Optimal Non-Uniform Parametrization for Fourier Descriptor Based Path Synthesis of Four Bar Mechanisms

2018 ◽  
Author(s):  
Shashank Sharma ◽  
Anurag Purwar ◽  
Q. Jeffrey Ge
Keyword(s):  
Input Data ◽  
Design Space ◽  
Fourier Descriptors ◽  
Fourier Descriptor ◽  
Loop Closure ◽  
The Core ◽  
Closure Equation ◽  
Harmonic Decomposition ◽  
Path Synthesis

Fourier descriptor based path synthesis algorithms rely on harmonic decomposition of four-bar loop closure equation to split the design space into smaller subsets. The core of the methodology depends on calculation and fitting of Fourier descriptors. However, a uniform time parametrization is assumed in existing literature. This paper aims to explore the use of non-uniform time parametrization of input data and calculation of an optimal parametrization. Additionally, design-centric constraints have been proposed to give user enhanced control over coupler speed. As a result, this work improves the existing algorithm tremendously.

An Optimal Parametrization Scheme for Path Generation Using Fourier Descriptors for Four-Bar Mechanism Synthesis

2018 ◽  
Vol 19 (1) ◽  
Author(s):  
Shashank Sharma ◽  
Anurag Purwar ◽  
Q. Jeffrey Ge
Keyword(s):  
Time Parameter ◽  
Fourier Descriptors ◽  
Fourier Descriptor ◽  
Mechanism Synthesis ◽  
Parametrization Scheme ◽  
Time Parameters ◽  
Path Synthesis ◽  
Parameter Values ◽  
The Given ◽  
Selection Of

Fourier descriptor (FD)-based path synthesis algorithms for generation of planar four-bar mechanisms require assigning time parameter values to the given points along the path. An improper selection of time parameters leads to poor fitting of the given path and suboptimal four-bar mechanisms while also ignoring a host of mechanisms that could be potentially generated otherwise. A common approach taken is to use uniform time parameter values, which does not take into account the unique harmonic properties of the coupler path. In this paper, we are presenting a nonuniform parametrization scheme in conjunction with an objective function that provides a better fit, leverages the harmonics of the four-bar coupler, and allows imposing additional user-specified constraints.

A window detection technique with adjustable threshold for transmitted reference receivers

2013 ◽  
Vol 3 (1) ◽  
Author(s):  
Apratim Roy ◽  
A. Rashid
Keyword(s):  
Input Data ◽  
Cmos Technology ◽  
Ultra Wideband ◽  
Power Requirement ◽  
The Core ◽  
Transmitted Reference ◽  
Detection Circuit ◽  
Detection Window ◽  
Improved Performance ◽  
Decision Circuit

AbstractThis paper presents a threshold decision circuit with an adjustable detection window designed in a 90-nm IBM CMOS technology. Together with an RF mixer, the decision Section realizes the circuit implementation of the back-end of a transmitted reference ultra wideband receiver, which is yet to be reported in literature. The proposed circuit is built on a differential amplifier core and avoids the use of integrator and sampling blocks, which reduces the device burden necessary for the architecture. Moreover, the detection window threshold of the design can be regulated by three independent factors defined by the circuit elements. The circuit is tested at an input data rate of 0.1∼2.0 Gbps and the core decision section consumes 9.14 mW from a 1.2-V bias supply (with a maximum capacity/Pdc ratio of 218.8 GHz/W). When compared against other reported decision blocks, the proposed detection circuit shows improved performance in terms of capacity and power requirement.

ROBUST MORPHOLOGICALLY CONTINUOUS FOURIER DESCRIPTORS I: PROJECTION-GENERATED DESCRIPTORS

1992 ◽  
Vol 06 (05) ◽  
pp. 873-892 ◽  
Author(s):  
EDWARD R. DOUGHERTY ◽  
ROBERT P. LOCE
Keyword(s):  
Hausdorff Metric ◽  
Companion Paper ◽  
Morphological Properties ◽  
Fourier Descriptors ◽  
Fourier Descriptor ◽  
Additional Advantage ◽  
First Finding ◽  
Orientation Determination

By generating Fourier descriptors based upon the waveform induced by a pattern's geometric projection, a number of classic difficulties with the Fourier-descriptor methodology are mitigated. Not only are the descriptors invariant with respect to scale, translation, and rotation (as is usually the case), they are also continuous in the Hausdorff metric and robust with respect to both point noise and occlusion. An additional advantage is that they can be computed relative to a thresholded image without first finding an edge, thereby avoiding the difficulties typically present in thinning and orientation determination. The present paper discusses the method of projection-generated Fourier descriptors, as well as a study of the sensitivity to point noise. A companion paper will present the morphological properties and the effect of pattern occlusion.

Analysis of the single toggle jaw crusher kinematics

2015 ◽  
Vol 13 (2) ◽  
pp. 213-239 ◽  
Author(s):  
Moses Frank Oduori ◽  
Stephen Mwenje Mutuli ◽  
David Masinde Munyasi
Keyword(s):  
Design Methodology ◽  
Loop Closure ◽  
Content Type ◽  
Drive Mechanism ◽  
Jaw Crusher ◽  
Closure Equation

Purpose – This paper aims to obtain equations that can be used to describe the motion of any given point in the swing jaw of a single toggle jaw crusher. Design/methodology/approach – The swing jaw drive mechanism of a single toggle jaw crusher is modelled as a planar crank and rocker mechanism with the swing jaw as the coupler link. Starting with the vector loop closure equation for the mechanism, equations of the position, velocity and acceleration of any given point in the swing jaw are obtained. Findings – Application of the kinematical equations that were obtained is demonstrated using the dimensional data of a practical single toggle jaw crusher. Thus, a description of the kinematics of any given point in the swing jaw of a single toggle jaw crusher is realized. Originality/value – The model of the single toggle jaw crusher mechanism as a planar crank and rocker mechanism is a realistic one. The equations obtained in this paper should be useful in further studies on the mechanics and design of the single toggle jaw crusher.

Optimal Synthesis of Mechanisms for Path Generation Using Fourier Descriptors and Global Search Methods

1997 ◽  
Vol 119 (4) ◽  
pp. 504-510 ◽  
Author(s):  
Irfan Ullah ◽  
Sridhar Kota
Keyword(s):  
Objective Function ◽  
Design Space ◽  
Initial Guess ◽  
Global Search ◽  
Search Method ◽  
Fourier Descriptors ◽  
Path Generation ◽  
Local Optima ◽  
Structural Error ◽  
Synthesis Of Mechanisms

Generally, success in synthesis of mechanisms for path generation is limited to finding a reasonable local optima at best in spite of a very good initial guess. The most widely used Structural Error objective function is not effective in leading to practical solutions as it misrepresents the nature of the design problem by requiring the shape, size, orientation and position of the coupler curve to be optimized all at once. In this paper, we present an effective objective function based on Fourier descriptors that evaluates only the shape differences between two curves. This function is first minimized using a stochastic global search method derived from simulated annealing followed by Powell’s method. The size, orientation and position of the desired curve are addressed in a later stage by determining analogous points on the desired and candidate curves. In spite of highly non-linear mechanisms design space, our method discovers near-global and practical solutions consistently without requiring any initial guess.

ON THE COUPLER CURVE OF 3R2C LINKAGES

1998 ◽  
Vol 22 (3) ◽  
pp. 251-267
Author(s):  
H.S. Yan ◽  
W.H. Hsieh
Keyword(s):  
Algebraic Curve ◽  
Three Dimensions ◽  
Critical Properties ◽  
Dimensional Synthesis ◽  
Analytical Geometry ◽  
Loop Closure ◽  
Input And Output ◽  
Closure Equation

The purpose of this paper is to investigate the properties of the coupler curves generated by all 3R2C linkages. First, the 3x3 matrix with dual elements is used to derive the loop closure equation, the displacement equations are derived, and all joints variables are expressed in terms of input and output variables. Then, the parametric equations of the coupler curve are found by the D-H matrix. Finally, homogeneous coordinate is introduced to those displacement equations, and the order and some critical properties of the coupler curve are investigated based on the theories of algebraic curve and analytical geometry of three dimensions. In addition, RCRCR and RRCCR linkages are used as examples for illustration. Moreover, the results on the application of dimensional synthesis are discussed.

scholarly journals A Parametrization-Invariant Fourier Approach to Planar Linkage Synthesis for Path Generation

2017 ◽  
Vol 2017 ◽  
pp. 1-16 ◽  
Author(s):  
Xiangyun Li ◽  
Peng Chen
Keyword(s):  
Design Space ◽  
Fourier Descriptors ◽  
Path Generation ◽  
Arc Length ◽  
Efficient Synthesis ◽  
Practical Applications ◽  
Classic Problem ◽  
Fourier Theory ◽  
Planar Linkages ◽  
Synthesis Approach

This paper deals with the classic problem of the synthesis of planar linkages for path generation. Based on the Fourier theory, the task curve and the synthesized four-bar coupler curve are regarded as the same curve if their Fourier descriptors match. Using Fourier analysis, a curve must be given as a function of time, termed a parametrization. In practical applications, different parametrizations can be associated with the same task and coupler curve, respectively; however, these parametrizations are Fourier analyzed to different Fourier descriptors, thus resulting in the mismatch of the task and coupler curve. In this paper, we present a parametrization-invariant method to eliminate the influence of parametrization on the values of Fourier descriptors by unifying given parametrizations to the arc length parametrization; meanwhile, a new design space decoupling scheme is introduced to separate the shape, size, orientation, and location matching of the task and four-bar curve, which leads naturally to an efficient synthesis approach.

A Unified Algorithm for Analysis and Simulation of Planar Four-Bar Motions Defined With R- and P-Joints

2014 ◽  
Author(s):  
Xiangyun Li ◽  
Xin Ge ◽  
Anurag Purwar ◽  
Q. J. Ge
Keyword(s):  
Linkage Analysis ◽  
Least Squares ◽  
Efficient Algorithm ◽  
Image Space ◽  
Loop Closure ◽  
Closure Equation ◽  
Unified Algorithm ◽  
Four Bar Linkage ◽  
Best Fit ◽  
Linkage Synthesis

This paper presents a single, unified and efficient algorithm for animating the motions of the coupler of all four-bar mechanisms formed with revolute (R) and prismatic (P) joints. This is achieved without having to formulate and solve the loop closure equation associated with each type of four-bar linkages separately. In our previous paper on four-bar linkage synthesis, we map the planar displacements from Cartesian to image space using planar quaternion. Given a set of image points that represent planar displacements, the problem of synthesizing a planar four-bar linkage is reduced to finding a pencil of Generalized- or G-manifolds that best fit the image points in the least squares sense. The three planar dyads associated with Generalized G-manifolds are RR, PR and RP which could construct six types of four-bar mechanisms. In this paper, we show that the same unified formulation for linkage synthesis leads to a unified algorithm for linkage analysis and simulation as well. Both the unified synthesis and analysis algorithms have been implemented on Apple’s iOS platform.

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