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.

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.

scholarly journals Stiffness Modeling of Robotic-Manipulators Under Auxiliary Loadings

2012 ◽  
Author(s):  
Alexandr Klimchik ◽  
Anatol Pashkevich ◽  
Stéphane Caro ◽  
Damien Chablat
Keyword(s):  
Robotic Manipulators ◽  
Computationally Efficient ◽  
End Effector ◽  
Efficient Procedure ◽  
Stiffness Modeling ◽  
Cartesian Stiffness Matrix ◽  
Different Types ◽  
Mapping Equation ◽  
Linear Force ◽  
Cartesian Stiffness

The paper focuses on the extension of the virtual-joint-based stiffness modeling technique for the case of different types of loadings applied both to the robot end-effector and to manipulator intermediate points (auxiliary loading). It is assumed that the manipulator can be presented as a set of compliant links separated by passive or active joints. It proposes a computationally efficient procedure that is able to obtain a non-linear force-deflection relation taking into account the internal and external loadings. It also produces the Cartesian stiffness matrix. This allows to extend the classical stiffness mapping equation for the case of manipulators with auxiliary loading. The results are illustrated by numerical examples.

Stiffness characterization of a 3-PPR planar parallel manipulator with actuation compliance

2014 ◽  
Vol 229 (12) ◽  
pp. 2291-2302 ◽  
Author(s):  
Guanglei Wu ◽  
Shaoping Bai ◽  
Jørgen Kepler
Keyword(s):  
Eigenvalue Problem ◽  
Stiffness Matrix ◽  
Parallel Manipulator ◽  
Rotational Stiffness ◽  
Planar Mechanisms ◽  
Spatial Mechanisms ◽  
Generalized Eigenvalue ◽  
Stiffness Model ◽  
Planar Parallel Manipulator

This paper investigates the stiffness of a compliant planar parallel manipulator. Instead of establishing stiffness matrix directly for planar mechanisms, we adopt the modeling approach for spatial mechanisms, which allows us to derive two decoupled homogeneous matrices, corresponding to the translational and rotational stiffness. This is achieved by resorting to the generalized eigenvalue problem, through which the eigenscrew decomposition is implemented to yield six screw springs. The principal stiffnesses and their directions are then identified from the eigenvalue problem of the two separated submatrices. In addition, the influence of the nonlinear actuation compliance to the manipulator stiffness is investigated, and the established stiffness model is experimentally verified.

A Non-Linear Stiffness Model for Serial and Parallel Manipulators

2017 ◽  
Vol 5 (1) ◽  
pp. 34-62
Author(s):  
Manoj Kumar
Keyword(s):  
Numerical Technique ◽  
Sudden Change ◽  
Parallel Manipulators ◽  
Rigid Bodies ◽  
Stiffness Analysis ◽  
Cartesian Stiffness Matrix ◽  
Stiffness Model ◽  
Non Linear ◽  
Linear Behaviour ◽  
Cartesian Stiffness

The paper presents a methodology to enhance the stiffness analysis of serial and parallel manipulators with passive joints. It directly takes into account the loading influence on the manipulator configuration and, consequently, on its Jacobians and Hessians. The main contributions of this paper are the introduction of a non-linear stiffness model for the manipulators with passive joints, a relevant numerical technique for its linearization and computing of the Cartesian stiffness matrix which allows rank-deficiency. Within the developed technique, the manipulator elements are presented as pseudo-rigid bodies separated by multidimensional virtual springs and perfect passive joints. Simulation examples are presented that deal with parallel manipulators of the Ortholide family and demonstrate the ability of the developed methodology to describe non-linear behaviour of the manipulator structure such as a sudden change of the elastic instability properties (buckling).

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.

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