On puncturing of codes from Norm–Trace curves

The Peaucellier linkage is one of only a handful of known, single-degree-of-freedom mechanisms that trace an exact straight line. Although the traced output is straight, the relation between input rotation angle and output position along the traced line is nonlinear. The purpose of this study is to investigate the composite motion of stacked Peaucellier straight-line mechanisms. After stacking, the original straight-line output transforms into a complex curve whose shape is dependent on the motion of all of the component mechanisms, their geometric parameters, and how the component Peaucellier cells are interconnected. MATLAB software was used to generate output curves considering different stacking configurations and mechanism sizes. MATLAB was also used to analyze the final data and identify correlations between the mechanism link sizes, stacking configurations, and relative output curves. Based on a polynomial fitting technique, resultant output of the stacked mechanisms was generally found to be of 6th order except when purposefully constrained. This is a first attempt to characterize kinematic trace curves for this type of stacked straight-line linkage system.

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Roller Trace Design in Multi-Pass Conventional Spinning Based on Cylindrical Part

Volume 2A: Advanced Manufacturing ◽

10.1115/imece2020-23213 ◽

2020 ◽

Author(s):

Li Zixuan ◽

Shu Xuedao ◽

Ye Bohai ◽

Wang Jitai

Keyword(s):

Cylindrical Part ◽

Feed Ratio ◽

Thickness Uniformity ◽

First Pass ◽

Spinning Process ◽

Conventional Spinning ◽

Thickness Variations ◽

Product Thickness ◽

Trace Curves ◽

Involute Curve

Abstract Conventional spinning is a kind of ancient revolving process which controls the product’s shape by roller trace design. It is also widely used in civil, military, automobile, aerospace and other fields. Unlike the power spinning process, the roller trace used in conventional spinning is complex. Both thickness uniformity and crack defects are affected by it. However, roller trace design is still based on experience without a solid theoretical basis. This paper simulated five different roller trace curves: involute curve, circular curve, Bezier curve, conchoids and line. Experiments using superalloy GH3030 were conducted in conjunction with a multi-pass conventional spinning simulation model. Blank thickness variations, mandrel and roller forces of different roller traces in the first pass are analyzed and assessed through the verification experiments. The results suggest that the curve trace parameters play a key role on the product thickness uniformity. And the distribution of Bezier and conchoid roller traces is more uniform than the other traces. The axial force of mandrel is a very important factor in the design of tool load capability. Larger roller feed ratio and proper roller traces can reduce the thinning which may avoid the cracks.

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Design of Mechanisms to Trace Plane Curves

Volume 5B: 40th Mechanisms and Robotics Conference ◽

10.1115/detc2016-59689 ◽

2016 ◽

Cited By ~ 1

Author(s):

Yang Liu ◽

J. Michael McCarthy

Keyword(s):

Fourier Series ◽

Algebraic Curve ◽

Design Methodology ◽

Plane Curve ◽

Plane Curves ◽

The Third ◽

Universality Theorem ◽

Serial Chain ◽

Plane Algebraic Curve ◽

Trace Curves

This paper describes a mechanism design methodology that assembles standard components to trace plane curves that have a Fourier series parameterization. This approach can be used to approximate complex plane curves to interpolate image boundaries constructed from points. We describe three ways to construct a mechanism that generates a curve from a Fourier series parameterization. One uses Scotch yoke linkages for each term of Fourier series which are added using a belt drive. The second approach uses a coupled serial chain for each coordinate Fourier parameterization. The third method uses one constrained coupled serial chain to trace a specified plane curve. This work can be viewed as a version of the Kempe Universality Theorem that states that a linkage exists that can trace any plane algebraic curve. In our case, we include belts and pulleys, and obtain linkages that trace curves that have Fourier parameterizations.

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The minimum weights of two-point AG codes on norm-trace curves

Finite Fields and Their Applications ◽

10.1016/j.ffa.2018.06.005 ◽

2018 ◽

Vol 53 ◽

pp. 113-139 ◽

Cited By ~ 1

Author(s):

Boran Kim ◽

Yoonjin Lee

Keyword(s):

Ag Codes ◽

Trace Curves

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