deep Beams Based on the Study of Mechanical Properties

2013 ◽  
Vol 351-352 ◽  
pp. 782-785
Author(s):  
Yong Bing Liu ◽  
Xiao Zhong Zhang
Keyword(s):  
Mechanical Properties ◽  
Finite Element Analysis ◽  
Mechanical Model ◽  
Work Performance ◽  
Deep Beam ◽  
Analysis Software ◽  
Deep Beams ◽  
Element Analysis ◽  
Simply Supported ◽  
Force Characteristics

Established the mechanical model of simply supported deep beam, calculation and analysis of simple supported deep beams by using finite element analysis software ANSYS, simulated the force characteristics and work performance of the deep beam. Provides the reference for the design and construction of deep beams.

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