scholarly journals Conceptual contributions to the determination of the curvature in Engineering courses

2019 ◽  
pp. 9-19
Author(s):  
Benjamín Vázquez-González ◽  
Homero Jiménez-Rabiela ◽  
Adrian Gustavo Bravo-Acosta ◽  
María Berenice Guadalupe Quintana-Diaz
Keyword(s):  
Differential Geometry ◽  
Radius Of Curvature ◽  
Normal Vector ◽  
Planar Curves

Differential geometry began with the study of the characteristics of planar curves, then the behavior of the curves in space was analyzed, which led to the postulates of Frenet, and hence differential geometry evolved due to the contributions of Gauss. At the highly specialized undergraduate courses, most of the literature presents this topic based on definitions, which can be understood with some difficulty by both students and even some teachers. This work presents a detailed description of the terms defined in the concept of curvature. It is of great importance that students from engineering courses understand this concept with certainty and confidence, because it will allow perceiving abstract terms, such as radius of curvature, osculating circle, normal vector; thus, they will have complete handling in the basic description of the movement of bodies. Some examples are presented.

scholarly journals Clothoid fitting and geometric Hermite subdivision

2021 ◽  
Vol 47 (4) ◽  
Author(s):  
Ulrich Reif ◽  
Andreas Weinmann
Keyword(s):  
Building Block ◽  
Numerical Results ◽  
Normal Vector ◽  
Subdivision Schemes ◽  
Planar Curves ◽  
Nonlinear Subdivision ◽  
New Strategy ◽  
Vector Information ◽  
Hermite Subdivision

AbstractWe consider geometric Hermite subdivision for planar curves, i.e., iteratively refining an input polygon with additional tangent or normal vector information sitting in the vertices. The building block for the (nonlinear) subdivision schemes we propose is based on clothoidal averaging, i.e., averaging w.r.t. locally interpolating clothoids, which are curves of linear curvature. To this end, we derive a new strategy to approximate Hermite interpolating clothoids. We employ the proposed approach to define the geometric Hermite analogues of the well-known Lane-Riesenfeld and four-point schemes. We present numerical results produced by the proposed schemes and discuss their features.

Duplex Spread Blade Method for Cutting Hypoid Gears with Modified Tooth Surface

1998 ◽  
Vol 120 (3) ◽  
pp. 441-447 ◽  
Author(s):  
K. Kawasaki ◽  
H. Tamura
Keyword(s):  
Cutting Edge ◽  
Tooth Surface ◽  
Radius Of Curvature ◽  
Large Radius ◽  
Ring Gear ◽  
Circular Arc ◽  
Hypoid Gears ◽  
Manufacturing Method ◽  
Straight Line

In this paper, a duplex spread blade method for cutting hypoid gears with modified tooth surface is proposed. The duplex spread blade method provides a rapid and economical manufacturing method because both the ring gear and pinion are cut by a spread blade method. In the proposed method, the nongenerated ring gear is manufactured with cutting edge that is altered from the usual straight line to a circular arc with a large radius of curvature and the circular arc cutting edge produces a modified tooth surface. The pinion is generated by a cutter with straight cutting edges as usual. The main procedure of this method is the determination of the cutter specifications and machine settings. The proposed method was validated by gear manufacture.

scholarly journals Parameters and modes of the technological process of scattered rice sowing

2021 ◽  
Vol 285 ◽  
pp. 02007
Author(s):  
Ivan Masienko ◽  
Sergey Shevchenko ◽  
Kirill Glytyan
Keyword(s):  
Technological Process ◽  
Radius Of Curvature ◽  
Theoretical Studies ◽  
Technological Operation ◽  
Design Features ◽  
Operating Modes ◽  
Seed Material

The paper presents the determination of main parameters and operating modes of scattered centrifugal devices of technical units when using them in the technology with scattered sowing when performing the technological operation of sowing rice in liquid-flexible soil. Theoretical studies of the dependence of design features of the blade of a spreading disk on the number of blades installed on it and the radius of curvature of the end bend on the height of blades are carried out. The values of the diameter of the disk of a centrifugal dispenser and parameters of blades are set, which will increase the uniformity of distribution of seed material for a given width of a gripper and reduce its consumption.

scholarly journals THE REFRACTIVE INDICES OF WHOLE CELLS

1933 ◽  
Vol 17 (1) ◽  
pp. 41-47 ◽  
Author(s):  
E. S. Castle
Keyword(s):  
Focal Length ◽  
Refractive Indices ◽  
Radius Of Curvature ◽  
Whole Cells

Refractive indices of intact sporangiophores of Phycomyces were computed from measurements of focal length and radius of curvature of the cells. For the six cells studied, effective values of n were obtained ranging from 1.35 to 1.40. The average effective n was 1.38. Senn's determination of refractive indices of other plants cells gave much higher values: n = 1.37 to 1.52. The precision of the method and possible sources of this discrepancy are discussed.

scholarly journals Determination of the loads on the rollers of the tubular belt conveyor

2019 ◽  
Vol 109 ◽  
pp. 00096
Author(s):  
Andrii Smirnov ◽  
Tamara Mishchenko
Keyword(s):  
Service Life ◽  
Ritz Method ◽  
Radius Of Curvature ◽  
Inertial Forces ◽  
Belt Conveyor ◽  
Dynamic Forces ◽  
Plates And Shells ◽  
Bulk Load ◽  
Roller Support

The article presents methods for determining loads on rollers of a six-roll support of a tubular belt conveyor, based on the equilibrium laws of elastic cylindrical plates and shells filled with a freight. In this case, the forces acting on the rollers of the tubular conveyor are the sum of the forces caused by the weight and expansion of the bulk load, the weight and bend of the belt, as well as the inertial forces associated with the curvature and the deflection of the belt under the weight of the bulk load. The dynamic forces acting on the rollers as the belt moves are determined from the equation of the oscillations of a heavy flexible string using the Ritz method. As a result of the research, analytical dependences of the forces acting on the rollers of the six-roller support of the tubular conveyor on the parameters of the conveyor, the belt, the properties of the bulk load and the radius of curvature of the conveyor are obtained, and an assessment of the component these forces is given. The results can be used to determine the parameters of the tubular conveyors rollers and increase the service life of the rollers.

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