scholarly journals Design Method for N-Lobed Noncircular Bevel Gears

2020 ◽  
Vol 12 (2) ◽  
pp. 168781401989749
Author(s):  
Kan Shi ◽  
Yan-An Yao ◽  
Shuai Lin
Keyword(s):  
Design Method ◽  
Three Dimensional ◽  
Transmission Mechanism ◽  
Polar Coordinate System ◽  
Analytic Method ◽  
Bevel Gears ◽  
Variable Transmission ◽  
Polar Coordinate ◽  
Three Dimensional Models ◽  
Spatial Transmission

As a type of spatial transmission mechanism, noncircular bevel gears (NBGs) can transfer power and motion between two intersecting axes with variable transmission following a suitable program of motion. Utilizing the spherical triangle theorem and meshing principle, parametric equations are established in the spherical polar coordinate system for the driving and driven gears, for the pitch curves, and for the addendum and dedendum curves of a NBG for a given transmission ratio and axis angle. A formulation of the tooth profile of a NBG is deduced using an analytic method. Three-dimensional models of the 3- and 4-lobed NBGs are derived in verifying this method.

scholarly journals Synthesis of the base curves for <i>n</i>-lobed noncircular bevel gears

2020 ◽  
Vol 11 (2) ◽  
pp. 251-256
Author(s):  
Kan Shi ◽  
Yan'an Yao ◽  
Shuai Lin
Keyword(s):  
Coordinate System ◽  
Bevel Gear ◽  
Transmission Mechanism ◽  
Spherical Triangle ◽  
Polar Coordinate System ◽  
Arc Length ◽  
Bevel Gears ◽  
Variable Transmission ◽  
Polar Coordinate ◽  
Spatial Transmission

Abstract. As a type of spatial transmission mechanism, noncircular bevel gears can transfer power and motion between two intersecting axes with variable transmission. In this paper, the relation of arc length is expressed by Angle in spatial polar coordinate system, utilizing the spherical triangle theorem, the parametric equations of base curves are established by applying arc length relation. Further, an example is given to verify whether pitch curves is concave on osculating circle of noncircular bevel gear section cone. Similarly, this example illustrates the cause of the mutation for the base curves.

Design of noncircular bevel gear with concave pitch curve

2012 ◽  
Vol 227 (3) ◽  
pp. 542-553 ◽  
Author(s):  
Kan Shi ◽  
Jiqiang Xia ◽  
Chunjie Wang
Keyword(s):  
Design Method ◽  
Three Dimensional ◽  
Bevel Gear ◽  
Polar Coordinate System ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Profile Equation ◽  
Variable Transmission ◽  
Polar Coordinate ◽  
Pitch Curve

Noncircular bevel gear can achieve variable transmission between intersecting axes. This article proposes the design method of high-order noncircular bevel gear with concave pitch curve. The parametric equations for driving and driven gear, addendum and dedendum surface under given transmission ratio and axis angle are established in a spherical polar coordinate system. The tooth profile equation of noncircular bevel gear is derived according to the generation method by using bevel gear cutter. The three-dimensional model for noncircular bevel gear is developed to verify the correctness of the design method.

Design Method for a Pair of Oval Bevel Gears

2011 ◽  
Vol 299-300 ◽  
pp. 887-890 ◽  
Author(s):  
Kan Shi ◽  
Ji Qiang Xia ◽  
Chun Jie Wang
Keyword(s):  
Design Method ◽  
Three Dimensional ◽  
Bevel Gear ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Bevel Gears ◽  
Planar Curve ◽  
Variable Transmission ◽  
Polar Coordinate ◽  
Pitch Curve

Oval bevel gear is a kind of noncircular bevel gear which can achieve variable transmission between intersecting axes. We design the pitch curve by spherics cosine theorem in spatial polar coordinate because the pitch curve of oval bevel gear is not the planar curve. The bevel gear cutter is introduced, and we get the Three-dimensional model of oval bevel gear through extended development of UG. This method can make the calculation accurately, easily and get a wide variation of transmission ratio.

scholarly journals The method for synthesis of the contact ratio of noncircular bevel gears

2021 ◽  
Vol 12 (1) ◽  
pp. 165-172
Author(s):  
Kan Shi ◽  
Shuai Lin ◽  
Yan'an Yao
Keyword(s):  
Transmission Ratio ◽  
Polar Coordinate System ◽  
Contact Ratio ◽  
Bevel Gears ◽  
Innovative Methods ◽  
Ratio Curve ◽  
Pure Rolling ◽  
Variable Transmission ◽  
Polar Coordinate ◽  
Pitch Curve

Abstract. As a type of spatial transmission mechanism, noncircular bevel gears can be used to transfer the power and motion with a variable transmission ratio between intersecting axes. In this paper, utilizing the spherical triangle theorem and meshing principle, the parametric equations of the contact ratio are established in the space polar coordinate system. Two innovative methods are proposed to analyze the contact ratio by using the rotation angle of the driving (driven) gears and the arc length of pitch curve as pure rolling. In the case of modified gear and X-zero gear, whether the noncircular bevel gear is continuously driven is deduced. The simulation transmission ratio curve and theoretical transmission ratio curve are compared to verify the rationality of the design.

Nonrelative sliding of spiral bevel gear mechanism based on active design of meshing line

2018 ◽  
Vol 233 (3) ◽  
pp. 1055-1067 ◽  
Author(s):  
Zhen Chen ◽  
Ming Zeng
Keyword(s):  
Design Method ◽  
Bevel Gear ◽  
Transmission Mechanism ◽  
Tooth Surface ◽  
Design Parameters ◽  
Spiral Bevel Gear ◽  
Bevel Gears ◽  
Gear Mechanism ◽  
Active Design ◽  
Spiral Bevel

In this paper, an active design method of meshing line for a spiral bevel gear mechanism with nonrelative sliding is presented. First, the general meshing line equations for a nonrelative sliding transmission mechanism between two orthogonal axes are proposed based on the active design parameters. Then, parametric equations for contact curves on the drive and driven spiral bevel gears are deduced by coordinate transformation of the meshing line equations. Further to this, parametric equations for the tooth surface of each bevel gear are derived according to the conical spiral motion of a generatrix circle along the calculated contact curves. Finally, a set of numerical examples is presented based on two types of motion equation of the meshing points. Material prototypes are fabricated and experimentally tested to validate the kinematic performance of the functionally designed spiral bevel gear set.

scholarly journals A Design Method for Continuously Variable Transmission Mechanism Consisting of Slider-Cranks, Solid Cams and Non-Invertible Mechanisms

2021 ◽  
Vol 87 (3) ◽  
pp. 307-316
Author(s):  
Toshihiro YUKAWA ◽  
Akinori MURAKAMI ◽  
Shoma KUMAGAI ◽  
Yoshiaki OSHIDA ◽  
Youichi TAKEDA ◽  
...  
Keyword(s):  
Design Method ◽  
Continuously Variable Transmission ◽  
Transmission Mechanism ◽  
Variable Transmission

scholarly journals Topino: A Graphical Tool for Quantitative Assessment of Molecular Stream Separations

2021 ◽  
Author(s):  
Sven Kochmann ◽  
Nikita A. Ivanov ◽  
Kevin S. Lucas ◽  
Sergey Krylov
Keyword(s):  
Three Dimensional ◽  
Software Tool ◽  
Visual Assessment ◽  
Technical Note ◽  
Polar Coordinate System ◽  
Component Mixture ◽  
Graphical Tool ◽  
Integrated Intensity ◽  
Polar Coordinate ◽  
Indispensable Tool

<p><a></a> In molecular-stream separation (MSS), a stream of a multi-component mixture is separated into multiple streams of individual components. Quantitative evaluation of MSS data has been a bottleneck in MSS for decades as there was no conventional way to present the data in a reproducible and uniform fashion. The roots of the problem were in the multi-dimensional nature of MSS data; even in the ideal case of steady-state separation, the data is three-dimensional: intensity and two spatial coordinates. We recently found a way to reduce the dimensionality <i>via</i> presenting the MSS data in a polar coordinate system and convoluting the data <i>via</i> integration of intensity along the radius axis. The result of this convolution is an angulagram — a simple 2D plot presenting integrated intensity vs angle. Not only does an angulagram simplify the visual assessment, but it also allows the determination of three quantitative parameters characterizing the quality of MSS: stream width, stream linearity, and stream deflection. Reliably converting an MSS image into an angulagram and accurately determining the stream parameters requires an advanced and user-friendly software tool. In this technical note, we introduce such a tool: the open-source software Topino available at <u><a href="https://github.com/Schallaven/topino">https://github.com/Schallaven/topino</a></u>. Topino is a stand-alone program with a modern graphical user interface that allows processing an MSS image in a fast (<2 min) and straightforward way. The robustness and ruggedness of Topino were confirmed by comparing the results obtained by three users. Topino removes the analytical bottleneck in MSS and will be an indispensable tool for MSS users with varying levels of experience.</p> p { margin-bottom: 0.25cm; direction: ltr; line-height: 115%; text-align: left; orphans: 2; widows: 2 }a:link { color: #0000ff }

Noncircular Bevel Gear Transmission With Intersecting Axes

2008 ◽  
Vol 130 (5) ◽  
Author(s):  
Jiqiang Xia ◽  
Yuanyuan Liu ◽  
Chunming Geng ◽  
Jiangbin Song
Keyword(s):  
Design Method ◽  
Gear Tooth ◽  
Geometric Characteristic ◽  
Three Dimensional ◽  
Transmission Function ◽  
Spherical Geometry ◽  
Bevel Gear ◽  
Polar Coordinates ◽  
Three Dimensional Models ◽  
Conical Surfaces

Noncircular bevel gear can achieve variable transmission between intersecting axes. Based on polar coordinates, a design method for noncircular bevel gears is presented. The geometric characteristic of tooth profiles of the gears can be obtained by means of geometry principles for spherical engagement and a pair of conjugated crown racks, which can engage with the driver noncircular bevel gear and driven one, respectively. A series of new conception such as tangent azimuth angle, concavity of conical surfaces, and module angle are proposed to describe spherical geometry relationship in meshing. Meanwhile, geometrical characters of the crown rack cutter are derived. Based on this cutter, the accurate mathematical model of noncircular bevel gear tooth profile is deduced, and the determinant criterion for undercutting is presented. As an example, the three-dimensional models of noncircular bevel gear pair are established to demonstrate the feasibility of the proposed method. A noncircular bevel gear set can be designed by this method if the special included angle for intersecting axes and transmission function ratio are given.

Research on improved hough algorithm and its application in lunar crater

2021 ◽  
pp. 1-9
Author(s):  
Lanfeng Zhou ◽  
Ling Li
Keyword(s):  
Coordinate System ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Detection Algorithm ◽  
Polar Coordinate System ◽  
Circle Center ◽  
Traditional Algorithm ◽  
Polar Coordinate ◽  
Cartesian Coordinate ◽  
Three Dimensional Space

Traditional Hough circle detection algorithm usually determines the center and radius of a circle by mapping points in cartesian coordinate system to polar coordinate system. Since it accumulates in the three-dimensional space, it requires more calculation consumption. In this paper, we solve the problem of high time complexity of Hough algorithm in judging circle radius and circle center from two aspects of circle angle and circle radius according to the geometric features of quasi-circles. A large number of experiments show that, compared with the traditional algorithm, this algorithm can not only identify quasi-circles, but also improve the detection success rate of circles by about 10%, with efficient running speed, and obtain good experimental results in the detection of craters.

Plastic replicas as three-dimensional models of pulps

1975 ◽  
Vol 39 (8) ◽  
pp. 544-546
Author(s):  
HL Wakkerman ◽  
GS The ◽  
AJ Spanauf
Keyword(s):  
Three Dimensional ◽  
Dimensional Models ◽  
Three Dimensional Models
Sign in / Sign up

Export Citation Format

Share Document