Elliptical Gears Research Articles

Computer Aided Design of Elliptical Gears

An elliptical gear drive, whose rotation axis coincides with its geometric center, is simulated using generation with a rack cutter. The mathematical model of an elliptical gear based on the theory of gearing and gear generation mechanism is also developed. Owing to its complex geometry, the profile of elliptical gears may exhibit tooth undercutting, and pointed teeth. In addition, tooth undercutting of an elliptical gear based on the developed mathematical model of the elliptical gear and the theory of gearing is also investigated. Pointed teeth usually appear on the major axis of the gear elliptical pitch curve. Moreover, a geometric relation is developed and applied to prevent the pointed teeth appearing on elliptical gears. Furthermore, a computer simulation program is developed to generate the tooth profile of elliptical gears without tooth undercutting and pointed teeth. Various numerical examples illustrate the effectiveness of the computerized design process.

Computerized tooth profile generation of elliptical gears manufactured by shaper cutters

This work simulates an elliptical gear drive, the axis of rotation of which is coincident with its geometric center, manufactured by shaper cutters. The mathematical model of an elliptical gear is developed based on the theory of gearing and gear generation mechanisms. In addition, the tooth undercutting of the gear is also investigated based on the developed mathematical model of the elliptical gear, its unit normal vectors and a numerical method. A geometric relationship is developed and applied to prevent the occurrence of pointed teeth on elliptical gears. Further, this study also develops computer simulation programs to generate the tooth profile of elliptical gears without tooth undercutting and pointed teeth. Comparison of the angular velocity variations of the elliptical gear drives is also made. The results show that the developed elliptical gear drive can be utilized as an oil pump with a larger pumping volume and less angular velocity variation.

Output characteristics analysis of planetary elliptic gear train

Output characteristics analysis of planetary elliptic gear train

Interpolation algorithm based on central angle division

Second-order interpolation is essential in the manufacturing of curve contours. Especially, according to different part shape, corresponding interpolation algorithms are required. However, the problems of how to determine the parameters of conic sections, how to reduce computational time and how to minimize the contour error according to desired accuracy have not been completely solved. On the basis of the principle of central angle division of an arc, this paper develops an elliptic interpolation algorithm for elliptic gears. And the idea is extended to general second-order interpolation. Although their representing equations are different, the proposed recursive algorithm flows for different conic sections are similar, which is very easy for computer to satisfy the interpolation requirements.

Computer aided design of non-standard elliptical gear drives

An oil pump with a larger pumping volume and more compact size than conventional pumps is designed with elliptical gear drives. In this work, an elliptical gear drive with few teeth is used in the design of pumps with a large pumping volume. Also, a mathematical model of a profile-shifted elliptical gear is developed, based on the theory of gearing and the gear generation mechanism. This study also investigates the tooth undercutting of a non-standard elliptical gear, based on the proposed mathematical model of the profile-shifted elliptical gear and the theory of gearing. Pointed teeth generally appear on the major axis of the gear elliptical pitch curve. Moreover, a geometric relation is developed and applied to prevent pointed teeth on non-standard elliptical gears. Moreover, a computer simulation program is developed to generate the tooth profiles of non-standared elliptical gears with few teeth and a compact size, without tooth undercutting and pointed teeth. Numerical examples demonstrate the effectiveness of the computerized design process.

Computerized Tooth Profile Generation and Undercut Analysis of Noncircular Gears Manufactured With Shaper Cutters

Pitch curves of a conjugate noncircular gear pair are derived based on kinematic considerations. A method for considering the inverse mechanism relationship and the equation of meshing, is proposed here to derive a complete mathematical model of noncircular gears manufactured with involute-shaped shaper-cutters. The proposed method is similar to the contact line method and the envelope method, but is easier to apply to the determination of tooth profiles. A computer program is developed for generation the tooth profile with backlashes. Undercutting analysis is also investigated by considering the relative velocity and equation of meshing. Finally, modified elliptical gears are presented to illustrate the tooth profile generation when the proposed mathematical model is applied, and to investigate the phenomenon of tooth undercutting.

Mathematical model and undercutting analysis of elliptical gears generated by rack cutters

The theory of gearing and geometry of the straight-sided rack cutter are employed to develop a mathematical model of elliptical gears that takes backlash into consideration. The mathematical model also includes the bottom land of the elliptical gear, which is equidistant from the pitch ellipse. A computer program is developed to generate the tooth profile of elliptical gears. The profile of elliptical gears obtained by applying the proposed method is compared with that obtained by the evolute method. Undercutting of elliptical gears is also investigated. The results of this research should be helpful in the design, manufacture, and measurement of elliptical gears.

Mechanismen für die gleichmässige teilung der ellipse

The division of the ellipse into a given number of equal arcs is a classical problem of elliptical gear milling and of ornamental turning. It cannot be solved in closed form but easily numerically. Since it has practical relevance for the ornamentation of elliptical turned pieces ingenious mechanisms have been invented by lathe makers and used since the beginning of the last century. The paper presents the geometrical base for the division of the ellipse by means of the standard division plate and those compensating mechanisms, shows their aberration and optimum adjustment and proposes new types of mechanisms and mechanical devices giving better approximation and having simpler technical layout. The design draft of the compensating linkage for a modern dynamically balanced elliptical lathe is given.

A New Steering mechanism Using Noncircular Gears.

This paper describes a new steering mechanism proposed by one of the authors(T.E.). This steering mechanism using noncircular gears has the capability of turning a carrier with a small radius. In order to facilitate the analysis of the steering mechanism, the concept of a virtual two-wheeled vehicle was introduced. As a result of analysis made by the other author (A.A.), it was proven that the noncircular gear for the steering mechanism is an elliptical gear of which the pitch curve can be represented by a simple equation. In addition, a method to apply this mechanism to wheeled robots, such as the carrier robots used in industrial production lines, was studied. It was confirmed that the concept of the virtual two-wheeled vehicle is very useful in the design of the steering mechanism.

A new steering mechanism using non-circular gears. 2nd report. Trial manufacture and experiments.

This paper deals with experiments of the new steering mechanism which has been proposed in the first report. First of all, the elliptical gears for the steering mechanism were cut with the NC gear shaper developed by the authors, and the error of the rotational angles of the elliptical gears was measured. Then, the authors manufactured a wheeled robot for trial in order to confirm the usefulness of this steering mechanism and succeeded in controlling the wheeled robot using a TV camera for eyes. Moreover, they carried out fundamental experiments. These experiments proved that the new steering mechanism had high turning ability, and can turn the wheeled robot with the small radius.

A new steering mechanism using non-circular gears. 1st report. A proposal and analysis of mechanism.

In this paper, a new steering mechanism proposed by T. Emura is presented. This steering mechanism uses non-circular gears and has the capability of turning a carrier with a small radius. For the analysis of the steering mechanism, an idea of a virtual two-wheeled vehicle was introduced. As a result of the analysis by A. Arakawa, it was proved that the non-circular gear for steering is an elliptical gear. Besides, a method to apply this mechanism to wheeled robots such as carrier-robots in the industrial production lines was studied, and it was confirmed that the concept of the virtual two-wheeled vehicle is very useful for the design of the steering mechanism.

A method for evaluation of elliptical profiles

Measurement and evaluation of circular profiles of cylindrical components in terms of circularity has been well established using roundness measuring instruments. For elliptical sections having very little difference between the major and minor diameters this difference can be measured with the roudness measuring instrument. However, fitting of the best fit ellipse and hence the definition of ellipticity are not available. Applications of elliptical profiles include instruments, such as the photospectrometer developed at CMTI with accurate elliptical cams, elliptical gear blanks, and the pistons of internal combustion engines whose cross sections are elliptical. In this paper a method for the evaluation of the elliptical profiles for centre and orientation of major and minor axes is described and two concepts for defining ellipticity are discussed

The Rolling Method of the Elliptical Gears : On Prevention of Side Swells

The Rolling Method of the Elliptical Gears : On Prevention of Side Swells

Contribution to the geometry of elliptic gears

It is shown that the motion of elliptic wheels, usually derived from the antiparallelogram, can be constrained by a crossed transmission belt which is wound around two equal elliptic disks, confocal with the rolling ellipses. By considering the relative paths of belt points, one arrives at a simple gearing system for wheels of this kind which is the natural generalization of the usual involute system for circular wheels.

Study on an Automatic Loom for Splashed Pattern

This article aims to develope the automatic loom for splashed patterns.The following results are obtained.(1) This loom is provided with a single rapier for weft insertion.Apositive camand balls orthe combined mechanism of elliptic gears and a crank oscillate a rapier right and left.(2) The mechanical or electrical control mechanism has been developed to detect the gap of patterns.(3) The automatic loom for a splashed pattern, appling the electrical paint and some attachments has been developed.

On the Bennett Mechanism

Bennett chain is an exceptional chain having four turning pairs whose axes of rotation are neither parallel nor concurrent. To speak generally, such disposition of the axes is known to produce a four-link chain which is completely stiff, and so furnishes no kinematic chain at all. Now it is questionable whether there is any other such skew kinematic four-link chain than the Bennett chain or not, so this questionable point is studied and the following result is obtained : If a skew four-link mechanism which has four turning pairs and four central axes forming a skew quadrilateral has one degree of freedom, it must be the Bennett Mechanism. Next, it is pointed out that the relationship between input and output angles in the Bennett mechanism coincides with the one in the elliptic gears. This simple remark may give us a useful application of the Bennett mechanism.

Kinematic schemes for testing elliptical gears, or gears derived from them by transformation

Kinematic schemes for testing elliptical gears, or gears derived from them by transformation

Die-Rolled Noncircular Gears : Part 2, In the Case of Gear Blanks Being Shifted

In the last report under the similar title, a rolling method of noncircular gears was treated in that a die holder with two dies was fitted on the tool rest of a lathe and the tool rest was pushed toward the gear blank. In this report, a die holder with a die was fitted on the tool rest of a lathe, then the tool rest was pushed toward the gear blank which was shifted in the rectangular plane of the gear blank shaft. Elliptic gears were made by the above-mentiond equipment, and aluminium and steel were used as the materials of gears.

Die-Rolled Noncircular Gears : Part 1, on Elliptic Gears of Aluminium

Noncircular gears have been generally manufactured by cutting machines, such as hobbing machines or gear shapers fitted with special equipments. As the equipment, however, are very complicated, it is considered hard to cut the teeth of noncircular gears. Then, the author thought of an easier way of manufacturing noncircular gears. It is same way of rolling, not cutting, as in that of circular gears. In this research, a simple equipment was made for trial to roll elliptic gears, the most familiar ones of all the gears. First a die holder with two dies was fitted with the tool rest of a lathe, then the tool rest was pushed toward the gear blank by a spring to press the dies into the gear blank, which was rolled into gears. The two types of elliptic gears were made by the above mentiond experiments ; one is with module 1 and the number of teeth 75, and the other with module 1.25 and the number of teeth 60. The major axis is 93.72mm long and the minor, 54.12mm long for both cases. Aluminium was used as the material.

非円形歯車のシェービング仕上法

Noncircular gears have been generally manufactured by using cutting machines, such as hobbing machines or gear shapers fitted with special equipments. As the equipments, however, are very complicated, it is considered difficult to cut the teeth of noncircular gears ; besides accuracy is not satisfactory.In this study, to make the noncircular gears easily with satisfactory accuracy, they are first cast, and then shaved with the lathe fitted with a shaving installation. This time, two sorts of elliptic gears are made, one is with module 2, the number of teeth 51, major axis 118mm and minor axis 110mm, and the other with module 2, number of teeth 49, major axis 102mm and minor axis 95 mm. Both of these gears are made of Aluminium and Brass.