scholarly journals A Unified Approach to Exact and Approximate Motion Synthesis of Spherical Four-Bar Linkages Via Kinematic Mapping

2017 ◽  
Vol 10 (1) ◽  
Author(s):  
Xiangyun Li ◽  
Ping Zhao ◽  
Anurag Purwar ◽  
Q. J. Ge
Keyword(s):  
Null Space ◽  
Solution Space ◽  
Quadratic Equation ◽  
Image Space ◽  
Geometric Constraints ◽  
Design Parameters ◽  
Space Representation ◽  
Motion Synthesis ◽  
Four Bar Linkage ◽  
Spherical Motion

This paper studies the problem of spherical four-bar motion synthesis from the viewpoint of acquiring circular geometric constraints from a set of prescribed spherical poses. The proposed approach extends our planar four-bar linkage synthesis work to spherical case. Using the image space representation of spherical poses, a quadratic equation with ten linear homogeneous coefficients, which corresponds to a constraint manifold in the image space, can be obtained to represent a spherical RR dyad. Therefore, our approach to synthesizing a spherical four-bar linkage decomposes into two steps. First, find a pencil of general manifolds that best fit the task image points in the least-squares sense, which can be solved using singular value decomposition (SVD), and the singular vectors associated with the smallest singular values are used to form the null-space solution of the pencil of general manifolds; second, additional constraint equations on the resulting solution space are imposed to identify the general manifolds that are qualified to become the constraint manifolds, which can represent the spherical circular constraints and thus their corresponding spherical dyads. After the inverse computation that converts the coefficients of the constraint manifolds to the design parameters of spherical RR dyad, spherical four-bar linkages that best navigate through the set of task poses can be constructed by the obtained dyads. The result is a fast and efficient algorithm that extracts the geometric constraints associated with a spherical motion task, and leads naturally to a unified treatment for both exact and approximate spherical motion synthesis.

Constraint Manifold Synthesis of Planar Linkages

1996 ◽  
Author(s):  
A. P. Murray ◽  
J. M. McCarthy
Keyword(s):  
Design Theory ◽  
Geometric Constraints ◽  
Design Parameters ◽  
Design Problems ◽  
Constraint Manifold ◽  
Linkage Design ◽  
Versatile Tool ◽  
Algebraic Constraints ◽  
Planar Linkages

Abstract This paper formulates the design theory of planar four-bar linkages using the planar form of dual quaternions known as planar quaternions. The set of positions reachable by the floating link of a dyad is a quadratic algebraic surface called a constraint manifold. Determining the coefficients of the quadratic form defining this manifold is equivalent to setting the design parameters of the linkage. If the task of the linkage is specified as geometric constraints on the location of the floating link, then algebraic constraints are obtained on the quaternion components. We seek the coefficients of the constraint manifold that satisfies these constraints. The result is an algebraic formulation that is symmetric in its characterization of the linkage and task, and provides a versatile tool for the formulation and solution of linkage design problems.

The Image of the Coupler Motion of a Special Spherical Four Bar Linkage

1987 ◽  
Author(s):  
J. M. McCarthy
Keyword(s):  
Rational Functions ◽  
Global Properties ◽  
Kinematic Mapping ◽  
Curvature And Torsion ◽  
Four Bar Linkage ◽  
Spherical Motion

Abstract This paper uses a kinematic mapping of spherical motion to derive an image curve which represents the coupler motion of a doubly folding spherical four bar linkage. The image curve of this linkage, the so called “kite” linkage, can be parameterized by rational functions. This parameterization is presented as well as formulas which allow the computation of its curvature and torsion at any point. These formulas provide a link between the global properties of the coupler motion as represented by the image curve itself and its instantaneous properties given by the curvature and torsion functions.

scholarly journals A Globally Optimal Robust Design Method for Complex Systems

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-25
Author(s):  
Yue Chen ◽  
Jian Shi ◽  
Xiao-jian Yi
Keyword(s):  
Complex Systems ◽  
Design Parameter ◽  
Design Method ◽  
Solution Space ◽  
Maximum Size ◽  
Design Criterion ◽  
Design Parameters ◽  
Engineering System ◽  
Output Performance ◽  
Maximum Solution

The uncertainty of the engineering system increases with the growing complexity of the engineering system; therefore, the tolerance to the uncertainty is essential. In the design phase, the output performance should reach the design criterion, even under large variations of design parameters. The tolerance to design parameter variations may be measured by the size of a solution space in which the output performance is guaranteed to deliver the required performance. In order to decouple dimensions, a maximum solution hyperbox, expressed by intervals with respect to each design parameter, is sought. The proposed approach combines the metaheuristic algorithm with the DIRECT algorithm where the former is used to seek the maximum size of hyperbox, and the latter is used as a checking technique that guarantees the obtained hyperbox is indeed a solution hyperbox. There are three advantages of the proposed approach. First, it is a global search and has a considerable high possibility to produce the globally maximum solution hyperbox. Second, it can be used for both analytically known and black-box performance functions. Third, it guarantees that any point selected within the obtained hyperbox satisfies the performance criterion as long as the performance function is continuous. Furthermore, the proposed approach is illustrated by numerical examples and real examples of complex systems. Results show that the proposed approach outperforms the GHZ and CES-IA methods in the literature.

Kinematic Analysis of Spherical Four-Bar Linkages via the Inflection Cubic and Thales Ellipse

2015 ◽  
Author(s):  
Giorgio Figliolini ◽  
Jorge Angeles
Keyword(s):  
Special Interest ◽  
Kinematic Analysis ◽  
Vector Fields ◽  
Three Dimensions ◽  
Unique Point ◽  
Planar Case ◽  
Acceleration Vector ◽  
The Subject ◽  
Four Bar Linkage ◽  
Spherical Motion

The subject of this paper is the formulation of a specific algorithm for the kinematic analysis of spherical four-bar linkages via the inflection spherical cubic and spherical Thales ellipse by devoting particular attention to the crossed four-bar linkage (anti-parallelogram). Moreover, both the inflection and the elliptic cones, which represent the equivalent of the Bresse cylinders of the planar case in three-dimensions, are obtained by showing the particular properties of the spherical motion in terms of the curvature of a coupler curve and both the velocity and acceleration vector fields. Of special interest are also the cases in which the three acceleration poles coincide at one unique point or in two plus one, which depends on the intersections of two spherical curves of third and second degree.

Numerical Solutions of Polynomial Equations for the Eight-Position Synthesis of the Cylindrical-Spherical Dyad

2012 ◽  
Author(s):  
Chintien Huang ◽  
Chenning Hung ◽  
Kuenming Tien
Keyword(s):  
Rigid Body ◽  
Numerical Solutions ◽  
Continuation Method ◽  
Quadratic Equation ◽  
Geometric Constraints ◽  
Numerical Continuation ◽  
Polynomial Equations ◽  
Quartic Polynomial ◽  
Solutions Of Equations ◽  
Position Synthesis

This paper investigates the numerical solutions of equations for the eight-position rigid-body guidance of the cylindrical-spherical (C-S) dyad. We seek to determine the number of finite solutions by using the numerical continuation method. We derive the design equations using the geometric constraints of the C-S dyad and obtain seven quartic polynomial equations and one quadratic equation. We then solve the system of equations by using the software package Bertini. After examining various specifications, including those with random complex numbers, we conclude that there are 804 finite solutions of the C-S dyad for guiding a body through eight prescribed positions. When designing spatial dyads for rigid-body guidance, the C-S dyad is one of the four dyads that result in systems of equal numbers of equations and unknowns if the maximum number of allowable positions is specified. The numbers of finite solutions in the syntheses of the other three dyads have been obtained previously, and this paper provides the computational kinematic result of the last unsolved problem, the eight-position synthesis of the C-S dyad.

4MDS: A Geometric Constraint Based Motion Design Software for Synthesis and Simulation of Planar Four-Bar Linkages

2014 ◽  
Author(s):  
Anurag Purwar ◽  
Abhijit Toravi ◽  
Q. J. Ge
Keyword(s):  
Real Time ◽  
Geometric Constraints ◽  
Geometric Constraint ◽  
Design System ◽  
Dimensional Synthesis ◽  
Complete Control ◽  
Dimensional Changes ◽  
Design Software ◽  
Four Bar Linkage ◽  
Motion Design

This paper presents our recent work on designing and developing a geometric constraint based motion design software system for planar four-bar linkages. Given a motion task, the software computes possible four-bar linkage topologies as well as its dimensions. This capability to analyze the given task and find the best type of the linkage and the dimensions simultaneously sets it apart from any other linkage design software. The Four-Bar Motion Design System (4MDS) makes the synthesis and simulation capabilities available to mechanism designers in an intuitive graphical user interface (GUI) environment. Instead of taking a black box approach to mechanism design, wherein the user simply enters the motion requirements and the software outputs parameters of mechanisms, this software facilitates a dialog with the designer by providing various paths to simulation and synthesis in a design session. The designer has complete control over the specification of motion task, interactive tweaking of the motion, choice of linkage topology computed, dimensional changes, and their apparent effect on motion, all done in real time. This interactivity enhances designers kinematic experience. The underlying theoretical foundation of this paper is based on our earlier work on a task-driven approach to unified type and dimensional synthesis of planar four-bar linkage mechanisms. Instead of treating a planar four-bar mechanism as a set of connected rigid links and joints, we treat them as line or circle constraint generators. With that view, the synthesis problem is reduced to extracting geometric constraints hidden in a given motion task and the simulation is reduced to assembling constraints realizable by mechanical dyads. The algorithm employed is simple and efficient and permits real-time computation, and thus precludes using a limiting database-oriented approach. This tool should make innovation of mechanical motion generating devices accessible to novice and experienced designers alike.

Kinematic Mapping Based Evaluation of Assembly Modes for Planar Four-Bar Synthesis

2005 ◽  
Author(s):  
Hans-Peter Schro¨cker ◽  
Manfred L. Husty ◽  
J. Michael McCarthy
Keyword(s):  
Image Space ◽  
Synthesis Problem ◽  
New Method ◽  
Kinematic Mapping ◽  
Position Synthesis ◽  
Four Bar Linkage

This paper presents a new method to determine if two task positions used to design a four-bar linkage lie on separate circuits of a coupler curve, known as a “branch defect.” The approach uses the image space of a kinematic mapping to provide a geometric environment for both the synthesis and analysis of four-bar linkages. In contrast to current methods of solution rectification, this approach guides the modification of the specified task positions, which means it can be used for the complete five position synthesis problem.

scholarly journals Numerical Analysis of Design Parameters With Strong Influence on the Aerodynamic Efficiency of a Small-Scale Self-Pitch VAWT

2015 ◽  
Author(s):  
Carlos Xisto ◽  
José Páscoa ◽  
Michele Trancossi
Keyword(s):  
Wind Turbine ◽  
Strong Influence ◽  
Vertical Axis ◽  
Periodic Variation ◽  
Numerical Approach ◽  
Design Parameters ◽  
Speed Ratio ◽  
Small Scale ◽  
Vertical Axis Wind Turbine ◽  
Four Bar Linkage

In the paper, four key design parameters with a strong influence on the performance of a small-scale high solidity variable pitch VAWT (Vertical Axis Wind Turbine), operating at low tip-speed-ratio (TSR) are addressed. To this aim a numerical approach, based on a finite-volume discretization of two-dimensional Unsteady RANS equations on a multiple sliding mesh, is proposed and validated against experimental data. The self-pitch VAWT design is based on a straight blade Darrieus wind turbine with blades that are allowed to pitch around a feathering axis, which is also parallel to the axis of rotation. The pitch angle amplitude and periodic variation are dynamically controlled by a four-bar-linkage system. We only consider the efficiency at low and intermediate TSR, therefore the pitch amplitude is chosen to be a sinusoidal function with a considerable amplitude. The results of this parametric analysis will contribute to define the guidelines for building a full size prototype of a small scale turbine of increased efficiency.

Dynamic Modeling and Numeration of Flexible Multi-Body System with Closed Loop

2010 ◽  
Vol 44-47 ◽  
pp. 1519-1524
Author(s):  
Shu Qing Liu ◽  
Xing Song Wang
Keyword(s):  
Dynamic Model ◽  
Closed Loop ◽  
Narrow Range ◽  
Null Space ◽  
Orthogonal Basis ◽  
Natural Coordinates ◽  
Body System ◽  
Multi Body ◽  
Four Bar Linkage ◽  
Flexible Linkage

The dynamic model of flexible multi-body system with closed loop is described with natural coordinates. The method is formulaic and especially appropriate to the modeling of system with repetitive substructures, but Lagrange multipliers as unknown variables are contained in the model. The dynamic model is reduced to a system with minimum dimensions by means of null-space orthogonal basis of constraint Jacobin. The result is correspondence with the dynamic model of rigid multi- body system while the rigid and flexible coupling is considered. The numerical method and the simulation steps are given in detail. Numerical example dealing with a flexible parallel four-bar linkage widely used in engineering illustrates the performance of the proposed method. The dynamic response of the angle between flexible linkage and horizontal axis are presented. The results indicate that there are clearly fluctuation in the angular velocity and acceleration of crank. The motion of connecting linkage contains not only translation but also narrow range rotation especially in the start instant.

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