DESIGN AND ANALYSIS OF GENEVA MECHANISM WITH CURVED SLOTS

2014 ◽  
Vol 38 (4) ◽  
pp. 557-567 ◽  
Author(s):  
Jung-Fa Hsieh
Keyword(s):  
Analytical Description ◽  
Singular Points ◽  
Principal Curvatures ◽  
Surface Theory ◽  
Double Points ◽  
Pressure Angle ◽  
Comprehensive Method ◽  
Analytical Formulae ◽  
Indexing Mechanism

A simple yet comprehensive method is proposed for the design of a Geneva indexing mechanism with curved slots. In the proposed approach, conjugate surface theory is used to derive an analytical description of the profile of the curved slots with and without an offset feature. Analytical formulae are then presented for the pressure angle of the Geneva mechanism and the principal curvatures of the curved slots. The effectiveness of an appropriate offset angle in eliminating the singular points and double-points on the curved slot profile is then demonstrated. Finally, a Geneva mechanism is fabricated in order to demonstrate the feasibility of the proposed approach.

Design of Geneva Mechanism with Curved Slots

2013 ◽  
Vol 479-480 ◽  
pp. 259-263
Author(s):  
Jung Fa Hsieh ◽  
Fu Shou Wang
Keyword(s):  
Production Process ◽  
Analytical Description ◽  
Design Analysis ◽  
Singular Points ◽  
Automatic Production ◽  
Surface Theory ◽  
Double Points ◽  
Comprehensive Method ◽  
Indexing Mechanism

A simple yet comprehensive method is proposed for the design of a Geneva indexing mechanism with curved slots. In the proposed approach, conjugate surface theory is employed to derive an analytical description of the profile of the curved slots with and without an offset feature. The use of an appropriate offset angle to eliminate the singular points and double-points on the profile of the curved slots is then demonstrated. Finally, a mock-up Geneva mechanism is constructed to demonstrate the feasibility of the proposed approach. The results confirm that the methodology presented in this study enables the integration of the design, analysis and machining tasks for a Geneva indexing mechanism, and therefore makes possible a flexible and automatic production process.

Application of homogenous transformation matrix to the design and machining of a Geneva mechanism with curved slots

2007 ◽  
Vol 221 (11) ◽  
pp. 1435-1443 ◽  
Author(s):  
J-F Hsieh
Keyword(s):  
Design Methodology ◽  
Kinematic Model ◽  
Cnc Machine ◽  
Principal Curvatures ◽  
Surface Theory ◽  
Comprehensive Method ◽  
Design And Manufacturing ◽  
Cost Efficient ◽  
Indexing Mechanism ◽  
Nc Data

The current paper presents a simple yet comprehensive method for the design and machining of a Geneva indexing mechanism with curved slots. In the proposed approach, a kinematic model of the Geneva mechanism is developed using homogenous coordinate transformation and conjugate surface theory. The pressure angle of Geneva mechanism and the principal curvatures of the curved slots are analysed using an analytical expression derived for the slot profile. The NC data required to machine the driven with curved slots are derived from the CNC link variables by equating the machine tool ability function and the tool location matrix. The proposed design methodology is verified by machining the designed curved slots using a three-axis CNC machine. The results confirm that the approach presented in this study enables the Geneva mechanism design and manufacturing tasks to be successfully integrated, thus making possible a flexible, automatic, cost efficient, and controllable production process.

DESIGN AND ANALYSIS OF CAM MECHANISM WITH TRANSLATING FOLLOWER HAVING DOUBLE ROLLERS

2015 ◽  
Vol 39 (3) ◽  
pp. 397-406
Author(s):  
Jung-Fa Hsieh
Keyword(s):  
Kinematic Model ◽  
Cnc Machine Tool ◽  
Cnc Machine ◽  
Principal Curvatures ◽  
Surface Theory ◽  
Cam Mechanism ◽  
Pressure Angle ◽  
Straightforward Method ◽  
Cam Profile ◽  
Analytical Expressions

The pressure angle is one of the primary considerations in designing a cam mechanism since an inappropriate angle may cause excessive sliding loads on the follower. This paper presents a simple yet straightforward method for the design and analysis of a cam mechanism with a translating follower having double rollers. In the proposed approach, conjugate surface theory is employed to derive a kinematic model of the cam mechanism. Analytical expressions for the pressure angle and principal curvatures of the cam profile are then derived. The validity of the analytical expressions is confirmed by machining a designed cam using a 3-axis CNC machine tool.

DESIGN AND ANALYSIS OF CONSTANT-BREADTH CAM MECHANISM WITH OSCILLATING FLAT-FACED FOLLOWER

2017 ◽  
Vol 41 (2) ◽  
pp. 211-225
Author(s):  
Jung-Fa Hsieh
Keyword(s):  
Design Methodology ◽  
Sliding Velocity ◽  
Principal Curvatures ◽  
Surface Theory ◽  
Cam Mechanism ◽  
Contact Points ◽  
Comprehensive Method ◽  
Cam Follower ◽  
Cam Profile ◽  
Constant Breadth

A simple yet comprehensive method is presented for the design and analysis of a constant-breadth cam mechanism with an oscillating flat-faced follower. In the proposed approach, the kinematic characteristics of the cam mechanism are first derived. The cam profile is then designed using homogenous coordinate transformation and conjugate surface theory. Moreover, the sliding velocity at the cam-follower contact points is determined. Finally, the pressure angle of the constant-breadth cam mechanism and the principal curvatures of the cam are analyzed. The validity of the proposed design methodology is verified by means of motion simulations performed using CAD software.

Limitations of Conjugate Gear Tooth Surfaces in Order to Avoid Undercutting and Appearance of Envelope of Lines of Contact

1988 ◽  
Author(s):  
F. L. Litvin ◽  
D. J. Kin ◽  
Y. Zhang
Keyword(s):  
Computer Graphics ◽  
Gear Tooth ◽  
Worm Gear ◽  
Singular Points ◽  
Line Contact ◽  
Gear Drive ◽  
Pressure Angle ◽  
Tooth Surfaces ◽  
Limiting Pressure

Abstract Gear tooth surfaces being in line contact at every instant are considered. The dimensions of the contacting surfaces must be limited in order to avoid: (i) the appearance of the envelope of lines of contact on the generating surface Σ1 and (ii) the appearance of singular points on the generated surface Σ2. The relations between the developed concepts and the Wildhaber’s concept of the limiting pressure angle are investigated. Applications to the worm-gear drive and the generation of a pinion of a formate gear drive are considered. Computer graphics have been used to illustrate the results of computation.

On certain types of isolated s-ple points on algebraic primals in Sd

1962 ◽  
Vol 58 (3) ◽  
pp. 465-475
Author(s):  
J. Herszberg
Keyword(s):  
Finite Number ◽  
Tangent Cone ◽  
Double Point ◽  
Complete Classification ◽  
Singular Points ◽  
Multiple Points ◽  
Rank Zero ◽  
Double Points

Singular points on irreducible primals were investigated briefly by C. Segre(8), where the author classified multiple points by the nature of the nodal tangent cone. For surfaces the problem of classification was investigated by, amongst others, Du Val(1) and a complete classification of isolated double points of surfaces lying on non-singular threefolds was given by Kirby(5). In (3) we classified certain types of double points on algebraic primals in Sn. An isolated double point which after a finite number of resolutions gave rise to at most a finite number of isolated double points was called a double point of rank zero. We found that the only isolated double points of rank zero are those which are analogous to the binodes, unodes and exceptional unodes (2) of surfaces.

Principal curvatures and parallel surfaces of wave fronts

2019 ◽  
Vol 19 (4) ◽  
pp. 541-554 ◽  
Author(s):  
Keisuke Teramoto
Keyword(s):  
Principal Curvature ◽  
Singular Points ◽  
Principal Curvatures ◽  
Wave Fronts ◽  
Geometric Invariants ◽  
Parallel Surfaces

Abstract We give criteria for which a principal curvature becomes a bounded C∞-function at non-degenerate singular points of wave fronts by using geometric invariants. As applications, we study singularities of parallel surfaces and extended distance squared functions of wave fronts. Moreover, we relate these singularities to some geometric invariants of fronts.

scholarly journals Variation of Mixed Hodge Structures Associated to an Equisingular One-dimensional Family of Calabi-Yau Threefolds

2020 ◽  
pp. 1-24
Author(s):  
Isidro Nieto-Baños ◽  
Pedro Luis del Angel-Rodriguez
Keyword(s):  
General Position ◽  
Singular Points ◽  
Good Position ◽  
Hodge Structures ◽  
One Dimensional ◽  
Double Points ◽  
Hodge Filtration ◽  
Starting Point ◽  
Mixed Hodge Structures

Abstract We study the variations of mixed Hodge structures (VMHS) associated with a pencil ${\mathcal{X}}$ of equisingular hypersurfaces of degree $d$ in $\mathbb{P}^{4}$ with only ordinary double points as singularities, as well as the variations of Hodge structures (VHS) associated with the desingularization of this family $\widetilde{{\mathcal{X}}}$ . The notion of a set of singular points being in homologically good position is introduced, and, by requiring that the subset of nodes in (algebraic) general position is also in homologically good position, we can extend Griffiths’ description of the $F^{2}$ -term of the Hodge filtration of the desingularization to this case, where we can also determine the possible limiting mixed Hodge structures (LMHS). The particular pencil ${\mathcal{X}}$ of quintic hypersurfaces with 100 singular double points with 86 of them in (algebraic) general position that served as the starting point for this paper is treated with particular attention.

Analytical Description of Meshing of Constant Pressure Angle Teeth Profiles on a Variable Radius Gear and its Applications

2000 ◽  
Vol 122 (1) ◽  
pp. 123-129 ◽  
Author(s):  
Guido A. Danieli
Keyword(s):  
Constant Pressure ◽  
New Technology ◽  
Planetary Gear ◽  
Analytical Description ◽  
Gear Train ◽  
Design Phase ◽  
Variable Radius ◽  
Pressure Angle ◽  
Low Efficiency ◽  
The Individual

This paper presents a method for determining the profile of the gear teeth on a variable radius wheel characterized by a constant pressure angle. The method can generate special gears using numerically controlled milling machines. As will be shown, the method, applied to a constant radius gear, generates an involute profile. The method is based on the integration of a differential equation describing the mesh between gears of variable radius, where the mesh point position is computed during rotation starting from the point, freely selected, where the tooth crosses the pitch line. The individual point is subsequently rotated in the opposite direction by an angle equal to the angle of rotation from the initial pitch line point, thereby generating the tooth profile. The method, applied to a wheel of variable radius, defined analytically or numerically, can compute teeth profiles on pairs of pitch lines of any shape. In particular, the motion of a slotted rotating link mechanism has been reproduced, but for the sign. Teeth profiles of other variable radius wheels have also been obtained. The results are more than satisfactory and are presented below. A numerically controlled milling machine has been programmed to actually build the antirotating slotted link equivalent gear. The present method, however, has much broader application, such as assigning the speed law to consequentially determine the gear form, as can be done with cams. Furthermore, a special planetary gear train makes it also possible to obtain reciprocating motion driven solely by gears. This has been built and its picture and scheme are presented in the paper. However, due to the low efficiency of the said mechanism, the best way to utilize this new technology seems to be to couple a crank and a rod to the pair of variable radius gears, as has been done at Hanover University. Some possible applications are presented. The special feature of these gears is the programmability of the shape of the pitch lines during the design phase, and thus of the velocity and acceleration profiles. In this way velocity profiles that could formerly only be obtained electro-pneumatically can be produced from purely mechanical components, with the added advantage of being able to control the level of inertia forces during the design phase. [S1050-0472(00)01601-9]

Sign in / Sign up

Export Citation Format

Share Document