An application of graph theory and nonlinear programming to the kinematic synthesis of mechanisms

1991 ◽  
Vol 26 (6) ◽  
pp. 553-563 ◽  
Author(s):  
Damir Vucina ◽  
Ferdinand Freudenstein
Keyword(s):  
Graph Theory ◽  
Nonlinear Programming ◽  
Kinematic Synthesis ◽  
Synthesis Of Mechanisms

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.

Construction of Baranov Trusses Using a Single Universal Construction Rule

2016 ◽  
Author(s):  
Elad Hahn ◽  
Offer Shai
Keyword(s):  
Graph Theory ◽  
Construction Rule ◽  
Graph Representation ◽  
Kinematic Structure ◽  
Mathematical Basis ◽  
Synthesis Of Mechanisms ◽  
Complete Set ◽  
Universal Construction ◽  
Planar Linkages ◽  
Mechanism Theory

The kinematic structure of Baranov trusses has been widely studied in the field of mechanism theory. Baranov trusses are seen as the fundamental planar linkages which are a basis for all other planar linkages. As such, they have been used for synthesis of mechanisms as well as their analysis. However, up until now only a limited number Baranov trusses are known and cataloged. In this paper, a method is proposed for generation of Baranov trusses using a new graph representation suitable for linkages of the sort. This method, named the Universal construction rule, is capable of generating a complete set of all feasible Baranov trusses with any number of links. The method has been proven using a mathematical basis from rigidity theory. It is based on the correspondence between Baranov trusses and Assur groups, which are reformulated in terms of graph theory to be known as Assur graphs.

scholarly journals Synthesis of Mechanisms by Methods of Nonlinear Dynamics

10.14311/1684 ◽  
2012 ◽  
Vol 52 (6) ◽  
Author(s):  
Michael Valášek ◽  
Zbynek Šika
Keyword(s):  
Dynamical System ◽  
Dissipative System ◽  
New Method ◽  
Time Varying ◽  
Objective Functions ◽  
Mechanism Synthesis ◽  
Kinematic Synthesis ◽  
Nonlinear Dynamical ◽  
Synthesis Of Mechanisms ◽  
Synthesis Procedure

This paper deals with a new method for parametric kinematic synthesis of mechanisms. The traditional synthesis procedure based on collocation, correction and optimization suffers from the local minima of objective functions, usually due to the local unassembled configurations which must be overcome. The new method uses the time varying values of the synthesized dimensions of the mechanism as if the mechanism had elastic links and guidances. The time varying dimensions form the basis for an accompanying nonlinear dynamical dissipative system and the synthesis is transformed into the time evolution of this accompanying dynamical system. Its dissipativity guarantees the termination of thesynthesis. The synthesis always covers the parametric kinematic synthesis, but it can be advantageously extended into the optimization of any further criteria. The main advantage of the method described here for dealing with mechanism synthesis is that it overcomes the unassembled configurations of the synthesized mechanisms and enables any further synthesis criteria to be introduced, and terminates due to dissipation of the accompanied dynamical system.

AN INTUITIVE APPROACH TO THE KINEMATIC SYNTHESIS OF MECHANISMS

2016 ◽  
Author(s):  
Bruno Fausto Zappa ◽  
Vittorio Lorenzi ◽  
Paolo Righettini ◽  
Roberto Strada
Keyword(s):  
Kinematic Synthesis ◽  
Synthesis Of Mechanisms

Kinematic Synthesis of Deployable-Foldable Truss Structures Using Graph Theory, Part 2: Generation of Deployable Truss Module Design Concepts

1995 ◽  
Vol 117 (1) ◽  
pp. 117-122 ◽  
Author(s):  
D. B. Warnaar ◽  
M. Chew
Keyword(s):  
Graph Theory ◽  
Truss Structures ◽  
Kinematic Synthesis ◽  
Design Concepts ◽  
Module Design

A special type of truss structures, called truss modules, is presented. Graphs of this class of structures form a subset of the graphs that are generated using the approach presented in Part 1. Two procedures are presented that are applied to recognize these graphs among graphs of truss structures. The procedures also generate information on the relative lengths of the links in a truss module by examining the graph it represents. This enables the generation of numerous novel (deployable) truss modules as well as those that have been reported in the literature. Promising alternatives to existing designs are identified.

Application of Instantaneous Invariants to the Analysis and Synthesis of Mechanisms

1977 ◽  
Vol 99 (1) ◽  
pp. 97-103 ◽  
Author(s):  
B. Roth ◽  
A. T. Yang
Keyword(s):  
Problem Solving ◽  
Rigid Body ◽  
Rigid Body Motion ◽  
Geometric Constraint ◽  
Body Motion ◽  
Kinematic Synthesis ◽  
Systematic Procedure ◽  
Synthesis Of Mechanisms ◽  
Analysis And Synthesis ◽  
Kinematic Properties

The objective of this paper is to make instantaneous invariants a more accessible tool for problem solving in the field of kinematics. We present a systematic procedure to determine the instantaneous invariants of a rigid body under geometric constraint, develop a process by which kinematic properties of rigid body motion can be expressed in terms of instantaneous invariants, and apply instantaneous invariants to solve typical kinematic synthesis problems. Four examples are given in detail for illustrative purposes.

Kinematic Synthesis of Deployable-Foldable Truss Structures Using Graph Theory, Part 1: Graph Generation

1995 ◽  
Vol 117 (1) ◽  
pp. 112-116 ◽  
Author(s):  
D. B. Warnaar ◽  
M. Chew
Keyword(s):  
Graph Theory ◽  
Conceptual Design ◽  
Design Process ◽  
Degrees Of Freedom ◽  
Truss Structure ◽  
Truss Structures ◽  
Structural Synthesis ◽  
Deployable Structures ◽  
Kinematic Synthesis ◽  
Graph Generation

Kinematic structural synthesis has been relatively successful when applied to the conceptual design of mechanisms. The approach presented in this paper, however, views the design process from an initial standpoint of a truss structure. First, graphs are generated that represent truss structures with a given number of nodes and links. Each graph is then modified by designating certain edges in the graph to represent links in the structure that incorporate additional degrees of freedom. In so doing, the graph of a structure is transformed into one representing a mechanism. A procedure is presented that enables the exhaustive generation of these graphs for deployable structures of any given number of nodes and links. From these graphs, it is then possible to obtain enumerable novel deployable truss structures as well as those that have been reported in the literature.

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