On the Three Laws of Gearing

2002 ◽  
Vol 124 (4) ◽  
pp. 733-744 ◽  
Author(s):  
David B. Dooner
Keyword(s):  
Direct Contact ◽  
Angular Displacement ◽  
Geometric Theory ◽  
Gear Ratio ◽  
Second Law ◽  
The Third ◽  
Kinematic Geometry ◽  
Third Law ◽  
Conjugate Surfaces ◽  
Contact Mechanism

Three laws of gearing are presented in terms of a three link 1-dof spatial direct contact mechanism. The first law of gearing defines the instantaneous relationship between an infinitesimal displacement of an output body to an infinitesimal angular displacement of an input body for a specified tooth contact normal. A system of cylindroidal coordinates are introduced to facilitate a universal methodology to parameterize the kinematic geometry of generalized motion transmission between skew axes. The second law of gearing establishes a relation between the instantaneous gear ratio and the apparent radii of the hyperboloidal pitch surface in contact as parameterized using a system of cylindroidal coordinates. The third law of gearing establishes an instantaneous relationship for the relative curvature of two conjugate surfaces in direct contact and shows that this relation is independent of the tooth profile geometry. These three laws of gearing along with the system of cylindroidal coordinates establish, in part, a generalized geometric theory comparable to the existing theory for planar kinematics.

The Lex Agraria of 111 B.C. and Procedure in Legislative Assemblies

Antichthon ◽  
1978 ◽  
Vol 12 ◽  
pp. 45-50
Author(s):  
R. Develin
Keyword(s):  
Second Law ◽  
Land Distribution ◽  
The Third ◽  
The Poor ◽  
The Subject ◽  
Third Law ◽  
The Law ◽  
Land Holdings ◽  
Point Of Reference

Agrarian legislation in the immediate aftermath of the Gracchi is the subject of continuing debate. Appian (BC i 27) records three laws, the last two of which are specified as being tribunician: the first removed the inalienability of land holdings; the second was perhaps the measure of Sp. Thorius, mentioned also by Cicero, which stopped land distribution, confirmed possession rights on the land and imposed a rent, the proceeds of which were to help the poor; the third abolished this rent. Appian provides chronological clues of a sort: the first measure came ‘not long after’ the death of C. Gracchus, the third ‘not long after’ Thorius’ law, and the whole business was perhaps finished within fifteen years άπò τῆς Γράκχου νομοϑεσίας. I say ‘perhaps’ because it remains arguable whether the point of reference for these fifteen years is Tiberius or Gaius Gracchus. I intend to argue elsewhere that Tiberius is meant, but as such an argument cannot be regarded as conclusive, there is still a point in this respect in examining the lex agraria which is the inscription CIL i2 585. The law is naturally important in its own right. It is dated internally to 111 B.C. and attempts have been made to equate it with either the second or third of Appian’s laws. If it was the second, this allows a retention of the fifteen years and the placing of the third law in 109 or 108. But if Appian has accurately reported the second law, it imposed a rent, while the first part of the inscriptional law talks of removing rent.

A THEORY OF INNOVATION AND CASE STUDY

2010 ◽  
Vol 14 (05) ◽  
pp. 893-913 ◽  
Author(s):  
NAM P. SUH
Keyword(s):  
Energy Barrier ◽  
Necessary Conditions ◽  
Critical Size ◽  
Government Policies ◽  
Second Law ◽  
Activation Energy Barrier ◽  
Initial Size ◽  
The Third ◽  
Third Law

Three laws of innovation are advanced as the necessary conditions for creating innovations hubs and innovations. The first law states that for innovation to occur, all the required steps of an innovation continuum must be present. The second law states that an innovation hub can be nucleated if the initial size of the nucleate is larger than the critical size and if the activation energy barrier for nucleation can be overcome. Once the innovation hub is nucleated, heterogeneous nucleation of innovation can occur around the innovation hub. The third law states that for innovation to occur, the nucleation rate of innovation must be faster than the rate at which innovative talent and ideas can diffuse away from the region. This theoretical framework has been proposed as a means of formulating government policies for economic growth and innovation. A case study is presented.

2. Matter from the outside

2014 ◽  
pp. 22-37
Author(s):  
Peter Atkins
Keyword(s):  
Physical Chemistry ◽  
Free Energy ◽  
Gibbs Energy ◽  
Absolute Zero ◽  
Second Law ◽  
Conservation Of Energy ◽  
The Third ◽  
Laws Of Thermodynamics ◽  
Third Law

‘Matter from the outside’ focuses on the applications of thermodynamics in physical chemistry. Thermodynamics is the science of energy and the transformations that it can undergo. It plays a central role in understanding chemical reactions. There are four laws of thermodynamics: the Zeroth Law establishes the concept of temperature; the First Law concerns the conservation of energy; the Second Law deals with entropy (a measure of the quality of energy); and the Third Law concerns the absolute zero of temperature. The property enthalpy is explained along with Gibbs energy and free energy. Physical chemists can deploy the laws of thermodynamics, laws relating to matter from the outside, to establish relations between properties and to make important connections.

Unification of Newton's laws of motion

2003 ◽  
Vol 81 (5) ◽  
pp. 713-735
Author(s):  
A F Antippa
Keyword(s):  
Second Law ◽  
Mass Scaling ◽  
Self Energy ◽  
The Third ◽  
Inertial Frames ◽  
Third Law ◽  
Newton’S Laws ◽  
Laws Of Motion

Newton's three laws of motion are unified into one law (a slightly modified second law), valid in generalized inertial frames (defined by a slightly modified first law), invariant under mass scaling (guaranteed by the third law), and having important implications for the concept of force and the problem of self-energy. PACS Nos.: 45.20.Dd, 45.50.Jf, 45.05.+x

On Spatial Euler–Savary Equations for Envelopes

2006 ◽  
Vol 129 (8) ◽  
pp. 865-875 ◽  
Author(s):  
David B. Dooner ◽  
Michael W. Griffis
Keyword(s):  
Direct Contact ◽  
Order Approximation ◽  
Spatial Relations ◽  
Second Order ◽  
Gear Pair ◽  
Second Order Approximation ◽  
Planar Curves ◽  
Gear Teeth ◽  
Kinematic Geometry ◽  
Conjugate Surfaces

Presented are three equations that are believed to be original and new to the kinematics community. These three equations are extensions of the planar Euler–Savary relations (for envelopes) to spatial relations. All three spatial forms parallel the existing well established planar Euler–Savary equations. The genesis of this work is rooted in a system of cylindroidal coordinates specifically developed to parameterize the kinematic geometry of generalized spatial gearing and consequently a brief discussion of such coordinates is provided. Hyperboloids of osculation are introduced by considering an instantaneously equivalent gear pair. These analog equations establish a relation between the kinematic geometry of hyperboloids of osculation in mesh (viz., second-order approximation to the axode motion) to the relative curvature of conjugate surfaces in direct contact (gear teeth). Planar Euler–Savary equations are presented first along with a discussion on the terms in each equation. This presentation provides the basis for the proposed spatial Euler–Savary analog equations. A lot of effort has been directed to establishing generalized spatial Euler–Savary equations resulting in many different expressions depending on the interpretation of the planar Euler–Savary equation. This work deals with the interpretation where contacting surfaces are taken as the spatial analog to the contacting planar curves.

The Second Law of Thermodynamics

2018 ◽  
Author(s):  
Dennis Sherwood ◽  
Paul Dalby
Keyword(s):  
Second Law Of Thermodynamics ◽  
Worked Examples ◽  
Phase Changes ◽  
Second Law ◽  
The Third ◽  
Mathematical Properties ◽  
Third Law Of Thermodynamics ◽  
Third Law ◽  
Definition Of ◽  
Clausius Inequality

The Second Law. The definition of entropy, and its mathematical properties. The Clausius inequality, and the criterion of spontaneity of change in an isolated system. Worked examples of heat flow down a temperature gradient, and the adiabatic expansion of a gas into a vacuum. Combining the First and Second Laws, with worked examples, such as phase changes. Introduction to the Third Law of Thermodynamics. Introduction to T,S diagrams.

Quantification of Biological Resistance: Introducing a Unifying Unit and Scale of Resistance

2018 ◽  
Author(s):  
Rudolf Fullybright
Keyword(s):  
Drug Resistance ◽  
Living Organism ◽  
Pathogen Resistance ◽  
Absolute Quantification ◽  
Biological Resistance ◽  
The Third ◽  
Exact Measurement ◽  
Unit Function ◽  
Third Law ◽  
Accurate Quantification

Accurate quantification of biological resistance has been impossible so far. Among the various forms of biological resistance which exist in nature, pathogen resistance to drugs is a familiar one. However, as in the case of other forms of resistance, accurately quantifying drug resistance in pathogens has been impossible up to now. Here, we introduce a mathematically-defined and uniform procedure for the absolute quantification of biological resistance deployed by any living organism in the biological realm, including and beyond drug resistance in medicine. The scheme introduced makes possible the exact measurement or computation of the extent to which resistance is deployed by any living organism regardless of kingdom and regardless of the mechanism of resistance involved. Furthermore, the Second Law of Resistance indicating that resistance has the potential to increase to infinite levels, and the Third Law of Resistance indicating that resistance comes to an end once interaction stops, the resistance unit function introduced here is fully compatible with both the Second and Third Laws of Resistance.

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