The Duality Between Planar Kinematics and Statics

2005 ◽  
Author(s):  
Offer Shai ◽  
Gordon R. Pennock
Keyword(s):  
Mechanical Systems ◽  
Unique Point ◽  
Singular Configurations ◽  
New Concepts ◽  
Basic Concepts ◽  
Instantaneous Center ◽  
Pass Through ◽  
Planar Linkages ◽  
Insight Into ◽  
General Perspective

This paper shows that there is a correlation between basic concepts underlying the kinematics of mechanisms and the statics of trusses. The implication of this correlation, referred to here as duality, is that the science of kinematics can be utilized in a systematic manner to yield insight into the statics of mechanical systems. The paper begins by proving the existence of a unique line (referred to as the equimomental line) where the moments, at each point on this line, caused by two arbitrary co-planar forces are equal. The dual concept in kinematics is the instantaneous center of zero velocity and two theorems are presented based on the duality between equimomental lines and instantaneous centers. The first theorem states that the three equimomental lines defined by three co-planar forces must intersect at a unique point. The second theorem states that the equimomental line for two co-planar forces acting in a trusss with two degrees of indeterminacy must pass through a unique point. The paper presents several practical examples to demonstrate how the duality between kinematics and statics provides a better understanding of planar linkages and trusses. The new concepts are used to identify the singular configurations of linkages and the configurations of determinate trusses where they are not rigid. Finally, the paper takes advantage of some important relationships between linkages and trusses to provide a general perspective of the duality between the kinematics of mechanisms and the statics of trusses.

A Study of the Duality Between Planar Kinematics and Statics

2005 ◽  
Vol 128 (3) ◽  
pp. 587-598 ◽  
Author(s):  
Offer Shai ◽  
Gordon R. Pennock
Keyword(s):  
Unique Point ◽  
Planar Mechanisms ◽  
Unique Line ◽  
Original Contribution ◽  
Basic Concepts ◽  
Instantaneous Center ◽  
Force Variable ◽  
Pass Through ◽  
Insight Into ◽  
General Perspective

This paper provides geometric insight into the correlation between basic concepts underlying the kinematics of planar mechanisms and the statics of simple trusses. The implication of this correlation, referred to here as duality, is that the science of kinematics can be utilized in a systematic manner to yield insight into statics, and vice versa. The paper begins by introducing a unique line, referred to as the equimomental line, which exists for two arbitrary coplanar forces. This line, where the moments caused by the two forces at each point on the line are equal, is used to define the direction of a face force which is a force variable acting in a face of a truss. The dual concept of an equimomental line in kinematics is the instantaneous center of zero velocity (or instant center) and the paper presents two theorems based on the duality between equimomental lines and instant centers. The first theorem, referred to as the equimomental line theorem, states that the three equimomental lines defined by three coplanar forces must intersect at a unique point. The second theorem states that the equimomental line for two coplanar forces acting on a truss, with two degrees of indeterminacy, must pass through a unique point. The paper then presents the dual Kennedy theorem for statics which is analogous to the well-known Aronhold-Kennedy theorem in kinematics. This theorem is believed to be an original contribution and provides a general perspective of the importance of the duality between the kinematics of mechanisms and the statics of trusses. Finally, the paper presents examples to demonstrate how this duality provides geometric insight into a simple truss and a planar linkage. The concepts are used to identify special configurations where the truss is not stable and where the linkage loses mobility (i.e., dead-center positions).

Basic Concepts and Definitions of Allergology

2019 ◽  
Author(s):  
Zoran Vrucinic
Keyword(s):  
Immune Reaction ◽  
The Body ◽  
The Other ◽  
Specific Response ◽  
Other Hand ◽  
Medical Vocabulary ◽  
The Future ◽  
Basic Concepts ◽  
Basic Insight ◽  
Insight Into

The future of medicine belongs to immunology and alergology. I tried to not be too wide in description, but on the other hand to mention the most important concepts of alergology to make access to these diseases more understandable, logical and more useful for our patients, that without complex pathophysiology and mechanism of immune reaction,we gain some basic insight into immunological principles. The name allergy to medicine was introduced by Pirquet in 1906, and is of Greek origin (allos-other + ergon-act; different reaction), essentially representing the reaction of an organism to a substance that has already been in contact with it, and manifested as a specific response thatmanifests as either a heightened reaction, a hypersensitivity, or as a reduced reaction immunity. Synonyms for hypersensitivity are: altered reactivity, reaction, hypersensitivity. The word sensitization comes from the Latin (sensibilitas, atis, f.), which means sensibility,sensitivity, and has retained that meaning in medical vocabulary, while in immunology and allergology this term implies the creation of hypersensitivity to an antigen. Antigen comes from the Greek words, anti-anti + genos-genus, the opposite, anti-substance substance that causes the body to produce antibodies.

Two Precision Position Synthesis of Planar Linkages With Positional Rectification

1996 ◽  
Author(s):  
John A. Mirth
Keyword(s):  
Numerical Algorithms ◽  
All Solutions ◽  
Pass Through ◽  
Planar Linkages ◽  
Position Synthesis ◽  
Exact Positions

Abstract Precision position synthesis is used to generate planar linkages that pass through two exact positions and an additional number of approximate positions. The approximate positions provide a means of rectifying the solution linkages such that all solutions presented are more likely to describe a motion that remains within acceptable positional bounds. The rectification method involves the development of three different numerical algorithms that may be applied to a particular step in the dyad/triad method of precision position synthesis. The three algorithms presented can be applied in a variety of combinations to allow for the synthesis of both simple (four-bar) and complex (multiloop) planar linkages.

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.

Teaching Criminology and Police Science for Postgraduate Students at the Ruhr- University Bochum, Germany

2010 ◽  
pp. 177-193
Author(s):  
Diana Ziegleder ◽  
Felix Feldmann-Hahn
Keyword(s):  
Focal Point ◽  
Full Time ◽  
Master's Program ◽  
Postgraduate Students ◽  
New Concepts ◽  
History Of ◽  
E Learning ◽  
Set Up ◽  
Insight Into

This case study looks at the postgraduate program in Criminology and Police Science at the Ruhr- University Bochum, Germany. This practice oriented course of study is designed as a distance learning course (blended learning) and therefore focuses on techniques of e-learning. The case study describes the history of origins and examines the educational situation before this master’s program was established and how an idea became reality. It is one of the very few possibilities in Germany to receive a deeper insight into criminology and police science. Despite the fact, that the students are all professionals and thus working mostly full time, the technical premises make a discourse possible as in on-campus programs. These innovative forms of learning are the focal point of the following case study. It is our aim to provide insight into how a master’s program could be set up and to promote new concepts of e-learning in the field of criminology.

A New Approach for Locating the Instantaneous Centers of Zero Velocity for 1-DOF Planar Linkages

2018 ◽  
Author(s):  
Nadim Diab
Keyword(s):  
Degree Of Freedom ◽  
Planar Mechanisms ◽  
New Approach ◽  
Zero Velocity ◽  
Graphical Technique ◽  
Instantaneous Center ◽  
Planar Linkages ◽  
Consistent Approach

This paper presents a new graphical technique to locate the secondary instantaneous centers of zero velocity (ICs) for one-degree-of-freedom (1-DOF) kinematically indeterminate planar mechanisms. The proposed approach is based on transforming the 1-DOF mechanism into a 2-DOF counterpart by converting any ground-pivoted ternary link into two ground-pivoted binary links. Fixing each of these two new binary links, one at a time, results in two different 1-DOF mechanisms where the intersection of the loci of their instantaneous centers will determine the location of the desired instantaneous center for the original 1-DOF mechanism. This single and consistent approach proved to be successful in locating the ICs of various mechanisms reported in the literature that required different techniques to reach the same results obtained herein.

Inertia Matrix Singularity of Series-Chain Spatial Manipulators With Point Masses

1993 ◽  
Vol 115 (4) ◽  
pp. 723-725 ◽  
Author(s):  
Sunil K. Agrawal
Keyword(s):  
Computer Simulation ◽  
Dynamic Behavior ◽  
Mechanical Systems ◽  
Positive Definite ◽  
Degree Of Freedom ◽  
Numerical Errors ◽  
Singular Configurations ◽  
Spatial Series ◽  
Inertia Matrix ◽  
Incomplete Models

Often, the dynamic behavior of multi-degree-of-freedom mechanical systems such as robots and manipulators is studied by computer simulation. An important step in this simulation is the inversion of inertia matrix of the system. In singular configurations of the inertia matrix, the simulation is prone to large numerical errors. Usually, it is believed that an inertia matrix is always positive definite. In this paper, it is shown that for spatial series-chain manipulators, when the links are modeled as point masses, a multitude of configurations exists when the inertia matrix becomes singular. These singularities arise because point masses lead to incomplete models of the system.

Criterion-Referenced Reliability Indices Associated with the van Hiele Geometry Test

1990 ◽  
Vol 21 (3) ◽  
pp. 238-241
Author(s):  
Mary L. Crowley
Keyword(s):  
Teaching And Learning ◽  
Complete Model ◽  
Reliability Indices ◽  
Van Hiele ◽  
Geometric Concepts ◽  
Criterion Referenced ◽  
Pass Through ◽  
Insight Into ◽  
Geometry Test ◽  
Part Model

Recently the work of Pierre M. van Hiele and Dina van Hiele-Geldofhas gained prominence in the study of the teaching and learning of geometry. Their three-part model (a) describes five sequential and discrete levels learners pass through as geometric thought develops, (b) discusses the nature of insight into geometric concepts, and (c) presents a guide to the development of geometric lessons. A detailed description of the complete model can be found in Crowley (1987).

Conversation Analysis

2020 ◽  
pp. 764-779
Author(s):  
Maren Rüsch
Keyword(s):  
Conversation Analysis ◽  
Natural Environment ◽  
Natural Speech ◽  
Mutual Understanding ◽  
African Languages ◽  
Sequence Organization ◽  
Basic Concepts ◽  
The 1960S ◽  
Linguistic Approaches ◽  
Insight Into

Conversation analysis, which began to evolve in the 1960s, studies the structure of talk, and how speakers organize a mostly fluent talk without many gaps or overlaps in order to guarantee maximal mutual understanding. It is based on the analysis of natural speech in a culturally natural environment. In this chapter, basic concepts of conversation analysis as well as the methods used by scholars are explained. A collection of examples from several African languages illustrates terminologies such as turn-taking strategies, sequence organization, and repair of trouble-sources in talk and provides an insight into new linguistic approaches to conversation analysis, especially in African settings.

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