A Novel Paradigm for the Qualitative Synthesis of Simple Kinematic Chains Based on Complexity Measures

2011 ◽  
Vol 3 (3) ◽  
Author(s):  
Waseem A. Khan ◽  
Jorge Angeles
Keyword(s):  
Complexity Analysis ◽  
Vertical Axis ◽  
Synthesis Process ◽  
Geometric Complexity ◽  
Qualitative Synthesis ◽  
Complexity Measures ◽  
Kinematic Synthesis ◽  
Kinematic Chains ◽  
Loss Of Regularity ◽  
Four Bar Linkage

Proposed in this paper is a paradigm for the qualitative synthesis of simple kinematic chains that is based on the concept of complexity. Qualitative synthesis is understood here as the number and the type stages of the kinematic-synthesis process. The formulation hinges on the geometric complexity of the surface associated with lower kinematic pairs. First, the geometric complexity of curves and surfaces is recalled, as defined via the loss of regularity (LOR). The LOR, based in turn on the concept of diversity, measures the spectral richness of the curvature of either the curve or the surface under study. The paper closes with a complexity analysis of all six lower kinematic pairs, as a means to guide the mechanical designer into the conceptual stage of the design process. The paradigm is illustrated with the computation of the complexity of the four-bar linkage in all its versions, planar, spherical, and spatial, as well as that of a transmission for the conversion of a rotation about a vertical axis into one about a horizontal axis.

scholarly journals A New Algorithm for Unique Representation and Isomorphism Detection of Planar Kinematic Chains with Simple and Multiple Joints

Processes ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 601
Author(s):  
Mahmoud Helal ◽  
Jong Wan Hu ◽  
Hasan Eleashy
Keyword(s):  
Degree Of Freedom ◽  
Synthesis Process ◽  
Structural Synthesis ◽  
Joint Configuration ◽  
Unique Representation ◽  
Kinematic Chains

In this work, a new algorithm is proposed for a unique representation for simple and multiple joint planar kinematic chains (KCs) having any degree of freedom (DOF). This unique representation of KCs enhances the isomorphism detection during the structural synthesis process of KCs. First, a new concept of joint degree is generated for all joints of a given KC based on joint configuration. Then, a unified loop array (ULA) is obtained for each independent loop. Finally, a unified chain matrix (UCM) is established as a unique representation for a KC. Three examples are presented to illustrate the proposed algorithm procedures and to test its validity. The algorithm is applied to get a UCM for planar KCs having 7–10 links. As a result, a complete atlas database is introduced for 7–10-link non-isomorphic KCs with simple or/and multiple joints and their corresponding unified chain matrix.

A Hexagonal Prism Folding for Membrane Packaging Based on Concepts of Finite Rigid Motion and Kinematic Synthesis

2016 ◽  
Author(s):  
Kassim Abdul-Sater
Keyword(s):  
Spatial Configuration ◽  
Rigid Motion ◽  
Building Blocks ◽  
Computational Procedure ◽  
Hexagonal Prism ◽  
Linkage Mechanism ◽  
Space Applications ◽  
Kinematic Synthesis ◽  
Kinematic Chains ◽  
Position Synthesis

This paper discusses the use of concepts of finite rigid body kinematics as well as kinematic synthesis in non-rigid, engineering folding problems. The exemplary task consists in designing a folding pattern, which allows to fold a circular sheet from a flat unfolded state into a prescribed compact spatial configuration that forms a hexagonal prism. Other two-configuration design problems may be found for instance in space applications where membranes in tensegrity reflector antennas need to be stowed in a spacecraft. The folding motion could be actuated using an appropriately designed linkage mechanism attached to the membrane, which, however, is not considered in this paper. The specific result of this work is a creative but systematic and computational procedure for crease pattern design. The approach is essentially based on the relative kinematics equations of serial kinematic chains and the finite position synthesis of linkage building blocks. These techniques sucessively combine to segment a flat bounded surface, such that it can reach the prescribed spatial configuration.

Synthesis of planar kinematic chains with prismatic pairs based on a similarity recognition algorithm

2021 ◽  
pp. 1-13
Author(s):  
Rongjiang Cui ◽  
Zhizheng Ye ◽  
Shifu Xu ◽  
Chuan-yu Wu ◽  
Liang Sun
Keyword(s):  
Recognition Algorithm ◽  
Synthesis Process ◽  
Synthesis Methods ◽  
Structural Synthesis ◽  
Kinematic Chains

Abstract The structural synthesis of planar kinematic chains (KCs) with prismatic pairs (P-pairs) is the basis of innovating mechanisms containing P-pairs. In literature, only a little research has been carried out to synthesize planar KCs with P-pairs. Moreover, these synthesis methods for KCs with P-pairs involve all possible combinations of edges, resulting in a large number of isomorphic KCs and a low synthesis efficiency. In this study, our previous similarity recognition algorithm is improved and applied to synthesize planar KCs with P-pairs. Only a small number of isomorphic KCs are generated in the synthesis process, and the synthesis efficiency is greatly enhanced. Our method is applied to synthesize 9-link 2-DOF, 10-link 1-DOF, and 11-link 2-DOF KCs with one and two P-pairs. Our synthesis results are consistent with those of the existing literature. The present work is helpful to design mechanisms with P-pairs and can be extended to mechanisms with other types of kinematic pairs.

THE KINEMATIC SYNTHESIS OF STEERING MECHANISMS

2000 ◽  
Vol 24 (3-4) ◽  
pp. 453-476 ◽  
Author(s):  
Jin Yao ◽  
Jorge Angeles
Keyword(s):  
Polynomial Equation ◽  
Global Optimum ◽  
Polynomial Equations ◽  
Kinematic Synthesis ◽  
Local Optima ◽  
Speed Reduction ◽  
Design Variables ◽  
Transmission Quality ◽  
Four Bar Linkage ◽  
Maximum Transmission

We propose a computational-kinematics approach based on elimination procedures to synthesize a steering four-bar linkage. In this regard, we aim at minimizing the root-mean square error of the synthesized linkage in meeting the steering condition over a number of linkage configurations within the linkage range of motion. A minimization problem is thus formulated, whose normality conditions lead to two polynomial equations in two unknown design variables. Upon eliminating one of these two variables, a monovariate polynomial equation is obtained, whose roots yield all locally-optimum linkages. From these roots, the global optimum, as well as unfeasible local optima, are readily identified. The global optimum, however, turns out to be impractical because of the large differences in its link lengths, which we refer to as dimensional unbalance. To cope with this drawback, we use a kinematically-equivalent focal mechanism, i.e., a six-bar linkage with an input-output function identical to that of the four-bar linkage. Given that the synthesized linkage requires a rotational input, as opposed to most existing steering linkages, which require a translational input, we propose a spherical four-bar linkage to drive the steering linkage. The spherical linkage is synthesized so as to yield a speed reduction as close as possible to 2:1 and to have a maximum transmission quality.

A frame-independent comparison metric for discrete motion sequences

2020 ◽  
Vol 234 (9) ◽  
pp. 1764-1774
Author(s):  
Ping Zhao ◽  
Yong Wang ◽  
Lihong Zhu ◽  
Xiangyun Li
Keyword(s):  
Moving Frame ◽  
Kinematic Synthesis ◽  
Reference Motion ◽  
Comparison Results ◽  
Synthesis Of Mechanisms ◽  
Rotational Part ◽  
The Difference ◽  
Four Bar Linkage ◽  
The Given ◽  
Discrete Motion

To evaluate the kinematic performance of designed mechanisms, a statistical-variance-based metric is proposed in this article to measure the “distance” between two discrete motion sequences: the reference motion and the given task motion. It seeks to establish a metric that is independent of the choice of the fixed frame or moving frame. Quaternions are adopted to represent the rotational part of a spatial pose, and the variance of the set of relative displacements is computed to reflect the difference between two sequences. With this variance-based metric formulation, we show that the comparison results of two spatial discrete motions are not affected by the choice of frames. Both theoretical demonstration and computational example are presented to support this conclusion. In addition, since the deviation error between the task motion and the synthesized motion measured with this metric is independent of the location of frames, those corresponding parameters could be excluded from the optimization algorithm formulated with our frame-independent metric in kinematic synthesis of mechanisms, and the complexity of the algorithm are hereby reduced. An application of a four-bar linkage synthesis problem is presented to illustrate the advantage of the proposed metric.

Finding All Solutions to Unconstrained Nonlinear Optimization for Approximate Synthesis of Planar Linkages Using Continuation Method

1999 ◽  
Vol 121 (3) ◽  
pp. 368-374 ◽  
Author(s):  
A.-X. Liu ◽  
T.-L. Yang
Keyword(s):  
Continuation Method ◽  
Optimization Method ◽  
Global Optimum ◽  
Kinematic Synthesis ◽  
All Solutions ◽  
Approximate Synthesis ◽  
Unconstrained Nonlinear Optimization ◽  
Optimum Solution ◽  
Planar Linkages ◽  
Four Bar Linkage

Generally, approximate kinematic synthesis of planar linkage is studied using optimization method. But this method has two defects: i) the suitable initial guesses are hard to determine and ii) the global optimum solution is difficult to find. In this paper, a new method which can find all solutions to approximate kinematic synthesis of planar linkage is proposed. Firstly, we reduce the approximate synthesis problem to finding all solutions to polynomial equations. Polynomial continuation method is then used to find all solutions. Finally, all possible linkages can be obtained. Approximate syntheses of planar four-bar linkage for function generation, rigid-body guidance and path generation are studied in detail and three examples are given to illustrate the advantages of the proposed method.

Real Continuation Method and its Application in Kinematic Synthesis

2000 ◽  
Author(s):  
Liu Anxin ◽  
Yang Tingli
Keyword(s):  
High Efficiency ◽  
Continuation Method ◽  
Linear Equations ◽  
Path Generation ◽  
Kinematic Synthesis ◽  
Real Solutions ◽  
Non Linear ◽  
Four Bar Linkage ◽  
Non Linear Equations

Abstract Real continuation method for finding real solutions to non-linear equations is proposed. Synthesis of planar four-bar linkage for path generation with nine precision points is studied using this method. The proposed method has high efficiency and can best be used for solving synthesis problems.

A Survey of One Class of 7-Jointed Serially Connected Robots: Type-Synthesis to Obtain Controllably Dexterous Workspace

1989 ◽  
Vol 111 (2) ◽  
pp. 163-175 ◽  
Author(s):  
J. K. Davidson
Keyword(s):  
Screw Theory ◽  
Kinematic Chain ◽  
Synthesis Process ◽  
Geometric Description ◽  
Type Synthesis ◽  
End Effector ◽  
Identification Process ◽  
Kinematic Chains ◽  
Five Axes

A type-synthesis process, which is based on screw theory and geometry, is developed to identify certain robots, each of which can provide controllably dexterous workspace of a tool-point. The identification process is confined to only those robots which control the motion of the end-effector with seven series-connected joints, the axes for the outermost three of which are concurrent. Forty six types of robots are so identified, and, for each, the results are (i) a suitable kinematic chain for the arm and (ii) suitable angle-dimensions for the links of the arm, where the angle-choices are limited to the values 0, ± π/2, and π. A geometric description of the dominant function for control is included. The same kinematic chains are surveyed for all possible parallel and right-angle arrangements of adjacent axes in the four links of the arm. Again utilizing screw theory, 160 robots are identified which do not posses full-cycle axis-dependence among some or all of the first five axes.

Kinematic Synthesis of Minimally Actuated Multi-Loop Planar Linkages With Second Order Motion Constraints for Object Grasping

2013 ◽  
Author(s):  
Gim Song Soh ◽  
Nina Robson
Keyword(s):  
Second Order ◽  
Human Robot Interaction ◽  
Degree Of Freedom ◽  
Dimensional Synthesis ◽  
Open Problems ◽  
Kinematic Synthesis ◽  
Human Environment ◽  
Kinematic Chains ◽  
Curvature Effects ◽  
Planar Linkages

In this paper, we consider the dimensional synthesis of one degree-of-freedom multi-loop planar linkages such that they do not violate normal direction and second order curvature constraints imposed by contact with objects. Our goal is in developing minimally actuated multi-loop mechanical devices for human-robot interaction, that is, devices whose tasks will happen in a human environment. Currently no systematic method exists for the kinematic synthesis of robotic fingers that incorporate multi-loop kinematic structure with second order task constraints, related to curvature. We show how to use these contact and curvature effects to formulate the synthesis equations for the design of a planar one-degree-of-freedom six-bar linkage. An example for the design of a finger that maintains a specified contact with an object, for an anthropomorphic task, is presented at the end of the paper. It is important to note, that the theoretical foundation presented in this paper, assists in solving some of the open problems of this field, providing preliminary results on the synthesis of kinematic chains with multi-loop topology and the use of novel task specifications that incorporate curvature constraints with future applications in grasping and object manipulation.

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.

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