A Dual Number Approach to the Kinematic Analysis of Spatial Linkages With Dimensional and Geometric Tolerances

2004 ◽  
Author(s):  
Emanuele Cecchini ◽  
Ettore Pennestri` ◽  
Roberto Stefanelli ◽  
Leonardo Vita
Keyword(s):  
Kinematic Analysis ◽  
Tolerance Analysis ◽  
Rigid Bodies ◽  
Kinematic Modeling ◽  
Spatial Mechanisms ◽  
Analysis And Synthesis ◽  
Spatial Linkages ◽  
Joint Clearances ◽  
First Time ◽  
Cardan Joint

Design robustness is somewhat connected to tolerances. In fact, the lower is the sensitivity of the kinematic function to the deviations of manufacturing process, the higher is the robustness of the design. In this investigation is described a tolerance analysis method based on dual vectors kinematic modeling of spatial linkages and on Monte Carlo simulation of the random variables. In the present analysis the hypothesis of rigid bodies is valid and only kinematic variables are considered in output. The method is applied to a Cardan joint modelled as an RCCC linkage with main dimensions considered as stochastic variables with Gaussian distribution. Dual vectors are well known in kinematic analysis and synthesis of spatial mechanisms. When compared with traditional vectorial methods, dual vectors show an enhanced capability to model misalignments among kinematic pairs axes. Although this is not the first time that dual vectors are used for the kinematic and dynamic analysis of spatial mechanisms with manufacturing errors, the present use of dual vectors to model joint clearances seems somewhat novel.

Kinematic Analysis of Spatial Mechanisms by Means of Screw Coordinates. Part 1—Screw Coordinates

1971 ◽  
Vol 93 (1) ◽  
pp. 61-66 ◽  
Author(s):  
M. S. C. Yuan ◽  
F. Freudenstein
Keyword(s):  
Numerical Methods ◽  
Motion Analysis ◽  
Kinematic Analysis ◽  
Rigid Bodies ◽  
Spatial Mechanisms ◽  
Computer Aided

The concept of screw coordinates is developed in terms of motor algebra, and applied to the kinematics and statics of rigid bodies, in particular to the computer-aided motion analysis of spatial mechanisms. The laws of the composition and transformation of screw coordinates and their application to the kinematics and statics of rigid bodies are developed. These results form the basis for the development of numerical methods for the kinematic analysis of spatial mechanisms.

Theories of Kinematic Analysis and Synthesis of Spatial Mechanisms Containing Lower and Higher Pairs.

1983 ◽  
Author(s):  
George N. Sandor ◽  
Dilip Kohli ◽  
Charles F. Reinholtz ◽  
Ashitova Ghosal ◽  
Manuel Hernandez
Keyword(s):  
Kinematic Analysis ◽  
Spatial Mechanisms ◽  
Analysis And Synthesis

CONSTRUCTION OF SCREW GEOMETRY VIA 3-D CAD SYSTEM FOR THE ANALYSIS AND SYNTHESIS OF SPATIAL MECHANISMS

2000 ◽  
Vol 24 (2) ◽  
pp. 401-413
Author(s):  
F.Z. Chen ◽  
M.J. Tsai
Keyword(s):  
Kinematic Analysis ◽  
Computer Aided Design ◽  
Graphical Method ◽  
Graphic Method ◽  
Efficient Process ◽  
Cad System ◽  
Spatial Mechanisms ◽  
Computer Aided ◽  
Analysis And Synthesis ◽  
Aided Design

This paper investigates the application of computer-aided design and drawing (CAD) software to the kinematic analysis and synthesis of spatial mechanisms based upon screw geometry. The advantages of the graphic method for the synthesis and analysis of mechanisms are straightforward, comprehensive, clearly represented, and easy to correlate to a real mechanism. Using conventional 3-D CAD software, the screw axes and joint axes are constructed as virtual parts. The relationships of joint axes that are constrained by screw geometry are the assembly conditions for the virtual parts in the CAD system. This paper shows that, similar to the synthesis of a planar linkage, the synthesis of a spatial C-C dyad by the graphical method in a CAD system is an efficient process.

Kinematic Analysis of Spatial Mechanisms by Means of Screw Coordinates. Part 2—Analysis of Spatial Mechanisms

1971 ◽  
Vol 93 (1) ◽  
pp. 67-73 ◽  
Author(s):  
M. S. C. Yuan ◽  
F. Freudenstein ◽  
L. S. Woo
Keyword(s):  
Computer Program ◽  
Kinematic Analysis ◽  
Static Force ◽  
Single Degree Of Freedom ◽  
Numerical Examples ◽  
Spatial Mechanism ◽  
Single Degree ◽  
Spatial Mechanisms ◽  
Torque Analysis ◽  
Basic Concepts

The basic concepts of screw coordinates described in Part I are applied to the numerical kinematic analysis of spatial mechanisms. The techniques are illustrated with reference to the displacement, velocity, and static-force-and-torque analysis of a general, single-degree-of-freedom spatial mechanism: a seven-link mechanism with screw pairs (H)7. By specialization the associated computer program is capable of analyzing many other single-loop spatial mechanisms. Numerical examples illustrate the results.

scholarly journals Poly-predicative conditional constructions in Catalan (in comparaison with Spanish and French)

2021 ◽  
Vol 27 (3) ◽  
pp. 128-136
Author(s):  
T. V. Repnina
Keyword(s):  
Romance Languages ◽  
Complex Sentence ◽  
Syntactic Structures ◽  
Complex Sentences ◽  
Analysis And Synthesis ◽  
Syntactic Relations ◽  
Simple Sentences ◽  
First Time

By poly-predicative conditional constructions we mean complex sentences that contain at least three simple sentences, each representing either a condition or a consequence. Poly-predicative sentences can in addition contain other simple sentences that represent neither condition, nor consequence. Poly-predicative constructions that, apart from one condition and one consequence, also include other simple sentences, are not classified here as poly-predicative conditional constructions. While poly-predicative constructions in general have already been in the focus of researches attention, this article seems to address them on Catalan material for the first time. The purpose of this article is an analysis of syntactic relations in poly-predicative conditional constructions. Its objectives include their comparison in Catalan, Spanish, and French, identification of the main types of these constructions, and an analysis of their characteristics. Since the use of tenses and moods in the constructions addressed coincides with that in prototypical bi-predicative conditional constructions, we do not examine it here. The methods, used in this study, included: sampling during corpus collection, classification, description, comparison, transformational analysis and synthesis. The study is based on Catalan texts and their translations into Spanish and French. The findings of the study include: 1) Poly-predicative conditional constructions with several condition and/or consequence clauses are possible. Condition and consequence clauses can occupy different positions in poly-predicative conditional constructions; 2) In contrast to Catalan and Spanish, French admits the replacement of the conditional conjunction si by que; 3) Prototypical conditional and poly-predicative constructions are invariably characterized by subordination relations, with coordination parataxis possible as well. In addition, more complex syntactic structures are possible like, e. g., parallel co-coordination; 4) A prototypical conditional construction being a complex sentence, this limits possible syntactic types of poly-predicative conditional constructions. They cannot be structured as a string of simple sentences connected by coordination or subordination. Consecutive subordination of three or more subordinate sentences is not characteristic of conditional constructions; 5) The study identified a similarity between poly-predicative conditional constructions in Catalan, Spanish, and French. The present research is a contribution into the syntax of Romance languages.

Kinematic Analysis and Synthesis of Three-Input, Eight-Bar Mechanisms Driven by Relatively Small Cranks

1992 ◽  
Author(s):  
Kambiz Farhang ◽  
Partha Sarathi Basu
Keyword(s):  
Nonlinear Equations ◽  
Kinematic Analysis ◽  
Linear Equations ◽  
Output Link ◽  
Analysis And Design ◽  
Constraint Equations ◽  
Analysis And Synthesis ◽  
The Mean ◽  
Approximate Equations

Abstract Approximate kinematic equations are developed for the analysis and design of three-input, eight-bar mechanisms driven by relatively small cranks. Application of a method in which an output link is presumed to be comprised of a mean and a perturbational motions, along with the vector loop approach facilitates the derivation of the approximate kinematic equations. The resulting constraint equations are, (i) in the form of a set of four nonlinear equations relating the mean link orientations, and (ii) a set of four linear equations in the unknown perturbations (output link motions). The latter set of equations is solved, symbolically, to obtain the output link motions. The approximate equations are shown to be effective in the synthesis of three-input, small-crank mechanisms.

Mass Flow and Derivative Moment of Inertia Flow in Planar (Geared) Linkages

1992 ◽  
Author(s):  
Zhonghe Ye ◽  
M. R. Smith
Keyword(s):  
Mass Flow ◽  
Kinematic Analysis ◽  
Moment Of Inertia ◽  
Force Balance ◽  
New Concepts ◽  
Prismatic Joints ◽  
Planar Linkages ◽  
First Time ◽  
Shaking Moment

Abstract The paper describes a method for the determination of the conditions for the complete shaking force and shaking moment balancing of planar linkages, including geared linkages, with revolute and prismatic joints. The conditions may be written down without the need for any kinematic analysis of the linkage by the application of two new concepts. These are the concept of mass flow for complete shaking force balance and the concept of derivative moment of inertia flow for complete shaking moment balance, the second of which is described here for the first time. A number of examples demonstrate the power of the method.

Algebraic Representation of Geometric and Size Tolerances

1995 ◽  
Author(s):  
S. H. Mullins ◽  
D. C. Anderson
Keyword(s):  
Tolerance Analysis ◽  
Design Analysis ◽  
Algebraic Representation ◽  
Dimensional Metrology ◽  
Algebraic Form ◽  
Worst Case ◽  
Mechanical Component ◽  
Analysis And Synthesis ◽  
Statistical Tolerance ◽  
Statistical Tolerance Analysis

Abstract Presented is a method for mathematically modeling mechanical component tolerances. The method translates the semantics of ANSI Y14.5M tolerances into an algebraic form. This algebraic form is suitable for either worst-case or statistical tolerance analysis and seeks to satisfy the requirements of both dimensional metrology and design analysis and synthesis. The method is illustrated by application to datum systems, position tolerances, orientation tolerances, and size tolerances.

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