Synthesis of Four-Link Space Mechanisms Via Extension of Point-Position-Reduction Technique

1971 ◽  
Vol 93 (1) ◽  
pp. 85-89 ◽  
Author(s):  
A. H. Soni ◽  
Matthew Huang
Keyword(s):  
Reduction Technique ◽  
Planar Mechanisms ◽  
Point Position ◽  
Position Synthesis ◽  
Space Mechanisms

The principle of point-position-reduction technique, which is used for position-synthesis of planar mechanisms, is extended to synthesize spherical four-link and spatial four-link RCCC mechanisms for four precision positions.

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.

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.

Approximate Velocities in Mixed Exact-Approximate Position Synthesis of Planar Mechanisms

1999 ◽  
Vol 123 (3) ◽  
pp. 388-394 ◽  
Author(s):  
Jennifer E. Holte ◽  
Thomas R. Chase ◽  
Arthur G. Erdman
Keyword(s):  
Two Dimensional ◽  
Computer Implementation ◽  
Motion Generation ◽  
Planar Mechanisms ◽  
Form Complex ◽  
New Approach ◽  
Realistic Representation ◽  
Velocity Constraints ◽  
Position Synthesis ◽  
Exact Positions

A new approach to the synthesis of planar linkage mechanisms with approximate velocity constraints is proposed. The paper presents the first closed-form complex-number dyad solution to the ground pivot specification problem for two precision positions with velocity specified at one of the positions. The solution is then manipulated in order to add approximate velocity constraints to design methods for two exact positions and an unlimited number of approximate positions. The approximate position and velocity constraints facilitate more realistic representation of design objectives. Solution spaces are presented using two-dimensional ground-pivot maps. Computer implementation of the proposed methodologies would allow designers with little or no knowledge of the synthesis techniques to interactively explore maps of solutions for four-bar motion generation.

Planar Circle-Point Equations for Finitely Separated and Double-Point Positions

1998 ◽  
Vol 123 (1) ◽  
pp. 157-160
Author(s):  
Hyoung Jun Kim ◽  
Raj S. Sodhi
Keyword(s):  
Rigid Body ◽  
Double Point ◽  
Rigid Body Motion ◽  
Body Motion ◽  
New Method ◽  
Planar Mechanisms ◽  
Point Position ◽  
Point Curve ◽  
New Form ◽  
Position Problem

The rigid body motion is studied for a combination of finitely and infinitesimally separated positions in planar kinematics. A general new method is developed for determining the locations of points in a rigid body moving through finitely and infinitesimally separated positions. These points would satisfy the constraints of the crank links for planar mechanisms. A new form of the circle-point curve equations is derived for the double-point position problem and also for the finitely separated position problem in planar kinematics.

Mixed Exact-Approximate Position Synthesis of Planar Mechanisms

1998 ◽  
Vol 122 (3) ◽  
pp. 278-286 ◽  
Author(s):  
Jennifer E. Holte ◽  
Thomas R. Chase ◽  
Arthur G. Erdman
Keyword(s):  
Three Dimensional ◽  
Solution Space ◽  
Motion Generation ◽  
Planar Mechanisms ◽  
Dimensional Solution ◽  
New Approach ◽  
Fuzzy Constraints ◽  
Position Synthesis ◽  
Synthesis Approach ◽  
Exact Positions

A new approach to the synthesis of planar linkage mechanisms with fuzzy constraints is proposed. Design methods for two exact positions and an unlimited number of approximate positions are presented. The use of approximate specifications allows the designer to represent design objectives more realistically. A precision position synthesis approach is used to generate a three-dimensional solution space of dyads satisfying all exact and approximate constraints. The three-dimensional solution space is reduced to a two-dimensional ground-pivot map. Computer implementation of the proposed methodologies would allow designers with little or no knowledge of the synthesis techniques to interactively explore maps of solutions for four-bar motion generation. [S1050-0472(00)00803-5]

Using Optimization for the Mixed Exact-Approximate Synthesis of Planar Mechanisms

2015 ◽  
Author(s):  
Jugesh Sundram ◽  
Pierre Larochelle
Keyword(s):  
Euclidean Space ◽  
Rigid Body ◽  
Parameter Space ◽  
Design Parameter ◽  
Linear Optimization ◽  
Planar Mechanisms ◽  
Synthesis Algorithm ◽  
Approximate Synthesis ◽  
Position Synthesis ◽  
Novel Algorithm

Exact synthesis algorithms for planar mechanisms for rigid-body guidance are limited by the number of poses the mechanism can position the rigid-body in Euclidean space. The mixed exact-approximate synthesis algorithm described guides a rigid exactly through two positions and approximately through n guiding positions. It breaks down a rigid-body guidance task into n sub-problems of three positions to be solved by an exact synthesis algorithm. A novel algorithm utilizing MATLAB’s constrained non-linear optimization tools is proposed. The algorithm can be utilized to find within a bounded design parameter space the RR dyad that exactly reaches two positions and minimizes the distance to n positions. Two such dyads can be synthesized independently and then combined to yield a planar four-bar mechanism. An example using the proposed algorithm to design a planar four-bar mechanism to solve McCarthy’s 11-position synthesis problem stated at the 2002 ASME Conference is included.

Synthesis of Planar Mechanisms for Coupler Tangent-Line Envelope Generation: An Alternative to Coupler Point-Path Generation

1988 ◽  
Vol 110 (2) ◽  
pp. 122-129 ◽  
Author(s):  
Dev P. Sathyadev ◽  
A. H. Soni
Keyword(s):  
Plane Curve ◽  
Tangent Line ◽  
Path Generation ◽  
Planar Mechanisms ◽  
Novel Approach ◽  
Rigid Body Displacement ◽  
Synthesis Procedure ◽  
Position Synthesis ◽  
Four Bar Linkage ◽  
The Given

A synthesis procedure is developed to envelope a given plane curve by a tangent line carried by the coupler plane of a planar four-bar linkage. The synthesis procedure is based on a modification of the planar rigid-body displacement matrix developed by Suh [1]. The approach is based on considering a given curve as the envelope of a moving tangent line and synthesizing mechanisms to envelope the given curve. This is a novel approach in mechanism design and adds a new dimension to the path-generation problem of mechanism synthesis. The foregoing procedure is also extended to synthesize eight-link mechanisms to simultaneously coordinate the motion of two tangent lines. In addition to finite position synthesis, both infinitesimal and mixed position synthesis are considered.

Directional Probabilistic Design of Three-Coupler-Point Four-Bar Mechanisms

1992 ◽  
Author(s):  
George R. Schade ◽  
Douglas R. Korbel ◽  
Deena D. Shanmugam
Keyword(s):  
Monte Carlo ◽  
Probabilistic Model ◽  
Probabilistic Design ◽  
Monte Carlo Test ◽  
Point Position ◽  
Synthesis Technique ◽  
Position Synthesis

Abstract A standard four-bar coupler-point position synthesis technique is augmented with a probabilistic model of randomness coupler-point position caused by production variations in link dimension. The synthesis is optimized to reduce the variations in a chosen direction. The probabilistic optimum is verified by Monte-Carlo test.

The innovative space as the most important element of theregional socio-economic space

2019 ◽  
pp. 60-70
Author(s):  
Larysa Gromozdova ◽  
Inna Stenicheva
Keyword(s):  
Basic Element ◽  
Information Support ◽  
Space Region ◽  
Regional Innovation ◽  
Economic Space ◽  
Mechanisms Of Formation ◽  
Innovation Space ◽  
Space Mechanisms ◽  
Constituent Elements

Purpose of the article: to determine the essence of different elements ofsocio-economic space of the region. Construction of the structure and isolationof individual elements of socio-economic space as a multi-vector formation.This article highlights the essence and different approaches to defining theconcepts, structure and mechanisms of formation of economic and social spacesof the region, innovation space as a basic element of socio-economic space.Research Methods: The methodological basis of the research is the fundamentalprinciples of economic theory, regional economy, scientific views and approachesof foreign and domestic scientists. To achieve the purpose of the study, themethods used at the empirical and theoretical levels were used: axiomatic,abstract, system-structural analysis, analogies and comparisons, graphoanalytic,by which the characterization of the nature of the concepts of space, socioeconomic space, as well as innovation space region. Their general properties,structure and functions are described.The criteria of optimality and balancesof interests in the formation of different types of space in the region areconsidered. The classification of the regional space is proposed, and the networkconnections of the innovation space according to components and elements arerevealed, which allows to study deeply the social, economic and other problemsof development of the region.Scientific novelty: the classification of regionalspace by separate constituent elements is proposed. The concept of “innovationspace” was introduced into scientific circulation, the scheme of networkconnections of the innovation space with other elements of the regional socioeconomic space was developed. Conclusions and Prospects for Further Research:In today’s context, it is possible to significantly improve the economic stateof development of Ukrainian regions by using a scientifically sound andcomprehensive approach to defining and studying the concepts of socioeconomic and innovative space.In the further study it is necessary to considerin detail the mechanism of organizational activity of innovation space in theregion. It is very important to pay attention to information support for theformation of the innovation space, the creation of a regional legal field ofinnovation space, mechanisms for coordinating regional innovation activitieswithin the innovation space, as well as the influence of internal and externalfactors on the formation and development of the innovation space.

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