A Fourier Descriptor-Based Approach to Design Space Decomposition for Planar Motion Approximation

2016 ◽  
Vol 8 (6) ◽  
Author(s):  
Xiangyun Li ◽  
Jun Wu ◽  
Q. J. Ge
Keyword(s):  
Design Space ◽  
Shape Descriptor ◽  
Harmonic Series ◽  
Design Parameters ◽  
Fourier Descriptor ◽  
Rotational Component ◽  
Motion Generation ◽  
Motion Approximation ◽  
Four Bar Linkage ◽  
The Given

In an earlier work, we have combined a curve fitting scheme with a type of shape descriptor, Fourier descriptor (FD), to develop a unified method to the synthesis of planar four-bar linkages for generation of both open and closed paths. In this paper, we aim to extend the approach to the synthesis of planar four-bar linkages for motion generation in an FD-based motion fitting scheme. Using FDs, a given motion is represented by two finite harmonic series, one for translational component of the motion and the other for rotational component. It is shown that there is a simple linear relationship between harmonic content of the rotational component and that of the translational component for a planar four-bar coupler motion. Furthermore, it is shown that the rotational component of the given motion identifies a subset of design parameters of a four-bar linkage including link ratios, while the translational component determines the rest of the design parameters such as locations of the fixed pivots. This leads naturally to a decomposed design space for four-bar mechanism synthesis for approximate motion generation.

A Fourier Descriptor Based Approach to Design Space Decomposition for Planar Motion Approximation

2012 ◽  
Author(s):  
Xiangyun Li ◽  
Ping Zhao ◽  
Q. J. Ge
Keyword(s):  
Design Space ◽  
Translational Motion ◽  
Classical Problem ◽  
Harmonic Series ◽  
Design Parameters ◽  
Rotational Component ◽  
Dimensional Synthesis ◽  
Motion Generation ◽  
Motion Approximation ◽  
Four Bar Linkage

This paper deals with the classical problem of dimensional synthesis of planar four-bar linkages for motion generation. Using Fourier Descriptors, a given motion is represented by two finite harmonic series, one for translational component of the motion and the other for rotational component. It is shown that there is a simple linear relationship between harmonic content of the rotational motion and that of the translational motion for a planar four-bar linkage. Furthermore, it is shown that the rotational component can be used to identify the initial angle and the link ratios of a four-bar linkage. The rest of the design parameters of a four-bar linkage such as location of the fixed and moving pivots can be obtained from the translational component of the given motion. This leads naturally to a decomposed design space for four-bar motion synthesis for approximate motion generation.

A Task Driven Approach to Unified Synthesis of Planar Four-Bar Linkages Using Algebraic Fitting of a Pencil of G-Manifolds

2013 ◽  
Author(s):  
Q. J. Ge ◽  
Ping Zhao ◽  
Anurag Purwar
Keyword(s):  
Least Squares ◽  
Singular Values ◽  
Geometric Constraints ◽  
Motion Generation ◽  
Motion Approximation ◽  
Value Decomposition ◽  
Four Bar Linkage ◽  
The Given ◽  
Best Fit ◽  
Additional Constraints

This paper studies the problem of planar four-bar motion approximation from the viewpoint of extraction of geometric constraints from a given set of planar displacements. Using the Image Space of planar displacements, we obtain a class of quadrics, called Generalized- or G-manifolds, with eight linear and homogeneous coefficients as a unified representation for constraint manifolds of all four types of planar dyads, RR, PR, and PR, and PP. 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 G-manifolds that best fit the image points in the least squares sense. This least squares problem is solved using Singular Value Decomposition. The linear coefficients associated with the smallest singular values are used to define a pencil of quadrics. Additional constraints on the linear coefficients are then imposed to obtain a planar four-bar linkage that best guides the coupler through the given displacements. The result is an efficient and linear algorithm that naturally extracts the geometric constraints of a motion and leads directly to the type and dimensions of a mechanism for motion generation.

A Task Driven Approach to the Synthesis of Spherical 4R Linkages Using Algebraic Fitting Method

2013 ◽  
Author(s):  
Ping Zhao ◽  
Xiangyun Li ◽  
Anurag Purwar ◽  
Kartik Thakkar ◽  
Q. J. Ge
Keyword(s):  
Linear Method ◽  
Geometric Constraints ◽  
Motion Generation ◽  
Constraint Manifold ◽  
Fitting Method ◽  
Kinematic Mapping ◽  
Motion Approximation ◽  
The Given ◽  
Best Fit ◽  
Additional Constraints

This paper studies the problem of spherical 4R motion approximation from the viewpoint of extraction of circular geometric constraints from a given set of spherical displacements. This paper extends our planar 4R linkage synthesis work to the spherical case. By utilizing kinematic mapping and quaternions, we map spherical displacements into points and the workspace constraints of the coupler into intersection of algebraic quadrics (called constraint manifold), respectively, in the image space of displacements. The problem of synthesizing a spherical 4R linkage is reduced to finding a pencil of quadrics that best fit the given image points in the least squares sense. Additional constraints on the pencil identify the quadrics that represent a spherical circular constraint. The geometric parameters of the quadrics encode information about the linkage parameters which are readily computed to obtain a spherical 4R linkage that best navigates through the given displacements. The result is an efficient and largely linear method for spherical four-bar motion generation problem.

A Fourier Descriptor Approach to Integrated Type and Dimensional Synthesis of Coupled Serial Mechanism for Motion Generation

2019 ◽  
Author(s):  
Hao Lv ◽  
Yuanfei Han ◽  
Xiangyun Li ◽  
Liuxian Zhu
Keyword(s):  
Fourier Descriptor ◽  
Dimensional Synthesis ◽  
Type Synthesis ◽  
Motion Generation ◽  
End Effector ◽  
Novel Approach ◽  
Descriptor Approach ◽  
Harmonic Components ◽  
The Given ◽  
Serial Mechanism

Abstract Coupled serial mechanism is a class of mechanisms that couple the relative rotation of successive links utilizing gears or cable-pulley systems. They can be used to generate complex end-effector trajectories or motions with a single actuator. With the employment of Fourier descriptors, a novel approach to integrate type synthesis and dimensional synthesis of such mechanisms is proposed in this paper. Through the Fourier analysis of two arbitrary trajectories from the given motion, the simplest trajectory that contains the least number of harmonic components is identified. Then, characteristic information of those harmonics such as their numbers, amplitudes and initial phases are used to determine the topology and dimensions of the corresponding coupled serial mechanism, thus effectively solving the motion synthesis problem of this type of mechanisms. Finally, three examples are given to demonstrate the validity of the proposed method.

scholarly journals A Task-Driven Approach to Unified Synthesis of Planar Four-Bar Linkages Using Algebraic Fitting of a Pencil of G-Manifolds

2017 ◽  
Vol 17 (3) ◽  
Author(s):  
Q. J. Ge ◽  
Anurag Purwar ◽  
Ping Zhao ◽  
Shrinath Deshpande
Keyword(s):  
Least Squares ◽  
Singular Values ◽  
Singular Value ◽  
Geometric Constraints ◽  
Motion Generation ◽  
Value Decomposition ◽  
Four Bar Linkage ◽  
The Given ◽  
Best Fit ◽  
Additional Constraints

This paper studies the problem of planar four-bar motion generation from the viewpoint of extraction of geometric constraints from a given set of planar displacements. Using the image space of planar displacements, we obtain a class of quadrics, called generalized- or G-manifolds, with eight linear and homogeneous coefficients as a unified representation for constraint manifolds of all four types of planar dyads, RR, PR, and PR, and PP. 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 G-manifolds that best fit the image points in the least squares sense. This least squares problem is solved using singular value decomposition (SVD). The linear coefficients associated with the smallest singular values are used to define a pencil of quadrics. Additional constraints on the linear coefficients are then imposed to obtain a planar four-bar linkage that best guides the coupler through the given displacements. The result is an efficient and linear algorithm that naturally extracts the geometric constraints of a motion and leads directly to the type and dimensions of a mechanism for motion generation.

scholarly journals Evaluation of Static Mapping for Dynamic Space-Shared Multi-task Processing on FPGAs

2021 ◽  
Author(s):  
Umar Ibrahim Minhas ◽  
Roger Woods ◽  
Georgios Karakonstantis
Keyword(s):  
High Performance ◽  
Design Space Exploration ◽  
Design Space ◽  
System Throughput ◽  
Design Parameters ◽  
Temporal Constraints ◽  
Shared Resources ◽  
Task Processing ◽  
High Level ◽  
Performance Computing

AbstractWhilst FPGAs have been used in cloud ecosystems, it is still extremely challenging to achieve high compute density when mapping heterogeneous multi-tasks on shared resources at runtime. This work addresses this by treating the FPGA resource as a service and employing multi-task processing at the high level, design space exploration and static off-line partitioning in order to allow more efficient mapping of heterogeneous tasks onto the FPGA. In addition, a new, comprehensive runtime functional simulator is used to evaluate the effect of various spatial and temporal constraints on both the existing and new approaches when varying system design parameters. A comprehensive suite of real high performance computing tasks was implemented on a Nallatech 385 FPGA card and show that our approach can provide on average 2.9 × and 2.3 × higher system throughput for compute and mixed intensity tasks, while 0.2 × lower for memory intensive tasks due to external memory access latency and bandwidth limitations. The work has been extended by introducing a novel scheduling scheme to enhance temporal utilization of resources when using the proposed approach. Additional results for large queues of mixed intensity tasks (compute and memory) show that the proposed partitioning and scheduling approach can provide higher than 3 × system speedup over previous schemes.

THE NORMALIZED WAVELET DESCRIPTOR FOR SHAPE RETRIEVAL

2008 ◽  
Vol 06 (01) ◽  
pp. 25-36 ◽  
Author(s):  
KIMCHENG KITH ◽  
BAREND J. VAN WYK ◽  
MICHAËL A. VAN WYK
Keyword(s):  
Image Analysis ◽  
Image Retrieval ◽  
Shape Descriptor ◽  
Scale Space ◽  
Experimental Results ◽  
Shape Retrieval ◽  
Fourier Descriptor ◽  
Curvature Scale Space ◽  
Wavelet Descriptor

In many image analysis applications, such as image retrieval, the shape of an object is of primary importance. In this paper, a new shape descriptor, namely the Normalized Wavelet Descriptor (NWD), which is a generalization and extension of the Wavelet Descriptor (WD), is introduced. The NWD is compared to the Fourier Descriptor (FD), which in image retrieval experiments conducted by Zhang and Lu, outperformed even the Curvature Scale Space Descriptor (CSSD). Image retrieval experiments have been conducted using a dataset containing 2D-contours of 1400 objects extracted from the standard MPEG7 database. For the chosen dataset, our experimental results show that the NWD outperforms the FD.

Adaptive Geometry Representation of Turbine Vane Frames for Use in Optimization

2021 ◽  
Author(s):  
Sebastian F. Riebl ◽  
Christian Wakelam ◽  
Reinhard Niehuis
Keyword(s):  
Design Space ◽  
Cfd Simulation ◽  
A Priori ◽  
Three Dimensional ◽  
Optimization Method ◽  
Three Dimensions ◽  
Design Parameters ◽  
Adjustment Process ◽  
Turbine Vane ◽  
Integrated Concept

Abstract Turbine Vane Frames (TVF) are a way to realize more compact jet engine designs. Located between the high pressure turbine (HPT) and the low pressure turbine (LPT), they fulfill structural and aerodynamic tasks. When used as an integrated concept with splitters located between the structural load-bearing vanes, the TVF configuration contains more than one type of airfoil with sometimes pronouncedly different properties. This system of multidisciplinary demands and mixed blading poses an interesting opportunity for optimization. Within the scope of the present work, a full geometric parameterization of a TVF with splitters is presented. The parameterization is chosen as to minimize the number of parameters required to automatically and flexibly represent all blade types involved in a TVF row in all three dimensions. Typical blade design parameters are linked to the fourth order Bézier-curve controlled camber line-thickness parameterization. Based on conventional design rules, a procedure is presented, which sets the parameters within their permissible ranges according to the imposed constraints, using a proprietary developed code. The presented workflow relies on subsequent three dimensional geometry generation by transfer of the proposed parameter set to a commercially available CAD package. The interdependencies of parameters are discussed and their respective significance for the adjustment process is detailed. Furthermore, the capability of the chosen parameterization and adjustment process to rebuild an exemplary reference TVF geometry is demonstrated. The results are verified by comparing not only geometrical profile data, but also validated CFD simulation results between the rebuilt and original geometries. Measures taken to ensure the robustness of the method are highlighted and evaluated by exploring extremes in the permissible design space. Finally, the embedding of the proposed method within the framework of an automated, gradient free numerical optimization is discussed. Herein, implications of the proposed method on response surface modeling in combination with the optimization method are highlighted. The method promises to be an option for improvement of optimization efficiency in gradient free optimization of interdependent blade geometries, by a-priori excluding unsuitable blade combinations, yet keeping restrictions to the design space as limited as possible.

scholarly journals Optimal synthesis of a four-bar linkage by method of controlled deviation

2004 ◽  
Vol 31 (3-4) ◽  
pp. 265-280 ◽  
Author(s):  
Radovan Bulatovic ◽  
Stevan Djordjevic
Keyword(s):  
Objective Function ◽  
Optimal Synthesis ◽  
Straight Line ◽  
Individual Comparison ◽  
Four Bar Linkage ◽  
The Given ◽  
Initial Selection ◽  
Selection Of ◽  
Process Calculation ◽  
Made In

This paper considers optimal synthesis of a four-bar linkage by method of controlled deviations. The advantage of this approximate method is that it allows control of motion of the coupler in the four-bar linkage so that the path of the coupler is in the prescribed environment around the given path on the segment observed. The Hooke-Jeeves?s optimization algorithm has been used in the optimization process. Calculation expressions are not used as the method of direct searching, i.e. individual comparison of the calculated value of the objective function is made in each iteration and the moving is done in the direction of decreasing the value of the objective function. This algorithm does not depend on the initial selection of the projected variables. All this is illustrated on an example of synthesis of a four-bar linkage whose coupler point traces a straight line, i.e. passes through sixteen prescribed points lying on one straight line. .

Direct Optimization of Multi-Degree-of-Freedom Mechanisms for Near Time Optimal Motions Along Specified Paths

1991 ◽  
Author(s):  
Satish Sundar ◽  
Zvi Shiller
Keyword(s):  
Design Method ◽  
Close Correlation ◽  
Optimization Methods ◽  
Degree Of Freedom ◽  
Design Parameters ◽  
Direct Optimization ◽  
Fitting Procedure ◽  
Time Optimal ◽  
Approximate Cost ◽  
The Given

Abstract A design method for selecting system parameters of multi-degree-of-freedom mechanisms for near minimum time motions along specified paths is presented. The time optimization problem is approximated by a simple curve fitting procedure that fits, what we call, the acceleration lines to the given path. The approximate cost function is explicit in the design parameters, facilitating the formulation of the design problem as a constrained optimization. Examples for optimizing the dimensions of a five-bar planar mechanism demonstrate close correlation between the approximate and the exact solutions and better computational efficiency than the previous unconstrained optimization methods.

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