scholarly journals Cartesian Stiffness Matrix Mapping of a Translational Parallel Mechanism with Elastic Joints

10.5772/52145 ◽  
2012 ◽  
Vol 9 (5) ◽  
pp. 195 ◽  
Author(s):  
Maurizio Ruggiu
Keyword(s):  
Stiffness Matrix ◽  
Parallel Mechanism ◽  
Cartesian Stiffness Matrix ◽  
Matrix Mapping ◽  
Elastic Joints ◽  
Cartesian 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.

On the 6 × 6 cartesian stiffness matrix for three-dimensional motions

1998 ◽  
Vol 33 (4) ◽  
pp. 389-408 ◽  
Author(s):  
Stamps Howard ◽  
Milos Zefran ◽  
Vijay Kumar
Keyword(s):  
Stiffness Matrix ◽  
Three Dimensional ◽  
Cartesian Stiffness Matrix ◽  
Cartesian Stiffness

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.

The decoupling of the Cartesian stiffness matrix in the design of microaccelerometers

2014 ◽  
Vol 34 (1) ◽  
pp. 1-21 ◽  
Author(s):  
Ting Zou ◽  
Jorge Angeles
Keyword(s):  
Stiffness Matrix ◽  
Cartesian Stiffness Matrix ◽  
Cartesian Stiffness

Coordinate-Free Formulation of the Cartesian Stiffness Matrix

1996 ◽  
pp. 119-128 ◽  
Author(s):  
Milosš Žefran ◽  
Vijay Kumar
Keyword(s):  
Stiffness Matrix ◽  
Cartesian Stiffness Matrix ◽  
Cartesian Stiffness

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.

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