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 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 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.

Computer Simulation of Path and Motion Generation With Six-Bar Linkage

2003 ◽  
Author(s):  
Lu Yi ◽  
Tatu Leinonen
Keyword(s):  
Computer Simulation ◽  
Analytical Calculation ◽  
Geometric Constraint ◽  
Simulation Approach ◽  
Dimensional Synthesis ◽  
Motion Generation ◽  
Basic Tool ◽  
Kinematic Synthesis ◽  
Four Bar Linkage ◽  
Accuracy And Repeatability

The basic tool of path or motion generation synthesis for more than four prescribed positions is analytical calculation, but its process is quite complicated and far from straightforward. A novel computer simulation mechanism of six-bar linkage for path or motion generation synthesis is presented in this paper. In the case of five-precision points, using the geometric constraint and dimension-driving techniques, a primary simulation mechanism of four-bar linkage is created. Based on the different tasks of path and motion generation for kinematic dimensional synthesis, the simulation mechanisms of path and motion generation with Stephenson I, II and Watt six-bar linkages are developed from the primary simulation mechanism. The results of kinematic synthesis for five prescribed positions prove that the mechanism simulation approach is not only fairly quick and straightforward, but is also advantageous from the viewpoint of accuracy and repeatability.

scholarly journals Geometric Design-based Dimensional Synthesis of a Novel Metamorphic Multi-fingered Hand with Maximal Workspace

2021 ◽  
Vol 34 (1) ◽  
Author(s):  
Wei An ◽  
Jun Wei ◽  
Xiaoyu Lu ◽  
Jian S. Dai ◽  
Yanzeng Li
Keyword(s):  
Geometric Design ◽  
Practical Significance ◽  
Design Parameters ◽  
Control Algorithms ◽  
Discretization Method ◽  
Dimensional Synthesis ◽  
Symmetrical Structure ◽  
Design And Optimization ◽  
Total Length

AbstractCurrent research on robotic dexterous hands mainly focuses on designing new finger and palm structures, as well as developing smarter control algorithms. Although the dimensional synthesis of dexterous hands with traditional rigid palms has been carried out, research on the dimensional synthesis of dexterous hands with metamorphic palms remains insufficient. This study investigated the dimensional synthesis of a palm of a novel metamorphic multi-fingered hand, and explored the geometric design for maximizing the precision manipulation workspace. Different indexes were used to value the workspace of the metamorphic hand, and the best proportions between the five links of the palm to obtain the optimal workspace of the metamorphic hand were explored. Based on the fixed total length of the palm member, four nondimensional design parameters that determine the size of the palm were introduced; through the discretization method, the influence of the four design parameters on the workspace of the metamorphic hand with full-actuated fingers and under-actuated fingers was analyzed. Based on the analysis of the metamorphic multi-fingered hand, the symmetrical structure of the palm was designed, resulting in the largest workspace of the multi-fingered hand, and proved that the metamorphic palm has a massive upgrade for the workspace of underactuated fingers. This research contributed to the dimensional synthesis of metamorphic dexterous hands, with practical significance for the design and optimization of novel metamorphic hands.

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.

Workspace, dexterity and dimensional optimization of microhexapod

2015 ◽  
Vol 35 (4) ◽  
pp. 341-347 ◽  
Author(s):  
E. Rouhani ◽  
M. J. Nategh
Keyword(s):  
Degrees Of Freedom ◽  
Optimization Problem ◽  
Screw Theory ◽  
Design Parameters ◽  
Dimensional Synthesis ◽  
Content Type ◽  
Workspace Analysis ◽  
The Difference ◽  
Flexure Joints ◽  
6 Degrees Of Freedom

Purpose – The purpose of this paper is to study the workspace and dexterity of a microhexapod which is a 6-degrees of freedom (DOF) parallel compliant manipulator, and also to investigate its dimensional synthesis to maximize the workspace and the global dexterity index at the same time. Microassembly is so essential in the current industry for manufacturing complicated structures. Most of the micromanipulators suffer from their restricted workspace because of using flexure joints compared to the conventional ones. In addition, the controllability of micromanipulators inside the whole workspace is very vital. Thus, it is very important to select the design parameters in a way that not only maximize the workspace but also its global dexterity index. Design/methodology/approach – Microassembly is so essential in the current industry for manufacturing complicated structures. Most of the micromanipulators suffer from their restricted workspace because of using flexure joints compared to the conventional ones. In addition, the controllability of micromanipulators inside the whole workspace is very vital. Thus, it is very important to select the design parameters in a way that not only maximize the workspace but also its global dexterity index. Findings – It has been shown that the proposed procedure for the workspace calculation can considerably speed the required calculations. The optimization results show that a converged-diverged configuration of pods and an increase in the difference between the moving and the stationary platforms’ radii cause the global dexterity index to increase and the workspace to decrease. Originality/value – The proposed algorithm for the workspace analysis is very important, especially when it is an objective function of an optimization problem based on the search method. In addition, using screw theory can simply construct the homogeneous Jacobian matrix. The proposed methodology can be used for any other micromanipulator.

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.

Substantiation of amplitude-frequency characteristics and design parameters of vibration exciter in volume oscillation separator

2021 ◽  
Vol 12 (2) ◽  
Author(s):  
I Palamarchuk ◽  
◽  
V Vasyliv ◽  
V Sarana ◽  
M Mushtruk ◽  
...  
Keyword(s):  
Translational Motion ◽  
Operating Conditions ◽  
Design Parameters ◽  
Vibration Velocity ◽  
Vibration Exciter ◽  
Lagrange Equations ◽  
Bulk Materials ◽  
Vibrating Screen ◽  
Working Bodies ◽  
Oscillating Motion

The main effects of the developed design for vibratory separator: the increased driving force in the process of bulk material separation in this work, achieved by providing the working cylindrical-conical container with vibrational motion; improving the conditions for the passage of product particles through openings, achieved by providing the sieve surface with volume oscillations; reduction of energy consumption and improvement of operating conditions for support nodes during the operation of the designed vibrating screen, achieved due to the installation of additional elastic elements between the separator body and bearing assemblies of the vertical drive shaft in vibration exciter. Providing the working bodies of the designed vibrating screen with volume oscillating motion allows increasing the performance and quality of the separation process of solid bulk materials. To determine the rational parameters for vibration screening process, the equations of motion of working bodies as a conical sieve surface were obtained using the method of the Lagrange equations of the second order. When applying solutions of the Cauchy problem for linear nonhomogeneous differential equations, the solution of the latter was obtained. The obtained dependences of oscillation amplitudes, vibration velocity and vibration acceleration, and the intensity of oscillating motion allowed us to perform a mathematical analysis for power and energy parameters of vibration drive in the developed separator. The inclined placement of the conical sieve surface allows for spatial gyration or circular translational motion, which makes it possible to realize the advantages of volumetric separation of bulk materials. The results of the conducted analytical study made it possible to substantiate the optimal inclination angle for working sieve surface. Based on our analysis, the design parameters of vibration exciter were substantiated and clarified, and the design of this technical system was demonstrated.

Ball Drive Configurations and Kinematics for Holonomic Ground Mobility

2017 ◽  
Author(s):  
Biruk A. Gebre ◽  
Kishore Pochiraju
Keyword(s):  
Design Space ◽  
Kinematic Model ◽  
Design Parameters ◽  
Actuation Force ◽  
Confined Spaces ◽  
Naming Convention ◽  
Trade Offs ◽  
Vehicle Velocity ◽  
And Performance ◽  
Selection Of

Holonomic motion is desired for mobile ground robots and vehicles as it provides omnidirectional maneuvering capabilities, which can simplify the task of navigating around obstacles in confined spaces and unstructured environments. Mobility platforms that utilize spherical wheels are gaining popularity and interest due to the agile maneuvering and ground traversal capabilities they enable for mobility platforms. Ball-driven mobility platforms have a rich design space as various design parameters are available that can modify the physical and performance characteristics of the platforms. Various configurations for ball-driven mobility platforms are presented along with a generalized kinematic model that can be used for calculating motor velocities for a desired vehicle velocity. A naming convention is also presented in the paper for differentiating between configurations used for ball-driven mobility platforms. Metrics such as platform footprint, platform stability, and actuation force and efficiency are used to compare the configurations and to highlight some of the trade-offs associated with the selection of a configuration. Promising configurations are highlighted based on the metrics selected for the comparisons.

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