Design and Analysis of Symmetrical, Monolithic Tip-Tilt-Piston Flexure Stages

2017 ◽  
Author(s):  
Guangbo Hao
Keyword(s):  
High Precision ◽  
Cross Sections ◽  
Plane Motion ◽  
Cnc Milling ◽  
Compliance Matrix ◽  
Design Synthesis ◽  
Generic Structure ◽  
Symmetrical Structure ◽  
Out Of Plane ◽  
Physical Prototype

This paper mainly deals with the determinate design/synthesis of a class of symmetrical and monolithic flexure mechanisms. Each is composed of 6 identical in-plane wire beams with uniform square cross sections. These flexure stages can provide three out-of-plane tip-tilt-piston motions for applications in high-precision or miniaturisation environments. A generic symmetrical structure is proposed as first with a group of defined parameters considering constraint and non-interference conditions. Normalised static analytical compliance entries for the diagonal compliance matrix of a generic structure are derived and symbolically represented by the parameters. Comprehensive compliance analysis is then followed using the analytical results, and quick insights into effects of parameters on compliances in different directions are gained. Case studies without and with actuation consideration are finally discussed. As a second contribution, a physical prototype with three actuation legs is monolithically fabricated (using CNC milling machining), kinematically modelled and experimentally tested, which shows that the desired out-of-plane motion can be generated from the in-plane actuation.

Determinate Synthesis of Symmetrical, Monolithic Tip–Tilt–Piston Flexure Stages

2017 ◽  
Vol 139 (4) ◽  
Author(s):  
Guangbo Hao
Keyword(s):  
High Precision ◽  
Cross Sections ◽  
Plane Motion ◽  
Numerical Control ◽  
Compliance Matrix ◽  
Design Synthesis ◽  
Generic Structure ◽  
Symmetrical Structure ◽  
Out Of Plane ◽  
Physical Prototype

This paper mainly deals with the determinate design/synthesis of a class of symmetrical and monolithic flexure mechanisms. Each is composed of six identical in-plane wire beams with uniform square cross sections. These flexure stages can provide three out-of-plane tip–tilt–piston motions for applications in high-precision or miniaturization environments. A generic symmetrical structure is proposed at first with a group of defined parameters considering constraint and noninterference conditions. Normalized static analytical compliance entries for the diagonal compliance matrix of a generic structure are derived and symbolically represented by the parameters. Comprehensive compliance analysis is then followed using the analytical results, and quick insights into the effects of parameters on compliances in different directions are gained. Case studies without and with actuation consideration are finally discussed. As a second contribution, a physical prototype with three actuation legs is monolithically fabricated (using computer numerical control milling machining), kinematically modeled, and experimentally tested, which shows that the desired out-of-plane motion can be generated from the in-plane actuation.

Six Dimensional Compliance Analysis of Ortho-Planar Springs for a Continuum Manipulator

2014 ◽  
Author(s):  
C. Qiu ◽  
P. Qi ◽  
H. B. Liu ◽  
Kaspar Althoefer ◽  
Jian S. Dai
Keyword(s):  
Screw Theory ◽  
Numerical Study ◽  
Compliance Matrix ◽  
Beam Elements ◽  
Research Fields ◽  
Numerical Studies ◽  
Out Of Plane ◽  
Physical Prototype ◽  
Frame Work ◽  
Symbolic Formula

Ortho-planar spring is a compact spring that generates the motion based on the deformation of flexure elements, and it has wide applications in the compliant robotic designs. Previous studies only investigate the out-of-plane compliance of ortho-planar spring and fewer work pays attention to its angular compliance. To address this issue, this paper provides an analytical method to study both the linear and angular compliance characteristics of ortho-planar spring for the first time. In the frame work of screw theory, the symbolic formula of platform’s compliance matrix was obtained based on the hybrid integration of beam elements. Subsequently non-dimensional geometric parameters were introduced to compare the compliance characteristics of planar spring, which revealed the ortho-planar spring also demonstrates large bending compliance. Numerical studies of angular compliance of planar spring were provided, and they showed good agreements with the finite element simulations in a large working range. Based on the numerical study, a physical prototype of one continuum structure assembled with planar springs was provided and it demonstrated a large flexibility compared to other previous designs, which suggests the ortho-planar spring has potential value in developing continuum manipulators in related medical surgery and biorobotic research fields.

A Technique for Reliably Preparing Full-Length Metallographic Cross-Sections of Integrated Circuit Bond Wires

2006 ◽  
Author(s):  
Carl Nail
Keyword(s):  
Integrated Circuits ◽  
High Precision ◽  
Cross Sections ◽  
Integrated Circuit ◽  
Radiographic Analysis ◽  
Good Resolution ◽  
Metallographic Preparation ◽  
Bond Wires ◽  
Darkfield Imaging ◽  
Bond Wire

Abstract To overcome the obstacles in preparing high-precision cross-sections of 'blind' bond wires in integrated circuits, this article proposes a different technique that generates reliable, repeatable cross-sections of bond wires across most or all of their lengths, allowing unencumbered and relatively artifact-free analysis of a given bond wire. The basic method for cross-sectioning a 'blind' bond wire involves radiographic analysis of the sample and metallographic preparation of the sample to the plane of interest. This is followed by tracking the exact location of the plane on the original radiograph using a stereomicroscope and finally darkfield imaging in which the wire is clearly visible with good resolution.

Stress concentration factors for the torsion of curved beams of arbitrary cross-section

2006 ◽  
Vol 220 (12) ◽  
pp. 1709-1726 ◽  
Author(s):  
R E Cornwell
Keyword(s):  
Finite Element ◽  
Stress Concentration ◽  
Cross Section ◽  
Cross Sections ◽  
Shear Stresses ◽  
Curved Beams ◽  
Finite Element Implementation ◽  
Out Of Plane ◽  
Concentration Factors ◽  
Stress Concentration Factors

There are numerous situations in machine component design in which curved beams with cross-sections of arbitrary geometry are loaded in the plane of curvature, i.e. in flexure. However, there is little guidance in the technical literature concerning how the shear stresses resulting from out-of-plane loading of these same components are effected by the component's curvature. The current literature on out-of-plane loading of curved members relates almost exclusively to the circular and rectangular cross-sections used in springs. This article extends the range of applicability of stress concentration factors for curved beams with circular and rectangular cross-sections and greatly expands the types of cross-sections for which stress concentration factors are available. Wahl's stress concentration factor for circular cross-sections, usually assumed only valid for spring indices above 3.0, is shown to be applicable for spring indices as low as 1.2. The theory applicable to the torsion of curved beams and its finite-element implementation are outlined. Results developed using the finite-element implementation agree with previously available data for circular and rectangular cross-sections while providing stress concentration factors for a wider variety of cross-section geometries and spring indices.

Out-of-Plane Motion Effects in Microscopic Particle Image Velocimetry

2003 ◽  
Vol 125 (5) ◽  
pp. 895-901 ◽  
Author(s):  
Michael G. Olsen ◽  
Chris J. Bourdon
Keyword(s):  
Particle Image Velocimetry ◽  
Particle Image ◽  
Laser Sheet ◽  
Plane Motion ◽  
Entire Volume ◽  
Measurement Volume ◽  
Microscopic Particle ◽  
Image Velocimetry ◽  
Out Of Plane ◽  
Signal Peak

In microscopic particle image velocimetry (microPIV) experiments, the entire volume of a flowfield is illuminated, resulting in all of the particles in the field of view contributing to the image. Unlike in light-sheet PIV, where the depth of the measurement volume is simply the thickness of the laser sheet, in microPIV, the measurement volume depth is a function of the image forming optics of the microscope. In a flowfield with out-of-plane motion, the measurement volume (called the depth of correlation) is also a function of the magnitude of the out-of-plane motion within the measurement volume. Equations are presented describing the depth of correlation and its dependence on out-of-plane motion. The consequences of this dependence and suggestions for limiting its significance are also presented. Another result of the out-of-plane motion is that the height of the PIV signal peak in the correlation plane will decrease. Because the height of the noise peaks will not be affected by the out-of-plane motion, this could lead to erroneous velocity measurements. An equation is introduced that describes the effect of the out-of-plane motion on the signal peak height, and its implications are discussed. Finally, the derived analytical equations are compared to results calculated using synthetic PIV images, and the agreement between the two is seen to be excellent.

Vibrational potentials of the low frequency out‐of‐plane motion in the ground and excited singlet electronic states of 9,10‐dihydrophenanthrene

1992 ◽  
Vol 96 (10) ◽  
pp. 7229-7236 ◽  
Author(s):  
Marek Z. Zgierski ◽  
Francesco Zerbetto ◽  
Young‐Dong Shin ◽  
Edward C. Lim
Keyword(s):  
Low Frequency ◽  
Electronic States ◽  
Plane Motion ◽  
Excited Singlet ◽  
Out Of Plane

scholarly journals A Kollár and Pluzsik anisotropic composite beam theory for arbitrary multicelled cross sections

2016 ◽  
Vol 35 (23) ◽  
pp. 1696-1711 ◽  
Author(s):  
Danilo S Victorazzo ◽  
Andre De Jesus
Keyword(s):  
Finite Element ◽  
Cross Sections ◽  
Composite Beam ◽  
Linear Equations ◽  
Beam Theory ◽  
Element Formulation ◽  
Compliance Matrix ◽  
Asymmetric System ◽  
Anisotropic Composite ◽  
Stiffness Matrices

In this paper we extend Kollár and Pluzsik’s thin-walled anisotropic composite beam theory to include multiple cells with open branches and booms, and present a finite element formulation utilizing the stiffness matrix obtained from this theory. To recover the 4 × 4 compliance matrix of a beam containing N closed cells, we solve an asymmetric system of 2N + 4 linear equations four times with unitary section loads and extract influence coefficients from the calculated strains. Finally, we compare 4 × 4 stiffness matrices of a multicelled beam using this method against matrices obtained using the finite element method to demonstrate accuracy. Similarly to its originating theory, the effects of shear deformation and restrained warping are assumed negligible.

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