A Spatial Version of Octoidal Gears Via the Generalized Camus Theorem

2015 ◽  
Vol 8 (2) ◽  
Author(s):  
Giorgio Figliolini ◽  
Hellmuth Stachel ◽  
Jorge Angeles
Keyword(s):  
Single Point ◽  
Spherical Geometry ◽  
Ruled Surfaces ◽  
Line Contact ◽  
Dual Algebra ◽  
Bevel Gears ◽  
Involute Gears ◽  
The Right

Understanding the geometry of gears with skew axes is a highly demanding task, which can be eased by invoking Study's Principle of Transference. By means of this principle, spherical geometry can be readily ported into its spatial counterpart using dual algebra. This paper is based on Martin Disteli's work and on the authors' previous results, where Camus' auxiliary curve is extended to the case of skew gears. We focus on the spatial analog of one particular case of cycloid bevel gears: When the auxiliary curve is specified as a pole tangent, we obtain “pathologic” spherical involute gears; the profiles are always interpenetrating at the meshing point because of G2-contact. The spatial analog of the pole tangent, a skew orthogonal helicoid, leads to G2-contact at a single point combined with an interpenetration of the flanks. However, when instead of a line a plane is attached to the right helicoid, the envelopes of this plane under the roll-sliding of the auxiliary surface (AS) along the axodes are developable ruled surfaces. These serve as conjugate tooth flanks with a permanent line contact. Our results show that these flanks are geometrically sound, which should lead to a generalization of octoidal bevel gears, or even of bevel gears carrying teeth designed with the exact spherical involute, to the spatial case, i.e., for gears with skew axes.

The Role of the Orthogonal Helicoid in the Generation of the Tooth Flanks of Involute-Gear Pairs With Skew Axes

2015 ◽  
Vol 7 (1) ◽  
Author(s):  
Giorgio Figliolini ◽  
Hellmuth Stachel ◽  
Jorge Angeles
Keyword(s):  
Smooth Surface ◽  
Tangent Plane ◽  
Line Contact ◽  
Planar Surface ◽  
Screw Axis ◽  
Bevel Gears ◽  
Involute Gears ◽  
G2 Continuity ◽  
Instant Screw Axis

Camus' concept of auxiliary surface (AS) is extended to the case of involute gears with skew axes. In the case at hand, we show that the AS is an orthogonal helicoid whose axis (a) lies in the cylindroid and (b) is normal to the instant screw axis of one gear with respect to its meshing counterpart; in general, the helicoid axis is skew with respect to the latter. According to the spatial version of Camus' Theorem, any line or surface attached to the AS, in particular any line L of AS itself, can be chosen to generate a pair of conjugate flanks with line contact. While the pair of conjugate flanks is geometrically feasible, as they always share a line of contact and the tangent plane at each point of this line, they even have the same curvature, G2-continuity, when L coincides with the instant screw axis (ISA). This means that the two surfaces penetrate each other, at the same common line. The outcome is that the surfaces are not realizable as tooth flanks. Nevertheless, this is a fundamental step toward the synthesis of the flanks of involute gears with skew axes. In fact, the above-mentioned interpenetration between the tooth flanks can be avoided by choosing a smooth surface attached to the AS, instead of a line of the AS itself, which can give, in particular, the spatial version of octoidal bevel gears, when a planar surface is chosen.

Prediction of circulatory equilibrium in response to changes in stressed blood volume

2005 ◽  
Vol 289 (1) ◽  
pp. H301-H307 ◽  
Author(s):  
Kazunori Uemura ◽  
Toru Kawada ◽  
Atsunori Kamiya ◽  
Takeshi Aiba ◽  
Ichiro Hidaka ◽  
...  
Keyword(s):  
Blood Volume ◽  
Single Point ◽  
Point Estimation ◽  
Accurate Prediction ◽  
Atrial Pressure ◽  
Right Atrial ◽  
Right Heart ◽  
Left And Right ◽  
Failure Conditions ◽  
The Right

Accurate prediction of cardiac output (CO), left atrial pressure (PLA), and right atrial pressure (PRA) is a prerequisite for management of patients with compromised hemodynamics. In our previous study (Uemura et al. Am J Physiol Heart Circ Physiol 286: H2376–H2385, 2004), we demonstrated a circulatory equilibrium framework, which permits the prediction of CO, PLA, and PRA once the venous return surface and integrated CO curve are known. Inasmuch as we also showed that the surface can be estimated from single-point CO, PLA, and PRA measurements, we hypothesized that a similar single-point estimation of the CO curve would enable us to predict hemodynamics. In seven dogs, we measured the PLA-CO and PRA-CO relations and derived a standardized CO curve using the logarithmic function CO = SL[ln(PLA − 2.03) + 0.80] for the left heart and CO = SR[ln(PRA − 2.13) + 1.90] for the right heart, where SL and SR represent the preload sensitivity of CO, i.e., pumping ability, of the left and right heart, respectively. To estimate the integrated CO curve in each animal, we calculated SL and SR from single-point CO, PLA, and PRA measurements. Estimated and measured CO agreed reasonably well. In another eight dogs, we altered stressed blood volume (−8 to +8 ml/kg of reference volume) under normal and heart failure conditions and predicted the hemodynamics by intersecting the surface and the CO curve thus estimated. We could predict CO [ y = 0.93 x + 6.5, r 2 = 0.96, standard error of estimate (SEE) = 7.5 ml·min−1·kg−1], PLA ( y = 0.90 x + 0.5, r 2 = 0.93, SEE = 1.4 mmHg), and PRA ( y = 0.87 x + 0.4, r 2 = 0.91, SEE = 0.4 mmHg) reasonably well. In conclusion, single-point estimation of the integrated CO curve enables accurate prediction of hemodynamics in response to extensive changes in stressed blood volume.

Geometric Design of Smooth Composite Ruled Surface Strips Using Dual Spherical Geometry

1995 ◽  
Author(s):  
Q. J. Ge ◽  
Donglai Kang
Keyword(s):  
Spherical Geometry ◽  
Ruled Surface ◽  
Ruled Surfaces ◽  
Coordinate Frame ◽  
Geometric Continuity ◽  
Dual Numbers ◽  
Parametric Curve ◽  
Geometric Conditions ◽  
Line Segmentation ◽  
Unit Vectors

Abstract This paper deals with geometric construction of smooth composite ruled surface strips. Oriented lines that constitute the rulings of the ruled surfaces are represented by unit vectors with three components over the ring of dual numbers. The problem of designing a smooth ruled surface is studied as that of designing a one-real-parametric curve on the unit dual sphere. Geometric conditions for piecing two ruled surfaces smoothly are developed using differential geometry of curves on the dual sphere. A coordinate-frame invariant method for line segmentation is also presented. Finally, a geometric algorithm is presented for constructing composite Bézier ruled surface strips with second-order geometric continuity. The resulting surface strips are coordinate-frame invariant and their rulings are more uniformly parameterized than those obtained with other methods.

Modes of Knowing

2016 ◽  
Keyword(s):  
Social Science ◽  
Single Point ◽  
Ways Of Knowing ◽  
Alternative Techniques ◽  
The Right ◽  
Western Division

How might we think differently? This book is an attempt to respond to this question. Its contributors are all interested in non-standard modes of knowing. They are all more or less uneasy with the restrictions or the agendas implied by academic modes of knowing, and they have chosen to do this by working with, through, or against one important Western alternative - that of the baroque. Why the baroque? One answer is that the baroque made space for and fostered many forms of otherness. It involved knowing things differently, extravagantly, excessively, and in materially heterogeneous ways, and it apprehended that which is other and could not be caught in a cognitive or symbolic net. It also involved knowing in ways that did not gather into a single point and knew itself to be performative. As part of a great Western division between rationalist and non-rationalist modes of knowing, the baroque is therefore a possible resource for creating ways of knowing differently - a storehouse of possible alternative techniques. To say this is not to say that it is the right mode of knowing. The book's authors do not seek to create a 'baroque social science' whatever that might be, but instead work in a range of ways to explore how drawing on the 'resources of the baroque' can help us to think differently.

Elastohydrodynamic Lubrication of Involute Gears

1973 ◽  
Vol 95 (4) ◽  
pp. 1164-1170 ◽  
Author(s):  
A. Gu
Keyword(s):  
Steady State ◽  
Temperature Rise ◽  
Elastohydrodynamic Lubrication ◽  
Quasi Steady State ◽  
Line Contact ◽  
Viscosity Method ◽  
Temperature Calculation ◽  
Involute Gears ◽  
State Assumption ◽  
Zone Temperature

A criterion is suggested for the application of the steady state elastohydrodynamic theories to the analysis of involute gear contacts. The criterion is based on a comparison of two physical time scales characterizing the system. It is found that for heavily loaded gears the unsteadiness effect may be important. A mean-viscosity method using a composite pressure-viscosity model for the lubricant is introduced for contact zone temperature calculation. An example of involute gears is given for the computation of elastohydrodynamic contact variables based on quasi-steady state assumption. It is found that the surface temperature rise in the tooth tip contact is much higher than that in the pitch line contact.

Sheet Single Point Vibration Incremental Forming Process Simulation and Analysis of Process Parameters

2012 ◽  
Vol 430-432 ◽  
pp. 74-78 ◽  
Author(s):  
Gai Pin Cai ◽  
Cong Wen Xing ◽  
Zhi Hong Jiang ◽  
Zhong Kai Zhang
Keyword(s):  
Sheet Metal ◽  
Incremental Forming ◽  
Single Point ◽  
Product Yield ◽  
Simulation Software ◽  
Forming Force ◽  
Forming Process ◽  
Vibration Parameters ◽  
The Right ◽  
Theory Research

The deformation of vibration incremental forming process for sheet metal is in high complexity, theory research is not perfect. This subject using DEFORM simulation software, joined the vibration on the forming process of tool head and simulated the forming process base on different tool radius and vibration parameters. Simulation result indicated that vibration in greatly reduced the stress of the forming tool head. The right vibration parameters smoothed out the forming force largely, reduced sheet metal stress concentration, improved product quality and product yield. That has a higher degree of study and use value.

scholarly journals Computational Modeling of Pool Games: Sensitivity of Outcomes to Initial Conditions

2003 ◽  
Vol 1 (4) ◽  
Author(s):  
Christian Leerberg ◽  
M Roth
Keyword(s):  
Computational Modeling ◽  
Parameter Space ◽  
Initial Velocity ◽  
Initial Conditions ◽  
Single Point ◽  
Self Similarity ◽  
The Right

We present a study of the sensitivity of trajectories of pool balls to initial conditions. In the first component of the study our simulations include all sixteen balls. Variables include cue ball initial velocity and position on the “table”. We find that in a certain regime of initial conditions the system seems to show self-similarity, but as the range of initial cue ball angle and initial velocity is restricted, the system exhibits an interesting evolution towards a single point in parameter space, with the ball landing in only one pocket. We also examine the effects of varying the number of balls on the table, and how their dynamics may be interpreted using various plots and maps. Finally, the trajectory of a single cue ball is examined while it moves through the table space. Starting with the cue ball placed in the middle of the right wall of the table (traditional and rectangular in shape) and fired directly downward the system exhibits a two-cycle pattern. Then as the angle of fire is increased the system exhibits a four cycle, a three cycle and finally a two cycle all separated by noisy patterns. Effects of numerical artificialities are briefly discussed.

scholarly journals Cutter Head Approximation Machining Method of Line Contact Spiral Bevel Gear Pairs Based On Controlling Topological Deviations

2021 ◽  
Author(s):  
Mingyang Wang ◽  
Yuehai Sun
Keyword(s):  
Simulation Analysis ◽  
Gear Tooth ◽  
Bevel Gear ◽  
Spiral Bevel Gear ◽  
Line Contact ◽  
Bevel Gears ◽  
Spiral Bevel ◽  
Tooth Flank ◽  
Cutter Head ◽  
The Mathematical Model

Abstract To improve the meshing performance and increase the bearing capacity and service life of spiral gear pairs, the cutter head approximation machining method based on controlling topological deviations was proposed to solve the problem where line contact spiral bevel gears with tapered teeth depth cannot be directly machined by cutter heads. First, the mathematical model of line contact conjugate flanks was established, and meshing equations and conjugate flank equations of bevel gear pairs were derived. Second, the gear tooth flank was set as the datum tooth flank for priority machining, and the pinion theoretical tooth flank which is fully conjugate with the gear tooth flank and the pinion machining tooth flank matching with the gear were solved. Then, the geometric topological deviations model of the comparison between the pinion machining tooth flank and its theoretical tooth flank can be established. Finally, with the pinion machining tooth flank approaching its theoretical tooth flank as the modification, the additional cutting motions and machining compensation parameters of cutter heads were obtained to control the pinion machining tooth flank deviations and reduce them to the allowable deviations of its theoretical tooth flank. The contact simulation analysis and rolling test verified the correctness of the line contact conjugate flank model and feasibility of the cutter head approximation machining method.

Influence of port site on central venous pressure measurements from triple-lumen catheters in critically ill adults

1998 ◽  
Vol 7 (1) ◽  
pp. 60-63 ◽  
Author(s):  
SS Scott ◽  
KK Giuliano ◽  
E Pysznik ◽  
S Elliott ◽  
K Welsh ◽  
...  
Keyword(s):  
Central Venous Pressure ◽  
Repeated Measures ◽  
Single Point ◽  
Venous Pressure ◽  
Port Site ◽  
Central Venous ◽  
Lumen Catheter ◽  
The Difference ◽  
The Right ◽  
Critically Ill Adults

BACKGROUND: Measurements of central venous pressure are generally obtained through one of the three ports of centrally placed triple-lumen catheters. However, no scientifically based literature is available that guides clinical practice and indicates which of the lumens is most appropriate for obtaining these measurements. OBJECTIVE: To determine if a difference exists between measurements of central venous pressure obtained via the proximal, medial, and distal ports of a triple-lumen catheter. METHODS: Measurements of central venous pressure in 48 adult ICU patients were obtained via each of the three ports of a triple-lumen catheter. Catheters were placed in either the right or left subclavian vein or the right or left internal jugular vein. The flush system was single-transducer, trifurcated pressure tubing system. Data were evaluated for variation among the three ports of the catheter for readings taken at a single point. RESULTS: A repeated-measures analysis of variance showed significant differences across port sites. Post hoc univariate F tests showed significant differences between the proximal and distal ports and between the medial and distal ports. In some patients, the difference between central venous pressure obtained from the distal port and pressure obtained from the proximal or the medial port may be clinically significant. CONCLUSION: Because measurements of central venous pressure may not always be comparable for all three ports of a triple-lumen catheter, care should be taken to distinguish when changes in pressure readings are a result of a change in port site rather than in the patient's condition.

Protecting Citizen Privacy in Digital Government

2011 ◽  
pp. 1358-1363
Author(s):  
R R. Arnesen
Keyword(s):  
Data Collection ◽  
Privacy Protection ◽  
Personal Information ◽  
Single Point ◽  
Personal Data ◽  
Digital Government ◽  
Government Services ◽  
The Right To Privacy ◽  
Privacy Legislation ◽  
The Right

Protecting the privacy of citizens is a critical issue in digital government services. The right to privacy is widely recognized as a fundamental human right, as stated in Article 12 of the Universal Declaration of Human Rights (United Nations, 1948). The first definition of privacy was given by American lawyers Warren and Brandeis (1890), who defined it as “the right to be let alone.” However, the right to privacy has been recognized for millenniums. The Hippocratic oath (n.d.) dates back to around 400 B.C. and instructs medical doctors to respect the privacy of their patients. During the last three decades, many countries have passed privacy legislation, the Swedish Data Act from 1973 being the first national privacy act in the world. During the 1970s, many countries adopted data protection acts (Fischer-Hübner, 2001). In 1980, OECD published its privacy guidelines with the purpose of reducing the potential privacy problems incurred by cross-border trade (OECD, 1980). The European Council adopted Directive 95/46/EC in 1995, and all member states are required to implement national privacy legislation in compliance with this directive (European Union (EU) Directive 95/46/EC, 1995). Privacy is under increasing pressure in the digital age, and the introduction of digital government services may escalate this development. The way government has been organized until now, with separate departments with their own “silos” of personal data, has inherently provided some privacy protection. In such a distributed environment data matching is expensive and resource consuming. This form of privacy protection is referred to as “practical obscurity” in Crompton (2004, p.12). Some examples of threats to privacy related to the development of digital government are as follows: • Data collection capabilities increase as new technology for continuous and automatic data collection is introduced. Examples of such technologies include digital video surveillance, biometric identification and radio frequency identification (RFID). • Data processing capabilities are rapidly increasing. The very existence of large amounts of stored personal data, together with the availability of sophisticated tools for analysis, increases the probability for misuse of data. • There is a trend towards integration of formerly separated governmental services, including physical offices. Providing a single point of contact is more user friendly, but it may also provide an attacker with a single point of attack. • Outsourcing of services (e.g., customer relationship management) is increasingly popular both among companies and governmental organizations. Those who deliver such services to many customers have a unique opportunity to gather personal information from many different sources. If services are outsourced across country borders, and perhaps in several layers, responsibilities soon become unclear. • Even if the organization responsible for stored personal information does not have malicious intents, one cannot expect all its employees to be equally trustworthy. Disloyal employees are a severe threat when increasing amounts of information are stored. • Tax records and other public records made available on the Internet enable efficient searches and aggregation of information about individuals. Identity thefts and fraud are common uses of information gathered in this way.

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