Triad Synthesis for up to Five Design Positions With Application to the Design of Arbitrary Planar Mechanisms

1987 ◽  
Vol 109 (4) ◽  
pp. 426-434 ◽  
Author(s):  
T. R. Chase ◽  
A. G. Erdman ◽  
D. R. Riley
Keyword(s):  
Complex Number ◽  
Path Generation ◽  
Dimensional Synthesis ◽  
Planar Mechanisms ◽  
Relative Precision ◽  
Synthesis Techniques ◽  
New Synthesis ◽  
Actual Mechanism ◽  
Synthesis Tool

A new synthesis tool, the triad, is introduced to enable simplified synthesis of very complex planar mechanisms. The triad is a connected string of three vectors representing jointed rigid links of an actual mechanism. The triad is used as a tool to model an original mechanism topology with a set of simpler components. Each triad is then used to generate a set of “relative precision positions” which, in turn, enables the dimensional synthesis of each triad with well-established motion and path generation techniques for simple four-bar linkages. Two independent derivations of the relative precision positions are provided. All common triad geometries amenable to simple dyad synthesis techniques are presented. The triad geometries summarized here may be applied to two, three, four, and five precision position problems using graphical, algebraic, or complex number formulations of Burmester theory. Examples are provided.

Synthesis of Parallel Manipulator with Single DOF

2013 ◽  
Vol 330 ◽  
pp. 639-643 ◽  
Author(s):  
Chung Huang Yu ◽  
Wen Yeuan Chung
Keyword(s):  
Parallel Manipulator ◽  
Design Concept ◽  
Path Generation ◽  
Dimensional Synthesis ◽  
Type Synthesis ◽  
Numerical Example ◽  
Geometrical Constraints ◽  
Moving Platform ◽  
Manipulator Design

This paper proposed a new manipulator design concept which leads to a single DOF system. The system composed of a moving platform and several supporting legs. It can execute the tasks of 3D body guidance or path generation and thus replace expensive manipulators with high DOF in some conditions. There are mainly two steps in designing this manipulator. The first step is type synthesis to determine the number and types of legs. Dimensional synthesis is then executed based on the movement requirements and geometrical constraints. In this study the reduction of the DOF is also analyzed for various legs added between the moving platform and the ground. A numerical example of executing 3D body guidance is given to verify the proposed new concept.

On nonassembly in the optimal dimensional synthesis of planar mechanisms

2001 ◽  
Vol 21 (5) ◽  
pp. 345-354 ◽  
Author(s):  
R.J. Minnaar ◽  
D.A. Tortorelli ◽  
J.A. Snyman
Keyword(s):  
Dimensional Synthesis ◽  
Planar Mechanisms

Singular Solutions in Burmester Theory

1973 ◽  
Vol 95 (2) ◽  
pp. 572-576 ◽  
Author(s):  
R. E. Kaufman
Keyword(s):  
Complex Number ◽  
Singular Solutions ◽  
Design Technique ◽  
Planar Mechanisms ◽  
Point Position ◽  
Proper Interpretation ◽  
General Synthesis ◽  
Number Development

A unified complex number development of four position planar finite position theory is presented. This formulation shows that Burmester circlepoint-centerpoint theory specializes to include slider points, concurrency points, poles, and point position reduction by proper interpretation of the trivial roots of the general synthesis equations. Thus a single design technique can be used for the multiposition synthesis of most pin or slider-jointed planar mechanisms. Four position function, path, or motion generating linkages can all be designed in this manner.

Coriolis acceleration analysis of planar mechanisms by complex-number algebra

1982 ◽  
Vol 17 (6) ◽  
pp. 405-414 ◽  
Author(s):  
George N Sandor ◽  
E Raghavacharyulu ◽  
Arthur G Erdman
Keyword(s):  
Complex Number ◽  
Planar Mechanisms ◽  
Coriolis Acceleration ◽  
Acceleration Analysis

Designing Planar Mechanisms Using a Bi-Invariant Metric in the Image Space of SO (3)

1994 ◽  
Author(s):  
Pierre Larochelle ◽  
J. Michael McCarthy
Keyword(s):  
Rigid Body ◽  
Numerical Results ◽  
Image Space ◽  
Dimensional Synthesis ◽  
Invariant Metric ◽  
Planar Mechanisms ◽  
Position And Orientation ◽  
Position Synthesis

Abstract In this paper we present a technique for using a bi-invariant metric in the image space of spherical displacements for designing planar mechanisms for n (> 5) position rigid body guidance. The goal is to perform the dimensional synthesis of the mechanism such that the distance between the position and orientation of the guided body to each of the n goal positions is minimized. Rather than measure these distances in the plane, we introduce an approximating sphere and identify rotations which are equivalent to the planar displacements to a specified tolerance. We then measure distances between the rigid body and the goal positions using a bi-invariant metric on the image space of SO(3). The optimal linkage is obtained by minimizing this distance over all of the n goal positions. The paper proceeds as follows. First, we approximate planar rigid body displacements with spherical displacements and show that the error induced by such an approximation is of order 1/R2, where R is the radius of the approximating sphere. Second, we use a bi-invariant metric in the image space of spherical displacements to synthesize an optimal spherical 4R mechanism. Finally, we identify the planar 4R mechanism associated with the optimal spherical solution. The result is a planar 4R mechanism that has been optimized for n position rigid body guidance using an approximate bi-invariant metric with an error dependent only upon the radius of the approximating sphere. Numerical results for ten position synthesis of a planar 4R mechanism are presented.

Optimum dimensional synthesis of planar mechanisms with geometric constraints

Meccanica ◽  
2020 ◽  
Vol 55 (11) ◽  
pp. 2135-2158
Author(s):  
V. García-Marina ◽  
I. Fernández de Bustos ◽  
G. Urkullu ◽  
R. Ansola
Keyword(s):  
Geometric Constraints ◽  
Dimensional Synthesis ◽  
Planar Mechanisms

Optimum Synthesis of Rigid Mechanisms Using a Dynamic Ant-Search Method With Sensitivity Analysis

2019 ◽  
Author(s):  
Nadim Diab ◽  
Omar Itani ◽  
Ahmad Smaili
Keyword(s):  
Sensitivity Analysis ◽  
Optimization Technique ◽  
Design Parameters ◽  
Neighborhood Search ◽  
Intensity Level ◽  
Path Generation ◽  
Exploration And Exploitation ◽  
Planar Mechanisms ◽  
Optimum Synthesis ◽  
Synthesis Of Mechanisms

Abstract Four-bar linkages are commonly used mechanisms in various mechanical systems and components. Several techniques for optimum synthesis of planar mechanisms have been suggested in literature such as the Genetic, Tabu, Simulated Annealing, Swarm-Based and many other algorithms. This paper covers optimization of four-bar mechanisms with path generation tasks using a Dynamic Ant Search (DAS) algorithm. Unlike the Modified Ant Search (MAS) technique where ants unanimously moved between the exploration and exploitation phases, in the proposed algorithm, each ant is free to travel between the two aforementioned phases independent of other ants and as governed by its own pheromone intensity level. Moreover, sensitivity analysis is conducted on the design parameters to determine their corresponding neighborhood search boundaries and thus improve the search while in the exploitation mode. These implemented changes demonstrated a remarkable impact on the optimum synthesis of mechanisms for path generation tasks. A briefing of the MAS based algorithm is first presented after which the proposed modified optimization technique and its implementation on four-bar mechanisms are furnished. Finally, three case studies are conducted to evaluate the efficiency and robustness of the proposed methodology where the performances of the obtained optimum designs are benchmarked with those previously reported in literature.

A New Approach for Exact/Approximate Point Synthesis of Planar Mechanisms

2005 ◽  
Author(s):  
Ahmad Smaili ◽  
Nadim Diab
Keyword(s):  
Synthesis Method ◽  
Dimensional Synthesis ◽  
Gradient Search ◽  
Planar Mechanisms ◽  
Simple Method ◽  
New Approach ◽  
Optimum Synthesis ◽  
Approximate Synthesis ◽  
Optimum Solution ◽  
Synthesis Approach

The aim of this article is to provide a simple method to solve the mixed exact-approximate dimensional synthesis problem of planar mechanism. The method results in a mechanism that can traverse a closed path with the choice of any number of exact points while the rest are approximate points. The algorithm is based on optimum synthesis rather than on precision position methods. Ant-gradient search is applied on an objective function based on log10 of the error between the desired positions and those generated by the optimum solution. The log10 function discriminates on the side of generating miniscule errors (on the order of 10−14) at the exact points while allowing for higher errors at the approximate positions. The algorithm is tested by way of five examples. One of these examples was used to test exact/approximate synthesis method based on precision point synthesis approach.

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