Synthesis of the Pitch Cones of N-Lobed Elliptical Bevel Gears

2011 ◽  
Vol 133 (3) ◽  
Author(s):  
Giorgio Figliolini ◽  
Jorge Angeles
Keyword(s):  
Rolling Motion ◽  
Bevel Gears ◽  
Pure Rolling

A general formulation of the synthesis of the pitch cones of a pair of N-lobed elliptical bevel gears and the pitch surface of its conjugate crown-rack is proposed. In particular, two pitch cones and the pitch surface of their crown-rack are obtained for any number and combination of lobes and in any configuration during their pure-rolling motion. This formulation is implemented in MATLAB; several significant examples are included, with circular bevel gears becoming a particular case thereof.

Synthesis of the Pitch Cones of N-Lobed Elliptical Bevel Gears

2004 ◽  
Author(s):  
Giorgio Figliolini ◽  
Paolo Migliozzi
Keyword(s):  
Rolling Motion ◽  
Computer Animations ◽  
Bevel Gears ◽  
Matlab Program ◽  
Pure Rolling

A general formulation for the synthesis of the pitch cones of N-lobed elliptical bevel gears and the pitch surface of their conjugate crown-rack is proposed. In particular, both pitch cones and the pitch surface of their crown-rack can be obtained for any number and combination of lobes and in any configuration during their pure-rolling motion. This formulation has been implemented in a suitable Matlab program and several significant examples are shown, where circular bevel gears become a particular case. Computer animations are also available at URL: http://webuser.unicas.it/weblarm/larmindex.htm.

Algorithms for Involute and Octoidal Bevel-Gear Generation

2004 ◽  
Author(s):  
Giorgio Figliolini ◽  
Jorge Angeles
Keyword(s):  
Great Circle ◽  
Tooth Profile ◽  
Bevel Gear ◽  
Rolling Motion ◽  
Bevel Gears ◽  
Pure Rolling ◽  
Pitch Curve ◽  
Tooth Flank ◽  
Flank Surface

A suitable formulation and the implementing algorithms for involute and octoidal bevel-gear generation are proposed in this paper. In particular, the exact spherical involute tooth profile of bevel gears and their crown-rack is obtained through the pure-rolling motion of a great circle of the fundamental sphere on the base cone. Moreover, the tooth flank surface of octoidal bevel gears is obtained as the envelope of the tooth flat flank of the octoidal crown-rack during the pure-rolling motion of its flat pitch curve on the pitch cone. The proposed algorithms have been implemented in Matlab; several examples are included to illustrate their applicability.

Design of the Pitch Cones of Noncircular Bevel Gears

2012 ◽  
Author(s):  
Kan Shi ◽  
Jiqiang Xia ◽  
Chunjie Wang ◽  
Chunming Geng
Keyword(s):  
Design Method ◽  
Rolling Motion ◽  
Bevel Gears ◽  
Pure Rolling

A design method for the pitch cones of noncircular bevel gears is proposed. In particular, the accurate formulation of the pitch cones of the driving gear and the driven gear are obtained for any number and combination of lobes and in any configuration during their pure-rolling motion. This design method is implemented in Pro/E and several significant examples are included.

Algorithms for Involute and Octoidal Bevel-Gear Generation

2004 ◽  
Vol 127 (4) ◽  
pp. 664-672 ◽  
Author(s):  
Giorgio Figliolini ◽  
Jorge Angeles
Keyword(s):  
Great Circle ◽  
Tooth Profile ◽  
Bevel Gear ◽  
Rolling Motion ◽  
Bevel Gears ◽  
Pure Rolling ◽  
Tooth Flank ◽  
Flank Surface

A suitable formulation and the implementing algorithms for involute and octoidal bevel-gear generation are proposed in this paper. In particular, the exact spherical involute tooth profile of bevel gears and their crown rack is obtained through the pure-rolling motion of a great circle of the fundamental sphere on the base cone. Moreover, the tooth flank surface of octoidal bevel gears is obtained as the envelope of the tooth flat flank of the octoidal crown rack during the pure-rolling motion of its flat pitch (surface) on the pitch cone. The proposed algorithms have been implemented in MATLAB; several examples are included to illustrate their applicability.

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.

Nano-Meter Film Rheology and Asperity Lubrication

2002 ◽  
Vol 124 (3) ◽  
pp. 595-599 ◽  
Author(s):  
Bo Jacobson
Keyword(s):  
Contact Area ◽  
Pressure Fluctuations ◽  
Slip Rate ◽  
Hertzian Contact ◽  
Metal Contact ◽  
Rolling Motion ◽  
Oil Film ◽  
Pure Rolling ◽  
Total Separation ◽  
Molecular Dimensions

It is today possible to manufacture so smooth surfaces that they can elastically conform totally to each other over the whole Hertzian contact area. For pure rolling lubrication such surfaces only need an oil film of molecular dimensions to get total separation. When the rolling motion is combined with sliding, the pressure fluctuations inside the Hertzian contact redistribute the oil and make metal-to-metal contact possible. The redistribution velocity is a function of the slip rate S and the number of asperities N from the inlet to the outlet of the Hertzian contact area. The asperity top oil film thickness decreases with a factor of the order 2NS going from the inlet to the outlet of the Hertzian contact.

scholarly journals The Design of a Novel Prismatic Drive for a Three-DOF Parallel-Kinematics Machine

2005 ◽  
Vol 128 (4) ◽  
pp. 710-718 ◽  
Author(s):  
D. Chablat ◽  
J. Angeles
Keyword(s):  
Parallel Robot ◽  
Rolling Motion ◽  
Parallel Kinematics ◽  
Cam Mechanism ◽  
Pure Rolling ◽  
Parallel Kinematics Machines

The design of a novel prismatic drive is reported in this paper. This transmission is based on Slide-o-Cam, a cam mechanism with multiple rollers mounted on a common translating follower. The design of Slide-o-Cam was reported elsewhere. This drive thus provides pure-rolling motion, thereby reducing the friction of rack-and-pinions and linear drives. Such properties can be used to design new transmissions for parallel-kinematics machines. In this paper, this transmission is intended to replace the ball-screws in Orthoglide, a three-dof parallel robot intended for machining applications.

scholarly journals Study on the Rolling-Type Microvibration Isolation Mechanisms Based on Completely Elastic Contact

2019 ◽  
Vol 2019 ◽  
pp. 1-6
Author(s):  
Gaofeng Guan ◽  
Dengfeng Xu ◽  
Yu Zhu ◽  
Qiang Yu ◽  
Qiang Li
Keyword(s):  
Natural Frequency ◽  
Large Error ◽  
Common Mechanism ◽  
Rolling Motion ◽  
Elastic Contact ◽  
Load Range ◽  
Proposed Model ◽  
Pure Rolling ◽  
Rigid Contact ◽  
Isolation Mechanisms

The previous models of rolling-type mechanisms were built based on rigid contact and pure rolling motion, but when applied to ground microvibration isolation, a large error in the natural frequency was sometimes observed in the experiments. A new model of a common mechanism based on completely elastic contact is developed, and the expression of the natural frequency is provided under a microvibration condition. The experiments and analysis show that the proposed model is more accurate than the previous model, and the natural frequency is independent of the payload. The analysis shows that the proposed model is only suitable in the range of completely elastic contact, and the load range is provided after comparing the experimental results with existing theory.

Type Synthesis of 2-DOF Rotational Parallel Manipulators With an Equal-Diameter Spherical Pure Rolling Motion

2013 ◽  
Author(s):  
Kang Wu ◽  
Jingjun Yu ◽  
Guanghua Zong ◽  
Xianwen Kong
Keyword(s):  
Theoretical Model ◽  
Parallel Manipulators ◽  
Rolling Motion ◽  
Geometrical Parameters ◽  
Graphic Method ◽  
Type Synthesis ◽  
Pure Rolling ◽  
Lower Mobility ◽  
Two Degree Of Freedom ◽  
Conventional Type

Two-degree-of-freedom (2-DOF) rotational parallel manipulators (RPMs) have been widely used in pointing devices and robot wrists. This paper focuses on a class of 2-DOF RPMs achieving an equal-diameter spherical pure rolling motion (ESPRM) around the base. At first, a theoretical model of spherical pure rolling motion is analyzed and the characteristic of the associated constraint space is derived. Taking the Omni-Wrist III as a typical 2-DOF RPMs with an equal-diameter spherical pure rolling motion, mappings between the geometry and the motion are established and eight useful constraint conditions are derived which will be instructive for the type synthesis. Then, with focus on symmetrical structures, nine classes of 2-DOF RPMs with equal-diameter spherical pure rolling motion are synthesized based on the graphic method. Most of these RPMs have already been used in practice. Unlike the conventional type synthesis of lower-mobility parallel manipulators in literatures, some geometrical parameters of links, in addition to the distributions of joints and limbs, are taken into consideration in the type synthesis in this paper. This proposed research may help produce novel architectures.

Sign in / Sign up

Export Citation Format

Share Document