Exploration of Translational Joint Design Using Corrugated Flexure Units With Bézier Curve Segments

2019 ◽  
Vol 141 (5) ◽  
Author(s):  
Nianfeng Wang ◽  
Zhiyuan Zhang ◽  
Fan Yue ◽  
Xianmin Zhang
Keyword(s):  
Stiffness Matrix ◽  
Matrix Method ◽  
Bézier Curve ◽  
Bezier Curve ◽  
Axial Stiffness ◽  
Shape Variation ◽  
Element Analysis ◽  
Joint Design ◽  
Translational Joint ◽  
Cubic Bezier Curve

In order to satisfy particular design specifications, shape variation for limited geometric envelopes is often employed to alter the elastic properties of flexure joints. This paper introduces an analytical stiffness matrix method to model a new type of corrugated flexure (CF) beam with cubic Bézier curve segments. The cubic Bézier curves are used to depict the segments combined to form CF beam and translational joint. Mohr's integral is applied to derive the local-frame compliance matrix of the cubic Bézier curve segment. The global-frame compliance matrices of the CF unit and the CF beam with cubic Bézier curve segments are further formed by stiffness matrix method, which are confirmed by finite element analysis (FEA). The control points of Bézier curve are chosen as optimization parameters to identify the optimal segment shape, which maximizes both high off-axis/axial stiffness ratio and large axial displacements of translational joint. The results of experimental study on the optimum translational joint design validate the proposed modeling and optimization method.

Design of a Micro-Positioning Stage Using Corrugated Flexure Beam With Cubic Bézier Curve Segments

2018 ◽  
Author(s):  
Nianfeng Wang ◽  
Zhiyuan Zhang ◽  
Xianmin Zhang
Keyword(s):  
Stiffness Matrix ◽  
Matrix Method ◽  
Bézier Curve ◽  
Bezier Curve ◽  
Axial Stiffness ◽  
Control Points ◽  
Stiffness Ratio ◽  
Element Analysis ◽  
Positioning Stage ◽  
Cubic Bezier Curve

The paper introduces an analytical stiffness matrix method to model a new type of corrugated flexure (CF) beam with cubic Bézier curve segments. In order to satisfy particular design specifications, shape variation for limited geometric envelopes are often employed to alter the elastic properties of flexure hinges. In this paper, cubic Bézier curves are introduced to replace the axis of CF unit to rebuild the CF beam and the micro-positioning stage. Mohr’s integral method is applied to derive the stiffness matrix of the cubic Bézier curve segment. Modeling of the CF unit and the CF beam with cubic Bézier curve segments are further carried out through stiffness matrix method, which are confirmed by finite element analysis (FEA). Discussions about the two control points of the cubic Bézier curve segments are then conducted through search optimization, which highlights the off-axis/axial stiffness ratio and the axial compliance on the position of the two control points, to enable the micro-positioning stage both achieving high off-axis/axial stiffness ratio and large axial compliance. The derived analytical model provides a new option for the design of the CF beam.

scholarly journals On the Involute of the Cubic Bezier Curve by Using Matrix Representation in E3

2020 ◽  
Vol 13 (2) ◽  
pp. 216-226
Author(s):  
Şeyda Kılıçoğlu ◽  
Süleyman Şenyurt
Keyword(s):  
Vector Fields ◽  
Matrix Representation ◽  
Matrix Form ◽  
Bézier Curve ◽  
Bezier Curve ◽  
Control Points ◽  
Cubic Bezier Curve

In this study we have examined, involute of the cubic Bezier curve based on the control points with matrix form in E3. Frenet vector fields and also curvatures of involute of the cubic Bezier curve are examined based on the Frenet apparatus of the first cubic Bezier curve in E3.  

A Patient-Specific Computer Tomography-Based Finite Element Methodology to Calculate the Six Dimensional Stiffness Matrix of Human Vertebral Bodies

2012 ◽  
Vol 134 (5) ◽  
Author(s):  
Yan Chevalier ◽  
Philippe K. Zysset
Keyword(s):  
Finite Element ◽  
Structural Properties ◽  
Vertebral Body ◽  
Computer Tomography ◽  
Stiffness Matrix ◽  
Anisotropic Elasticity ◽  
Patient Specific ◽  
Axial Stiffness ◽  
Element Analysis ◽  
Vertebral Bodies

In most finite element (FE) studies of vertebral bodies, axial compression is the loading mode of choice to investigate structural properties, but this might not adequately reflect the various loads to which the spine is subjected during daily activities or the increased fracture risk associated with shearing or bending loads. This work aims at proposing a patient-specific computer tomography (CT)-based methodology, using the currently most advanced, clinically applicable finite element approach to perform a structural investigation of the vertebral body by calculation of its full six dimensional (6D) stiffness matrix. FE models were created from voxel images after smoothing of the peripheral voxels and extrusion of a cortical shell, with material laws describing heterogeneous, anisotropic elasticity for trabecular bone, isotropic elasticity for the cortex based on experimental data. Validated against experimental axial stiffness, these models were loaded in the six canonical modes and their 6D stiffness matrix calculated. Results show that, on average, the major vertebral rigidities correlated well or excellently with the axial rigidity but that weaker correlations were observed for the minor coupling rigidities and for the image-based density measurements. This suggests that axial rigidity is representative of the overall stiffness of the vertebral body and that finite element analysis brings more insight in vertebral fragility than densitometric approaches. Finally, this extended patient-specific FE methodology provides a more complete quantification of structural properties for clinical studies at the spine.

scholarly journals Cubic Bezier Curve Approach for Automated Offline Signature Verification with Intrusion Identification

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Arun Vijayaragavan ◽  
J. Visumathi ◽  
K. L. Shunmuganathan
Keyword(s):  
Graph Matching ◽  
Image Correlation ◽  
Signature Verification ◽  
Bézier Curve ◽  
Bezier Curve ◽  
Signature Matching ◽  
Offline Signature Verification ◽  
Special Concern ◽  
Reference Signature ◽  
Cubic Bezier Curve

Authentication is a process of identifying person’s rights over a system. Many authentication types are used in various systems, wherein biometrics authentication systems are of a special concern. Signature verification is a basic biometric authentication technique used widely. The signature matching algorithm uses image correlation and graph matching technique which provides false rejection or acceptance. We proposed a model to compare knowledge from signature. Intrusion in the signature repository system results in copy of the signature that leads to false acceptance. Our approach uses a Bezier curve algorithm to identify the curve points and uses the behaviors of the signature for verification. An analyzing mobile agent is used to identify the input signature parameters and compare them with reference signature repository. It identifies duplication of signature over intrusion and rejects it. Experiments are conducted on a database with thousands of signature images from various sources and the results are favorable.

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