Kinematic Analysis and Synthesis of Deterministic 3-2-1 Locator Schemes for Machining Fixtures

2000 ◽  
Vol 123 (4) ◽  
pp. 708-719 ◽  
Author(s):  
Rodrigo A. Marin ◽  
Placid M. Ferreira
Keyword(s):  
Kinematic Analysis ◽  
Screw Theory ◽  
Sufficient Conditions ◽  
Search Space ◽  
Combinatorial Algorithms ◽  
Convex Region ◽  
Analysis And Synthesis ◽  
Synthesis Procedure ◽  
Machining Fixtures ◽  
Necessary And Sufficient

This paper addresses the problem of generating a well-conditioned, near-optimal deterministic 3-2-1 location scheme. Given are a workpart with identified planar datum faces, each with an associated convex region of admissible locator positions, and a set of disturbing twists (resulting from the processing operations on the workpart). First, screw theory is used to identify easily implementable necessary and sufficient conditions for deterministic positioning of the workpart in a 3-2-1 locator scheme. Next, the conditioning of a location scheme is studied and combinatorial algorithms are developed for synthesizing near-optimally conditioned locator schemes. Interesting decomposition and restrictions on the search space are identified to make the synthesis procedure efficient.

A Mathematical Approach to Automatic Configuration of Machining Fixtures: Analysis and Synthesis

1989 ◽  
Vol 111 (4) ◽  
pp. 299-306 ◽  
Author(s):  
Y-C. Chou ◽  
V. Chandru ◽  
M. M. Barash
Keyword(s):  
Screw Theory ◽  
Theory Analysis ◽  
Workpiece Surface ◽  
3 Dimensional ◽  
Prismatic Parts ◽  
Analysis And Synthesis ◽  
Engineering Mechanics ◽  
Machining Fixtures ◽  
Machining Operations

Drawing on screw theory and engineering mechanics, a mathematical theory for automatic configuration of machining fixtures for prismatic parts is developed. There are two parts in the theory: analysis and synthesis. The following functions of fixtures are analyzed: deterministic workpiece location, clamping stability, and total restraint. The synthesis of fixtures includes the determination of locating and clamping points on workpiece surface and the determination of clamping forces. The theory deals with the general case of 3-dimensional parts, polygon support (as opposed to three-point support), and multiple machining operations.

Software tools for analysis and synthesis of stochastic systems with high availability (XI)

2021 ◽  
Author(s):  
I.N. Sinitsyn ◽  
V.I. Sinitsyn ◽  
E.R. Korepanov ◽  
T.D. Konashenkova
Keyword(s):  
Stochastic Systems ◽  
Sufficient Conditions ◽  
Software Tools ◽  
High Availability ◽  
Mean Square ◽  
Canonical Expansion ◽  
Basic Wavelet ◽  
Analysis And Synthesis ◽  
Necessary And Sufficient ◽  
Statistical Criteria

The article proceeds the thematic cycle dedicated to software tools for stochastic systems with high availability (StSHA) functioning at shock disturbances (ShD) and is dedicated to wavelet synthesis according to complex statistical criteria (CsC). Short survey concerning corresponding works for mean square criteria (msc) is given. In Sect.1 basic CsC definitions and approaches are given. Sect. 2 dedicated to CsC wavelet necessary and sufficient conditions of optimality for scalar non-stationary shock StSHA (StSSHA). Methodological support is based on Haar wavelets. Sect. 4 and Sect.5 are devoted to CSK optimization ShStSHA (basic wavelet equations, algorithms, software tools and example). Several advantages of wavelet algorithms and tools are described and stated for complex ShD. Some generalization of CsC algorithms based on wavelet canonical expansion of StP in ShStSHA mentioned.

On Line Screw Systems and Their Application to Flexure Synthesis

2011 ◽  
Vol 3 (1) ◽  
Author(s):  
Hai-Jun Su ◽  
Hafez Tari
Keyword(s):  
Case Studies ◽  
Computational Algorithm ◽  
Screw Theory ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Constrained Motion ◽  
Motion Patterns ◽  
Linearly Independent ◽  
On Line ◽  
Necessary And Sufficient

Motivated by the problem of synthesizing a pattern of flexures that provide a desired constrained motion, this paper presents a new screw theory that deals with “line screws” and “line screw systems.” A line screw is a screw with a zero pitch. The set of all line screws within a screw system is called a line variety. A general screw system of rank m is a line screw system if the rank of its line variety equals m. This paper answers two questions: (1) how to calculate the rank of a line variety for a given screw system and (2) how to algorithmically find a set of linearly independent lines from a given screw system. It has been previously found that a wire or beam flexure is considered a line screw, or more specifically a pure force wrench. By following the reciprocity and definitions of line screws, we have derived the necessary and sufficient conditions of line screw systems. When applied to flexure synthesis, we show that not all motion patterns can be realized with wire flexures connected in parallel. A computational algorithm based on this line screw theory is developed to find a set of admissible line screws or force wrenches for a given motion space. Two flexure synthesis case studies are provided to demonstrate the theory and the algorithm.

Optimal Synthesis of Point Contact Restraint

1992 ◽  
Vol 206 (2) ◽  
pp. 95-103 ◽  
Author(s):  
Y L Xiong PhD ◽  
D J Sanger ◽  
D R Kerr
Keyword(s):  
Rigid Body ◽  
Point Contact ◽  
Sufficient Conditions ◽  
The Body ◽  
Point Contacts ◽  
Internal Forces ◽  
Synthesis Procedure ◽  
External Forces ◽  
Necessary And Sufficient ◽  
Synthesis Solution

The object of this paper is to develop a procedure that will allow the establishment of necessary and sufficient point contacts on a rigid body to ensure that the body has any desired state of instantaneous motion or restraint. The screw space and its sub-spaces are employed; these are vector spaces but not Euclidean spaces. The states of restraint and instantaneous motion of a body restrained by a system of screws of point contacts are specified by reciprocal sub-spaces of the screw space. This leads to a synthesis procedure for restraint of a rigid body by means of point contacts. The existence and uniqueness of the synthesis solution are discussed, and necessary and sufficient conditions for a realizable surface of a kinematic pair are given. Finally, two quality measures for a feasible set of screws are defined. One represents the uniformity of the distribution of internal forces while the other indicates the restraint's ability to resist external forces.

The extinction time of a general birth and death process with catastrophes

1986 ◽  
Vol 23 (04) ◽  
pp. 851-858 ◽  
Author(s):  
P. J. Brockwell
Keyword(s):  
Laplace Transform ◽  
Size Distribution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Death Process ◽  
Extinction Time ◽  
Birth And Death Process ◽  
Different Types ◽  
The Laplace Transform ◽  
Necessary And Sufficient

The Laplace transform of the extinction time is determined for a general birth and death process with arbitrary catastrophe rate and catastrophe size distribution. It is assumed only that the birth rates satisfyλ0= 0,λj> 0 for eachj> 0, and. Necessary and sufficient conditions for certain extinction of the population are derived. The results are applied to the linear birth and death process (λj=jλ, µj=jμ) with catastrophes of several different types.

Budgeting in Socio-economic Development Strategies (Raising a Problem)

2008 ◽  
pp. 134-151
Author(s):  
A. Shastitko ◽  
M. Ovchinnikov
Keyword(s):  
Economic Policy ◽  
Economic Development ◽  
Social Change ◽  
Eastern Europe ◽  
Statistical Data ◽  
Sufficient Conditions ◽  
Transitional Period ◽  
Socio Economic Development ◽  
Necessary And Sufficient ◽  
Economic Development Strategies

The article proposes an approach to the analysis of social change and contributes to the clarification of concepts of economic policy. It deals in particular with the notion of "change of system". The author considers positive and normative aspects of the analysis of capitalist and socialist systems. The necessary and sufficient conditions for the system to be changed are introduced, their fulfillment is discussed drawing upon the historical and statistical data. The article describes both economic and political peculiarities of the transitional period in different countries, especially in Eastern Europe.

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