Study of the Base Curve and Formation of Singular Points on the Tooth Profile of Noncircular Gears

2006 ◽  
Vol 129 (5) ◽  
pp. 538-545 ◽  
Author(s):  
Héctor Fabio Quintero Riaza ◽  
Salvador Cardona i Foix ◽  
Lluïsa Jordi Nebot
Keyword(s):  
A Priori ◽  
Tooth Profile ◽  
Singular Points ◽  
Curvature Radius ◽  
Base Curve ◽  
Minimum Number ◽  
Base Circle ◽  
Noncircular Gears ◽  
Gear Wheels ◽  
Pitch Curve

The base circle of a circular gear is concentric with the pitch circle and tangent to the action line. However, in a noncircular gear the base curve is not known a priori and not easy to determine. In this study, the base curves of noncircular gear wheels are obtained as the geometrical locus of the singular points on the involute tooth profile. Singular points—points from which a second involute branch begins to form on the tooth profile—restrict the allowable tooth height and allow the minimum number of teeth required to be estimated. We discuss the influence of the curvature radius of the pitch curve on the allowable tooth height and present an example to illustrate the proposed method.

Synthesis of the Base Curves For N-Lobed Elliptical Gears

2004 ◽  
Vol 127 (5) ◽  
pp. 997-1005 ◽  
Author(s):  
Giorgio Figliolini ◽  
Jorge Angeles
Keyword(s):  
Differential Geometry ◽  
Tooth Profile ◽  
Spur Gears ◽  
Profile Angle ◽  
Pressure Angle ◽  
Base Circle ◽  
Noncircular Gears ◽  
The Right ◽  
First Time ◽  
Envelope Theory

Motivated by the need to synthesize the tooth profiles of noncircular gears, we approach the synthesis of the tooth profile of circular spur gears using their pitch circle, rather than their base circle. We do this by means of envelope theory. The proposed formulation gives the involute tooth profile and its well-known base circle for any pitch radius and profile angle of the rack cutter, which coincides with the pressure angle for circular gears. Then, the foregoing approach applies to the synthesis of the base curves of noncircular gears with involute tooth profiles and of their rack. We do this by resorting to basic differential geometry using the Euler–Savary Theorem, rather than to envelope theory. In particular, the formulation of both base curves for the right and left involute tooth profiles is obtained, for the first time, for N-lobed elliptical gears and their rack through the formulation of the pitch curves and their evolutes. The proposed formulation is illustrated with numerical results.

On a Gearing Problem in Conventional Harmonic Drives With Involute Toothed Gear Set

2011 ◽  
Author(s):  
Bikash Routh ◽  
Rathindranath Maiti
Keyword(s):  
Applied Load ◽  
Harmonic Drive ◽  
Strain Wave ◽  
Base Circle ◽  
Pitch Curve

Circular pitches of flex spline teeth of a ‘Strain Wave Gearing’, also known as a ‘Harmonic Drive’, are deformed when the Strain Wave Generating Cam is inserted into the flex spline cup. In the present work the deformed pitch distances considering that flex spline teeth remain rigid while the rim deforms, are estimated. No applied load is considered. It is also shown that if the cam is elliptical then the pitch curve is not an ellipse and vice versa. Geometries of such curves can be defined following the analysis presented in this paper. Cases of both undeformed flex spline with circular spline and deformed flex spline with circular spline, with involute teeth, are considered to find out tooth positions. Geometries of involute teeth profiles in mesh are examined and compared considering oval shaped (on deformation) base drum of flex spline where as base circle of circular spline remained circular.

Research on Mathematical Modeling and Kinematic Simulation of Elliptic Family Gears

2013 ◽  
Vol 579-580 ◽  
pp. 300-304 ◽  
Author(s):  
Lian Xia ◽  
Da Zhu Li ◽  
Jiang Han
Keyword(s):  
Performance Analysis ◽  
Tooth Profile ◽  
High Order ◽  
Numerical Control ◽  
Gear Pair ◽  
Cylindrical Gear ◽  
Kinematic Simulation ◽  
Cad Modeling ◽  
Pure Rolling ◽  
Pitch Curve

Elliptic family gears are commonly used in non-circular gears, which include elliptic gear, high-order gear, elliptic deformed gear and high-order deformed gear, thereinto high-order deformed gear can include the elliptic family gears through adjust its order and deformed coefficient. Because non-circular gear has different tooth profile in different position of pitch curve and there is difference in the left and right tooth profile of the same gear tooth, thus the CAD modeling of non-circular gear is difficult for these characteristics; but the precise model of non-circular gear has important significance to the realization of numerical control machining, kinematic simulation and relevant mechanical analysis. This paper deduce the corresponding pure rolling mathematical model based on the pure rolling contact theory that cylindrical gear and non-circular gear mesh in the end face, and realize the CAD modeling of non-circular straight and helical gears by letting the cylindrical gear and non-circular gear make solid geometry operation, which is suitable for pitch curve with convex and concave. The non-circular gear shaping methods with equal polar and equal arc length are simulated by setting different discrete polar angles, and the transmission ratio curve and the angular acceleration curve of driven gear are get through the kinematic simulation of gear pair, which realize the transmission performance analysis of elliptic family gear pair. The above research results can be applied to the modeling and kinematic performance analysis of other non-circular gears.

scholarly journals Design of Vegetable Pot Seedling Pick-up Mechanism with Planetary Gear Train

2020 ◽  
Vol 33 (1) ◽  
Author(s):  
Zhipeng Tong ◽  
Gaohong Yu ◽  
Xiong Zhao ◽  
Pengfei Liu ◽  
Bingliang Ye
Keyword(s):  
Design Method ◽  
Planetary Gear ◽  
Gear Train ◽  
Dimensional Synthesis ◽  
Planetary Gear Train ◽  
Key Points ◽  
Physical Prototype ◽  
Noncircular Gears ◽  
Pitch Curve ◽  
Parameter Values

Abstract It has been challenging to design seedling pick-up mechanism based on given key points and trajectories, because it involves dimensional synthesis and rod length optimization. In this paper, the dimensional synthesis of seedling pick-up mechanism with planetary gear train was studied based on the data of given key points and the trajectory of the endpoint of seedling pick-up mechanism. Given the positions and orientations requirements of the five key points, the study first conducted a dimensional synthesis of the linkage size and center of rotation. The next steps were to select a reasonable solution and optimize the data values based on the ideal seedling trajectory. The link motion was driven by the planetary gear train of the two-stage gear. Four pitch curves of noncircular gears were obtained by calculating and distributing the transmission ratio according to the data. For the pitch curve with two convex points, the tooth profile design method of incomplete noncircular gear was applied. The seedling pick-up mechanism was tested by a virtual prototype and a physical prototype designed with the obtained parameter values. The results were consistent with the theoretical design requirements, confirming that the mechanism meets the expected requirements for picking seedlings up. This paper presents a new design method of vegetable pot seedling pick-up mechanism for an automatic vegetable transplanter.

scholarly journals Standardising the measurement of physical activity in people receiving haemodialysis: considerations for research and practice

2019 ◽  
Vol 20 (1) ◽  
Author(s):  
Hannah M. L. Young ◽  
Mark W. Orme ◽  
Yan Song ◽  
Maurice Dungey ◽  
James O. Burton ◽  
...  
Keyword(s):  
Physical Activity ◽  
Sample Size ◽  
Repeated Measures ◽  
A Priori ◽  
Intraclass Correlation ◽  
Correlation Coefficients ◽  
Future Research ◽  
Wear Time ◽  
Minimum Number ◽  
The Uk

Abstract Background Physical activity (PA) is exceptionally low amongst the haemodialysis (HD) population, and physical inactivity is a powerful predictor of mortality, making it a prime focus for intervention. Objective measurement of PA using accelerometers is increasing, but standard reporting guidelines essential to effectively evaluate, compare and synthesise the effects of PA interventions are lacking. This study aims to (i) determine the measurement and processing guidance required to ensure representative PA data amongst a diverse HD population, and; (ii) to assess adherence to PA monitor wear amongst HD patients. Methods Clinically stable HD patients from the UK and China wore a SenseWear Armband accelerometer for 7 days. Step count between days (HD, Weekday, Weekend) were compared using repeated measures ANCOVA. Intraclass correlation coefficients (ICCs) determined reliability (≥0.80 acceptable). Spearman-Brown prophecy formula, in conjunction with a priori ≥  80% sample size retention, identified the minimum number of days required for representative PA data. Results Seventy-seven patients (64% men, mean ± SD age 56 ± 14 years, median (interquartile range) time on HD 40 (19–72) months, 40% Chinese, 60% British) participated. Participants took fewer steps on HD days compared with non-HD weekdays and weekend days (3402 [95% CI 2665–4140], 4914 [95% CI 3940–5887], 4633 [95% CI 3558–5707] steps/day, respectively, p < 0.001). PA on HD days were less variable than non-HD days, (ICC 0.723–0.839 versus 0.559–0.611) with ≥ 1 HD day and ≥  3 non-HD days required to provide representative data. Using these criteria, the most stringent wear-time retaining ≥ 80% of the sample was ≥7 h. Conclusions At group level, a wear-time of ≥7 h on ≥1HD day and ≥ 3 non-HD days is required to provide reliable PA data whilst retaining an acceptable sample size. PA is low across both HD and non- HD days and future research should focus on interventions designed to increase physical activity in both the intra and interdialytic period.

Study on Meshing Characteristic and CAM Technology of Eccentric Involute Gears

2012 ◽  
Vol 479-481 ◽  
pp. 917-920
Author(s):  
Yong Ping Liu ◽  
Peng Fei Meng ◽  
Chi Bing Hu
Keyword(s):  
Design Method ◽  
Shape Design ◽  
Digital Manufacturing ◽  
Transmission Characteristics ◽  
Systemic Theory ◽  
Theoretical Design ◽  
Parameterized Modeling ◽  
Involute Gears ◽  
Noncircular Gears ◽  
Pitch Curve

According to the meshing principle of noncircular gears, the meshing characteristic and digital manufacturing technology of eccentric involute gears is studied. Based on analyzing the parameterized modeling of pitch curve, transmission characteristics and convex-concave property on eccentric involute gears, the transmission feasibility of this type gear is proved. Through tooth shape design, CAM calculation and processing simulation, the validity and manufacturability of theoretical design method on this type gear is proved. The research results can provide more systemic theory basis for the design, manufacture, measure and application of eccentric involute gears.

Measurement of tooth-profile error of cylindrical gear wheels, using a UIM-21 microscope

1976 ◽  
Vol 19 (12) ◽  
pp. 1700-1702
Author(s):  
N. P. Motora ◽  
A. E. Nesterovskii
Keyword(s):  
Tooth Profile ◽  
Profile Error ◽  
Cylindrical Gear ◽  
Gear Wheels

A Method for Constructing Standard Involute Gear Tooth Profile

2018 ◽  
Author(s):  
Edward E. Osakue ◽  
Lucky Anetor
Keyword(s):  
Gear Tooth ◽  
Contact Point ◽  
Contact Angles ◽  
Tooth Profile ◽  
Computer Design ◽  
Solid Models ◽  
Module Size ◽  
Involute Gears ◽  
Base Circle ◽  
Involute Curve

A simple but accurate combined computationaland graphical method for creating drawings and solid models of standard involute gears is presented. The method is predicated on the fact that the gear tooth angle at the base circle is fixed for a gear of specified module or size. As the contact point moves along the involute curve from the base circle point through the pitch point to the addendum circle point; the involute and gear tooth contact angles change continuously but their sum is fixed at the value it was at the base circle. This allows the coordinates of points on the involute curve to be generated analytically without employing the roll angle as current available methods. The generated data can be implemented in any computer design drafting (CDD) package platform to create an accurate gear tooth profile. The computations are done with Microsoft Excel which generates the graphical data for the gear tooth profile that are used in the CDD package. The required inputs to the Excel spreadsheet are the gear module size, the pressure angle, the number of teeth and the radial number of steps. A gearset example is considered and created with this method. The solid model of the example gearset in mesh and 2D drawing of the pinion are presented.

scholarly journals Nonlinear Vibration of Gears With Tooth Surface Modifications

2013 ◽  
Vol 135 (5) ◽  
Author(s):  
Tugan Eritenel ◽  
Robert G. Parker
Keyword(s):  
Nonlinear Vibration ◽  
Multiple Scales ◽  
Gear Tooth ◽  
A Priori ◽  
Surface Modifications ◽  
Element Model ◽  
Transmission Error ◽  
Tooth Profile ◽  
Tooth Surface ◽  
Partial Contact

This work provides an analytical solution for the nonlinear vibration of gear pairs that exhibit partial and total contact loss. Partial contact loss is where parts of contact lines lose contact although other parts remain in contact. The gear tooth surface modifications admit an arbitrary combination of profile and lead modifications. Modifications are a source of partial contact loss. The analysis also applies for total contact loss. Unlike models in the literature that are excited by static transmission error or time-varying mesh stiffness, the excitation and the nonlinearity are not a priori specified. Instead, the force-deflection function of the gear pair is provided by an independent source, such as a finite element model or Hertz contact formula. The manipulation of the single-degree-of-freedom oscillator equation of motion yields the excitation and the nonlinearity that arise from Fourier and Taylor series expansions of the force-deflection function. These expansions capture the essential contact behavior that includes tooth profile and lead modifications as well as the bending and shear flexibility of the gear teeth and gear blanks. The method of multiple scales gives the steady-state dynamic response in terms of a frequency-amplitude relation. Comparisons with gear vibration experiments and simulations from the literature that include spur and helical gears with tooth profile and lead modifications verify the method.

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