Surface Geometry of Variable Pitch Cylindrical Cams with Conical Meshing Elements

1994 ◽  
Vol 116 (3) ◽  
pp. 862-866 ◽  
Author(s):  
Jen-Yu Liu ◽  
Hong-Sen Yan
Keyword(s):  
Differential Geometry ◽  
Coordinate Transformation ◽  
Industrial Applications ◽  
Contact Lines ◽  
Input Output ◽  
Surface Geometry ◽  
Variable Pitch ◽  
Mathematical Expressions ◽  
Computer Aided ◽  
Conjugate Surfaces

This paper presents mathematical expressions for the surface geometry of variable pitch cylindrical cams with four conical meshing elements based on the theory of conjugate surfaces. The unit normal of the element is derived, with given surface geometry of the meshing element, by differential geometry. The contact lines of the conjugate surface are defined according to the equation of meshing and the specified input-output relation. By the coordinate transformation of contact lines, we have the complete profile of the variable pitch cylindrical cam. The results of this work are instrumental in computer-aided manufacturing of variable pitch cylindrical cams for industrial applications.

Geometry Design of Roller Gear Cams With Generalized Meshing Elements

1994 ◽  
Author(s):  
Hong-Sen Yan ◽  
Hsin-Hung Chen
Keyword(s):  
Computer Aided Design ◽  
Industrial Applications ◽  
Generalized Equation ◽  
Surface Geometry ◽  
Geometry Design ◽  
Mathematical Expressions ◽  
Computer Aided ◽  
Design And Manufacturing ◽  
Conjugate Surfaces ◽  
Aided Design

Abstract This paper derives the generalized expression of surface equation for cylindrical, conical, and hyperbolic meshing elements. Based on the generalized equation of meshing elements, generalized mathematical expressions of surface geometry for roller gear cams with cylindrical, conical, and hyperbolic meshing elements are derived by theory of conjugate surfaces, differential geometry, and coordinate transformation. Design examples are given. The result of this work is of necessary for the computer-aided design and manufacturing roller gear cams for industrial applications.

Geometry Design of Globoidal Cams With Generalized Meshing Turret-Rollers

1996 ◽  
Vol 118 (2) ◽  
pp. 243-249 ◽  
Author(s):  
Hong-Sen Yan ◽  
Hsin-Hung Chen
Keyword(s):  
Computer Aided Design ◽  
Industrial Applications ◽  
Generalized Equation ◽  
Surface Geometry ◽  
Geometry Design ◽  
Mathematical Expressions ◽  
Computer Aided ◽  
Design And Manufacturing ◽  
Conjugate Surfaces ◽  
Aided Design

This paper derives the generalized surface equation for cylindrical, conical, and hyperbolic meshing turret-rollers. Based on the generalized equation of meshing turret-rollers, generalized mathematical expressions of surface geometry for globoidal cams with cylindrical, conical, and hyperbolic meshing turret-rollers are derived using theory of conjugate surfaces, differential geometry, and coordinate transformation. A design example is presented for demonstrating procedures of surface generating of the globoidal cam. The result of this work is necessary for the computer-aided design and manufacturing of roller gear cams for industrial applications.

On the Surface Geometry of Variable Pitch Cylindrical Cams With Hyperboloidical Meshing Elements

1994 ◽  
Author(s):  
Yaw-Hong Kang ◽  
Feng-Chi Wu ◽  
Hong-Yih Cheng ◽  
Hong-Sen Yan
Keyword(s):  
Differential Geometry ◽  
Computer Program ◽  
Coordinate Transformation ◽  
Solid Modeling ◽  
Surface Geometry ◽  
Engineering Applications ◽  
Variable Pitch ◽  
Developed Surface ◽  
Mathematical Equations

Abstract The hyperpoloid of revolution is a kind of skew surface that has engineering applications. Based on differential geometry, theory of gearing, and coordinate transformation, this paper derive mathematical equations of the geometric profiles of a double threaded variable pitch cylindrical cams with four hyperboloidical meshing elements. And based on the developed surface equations, we develope a computer program for solid modeling to simulate the surface geometry. Two examples are given to prove the derived equations.

Geometric Design and Machining of Variable Pitch Lead Screws with Cylindrical Meshing Elements

1993 ◽  
Vol 115 (3) ◽  
pp. 490-495 ◽  
Author(s):  
Hong-Sen Yan ◽  
Jen-Yu Liu
Keyword(s):  
Computer Aided Design ◽  
Industrial Applications ◽  
Surface Geometry ◽  
Variable Pitch ◽  
Lead Screw ◽  
Transmission Mechanisms ◽  
Machining Center ◽  
Developed Surface ◽  
Before And After ◽  
Aided Design

This paper derives the surface geometry and machine tool settings for a double threaded variable pitch lead screw with four cylindrical meshing elements. A 4-axis machining center with a rotary milling head attachment is adopted for the manufacturing of the profiles of the screws. And, based on the developed surface equations and the required settings, the authors develop a computer program for solid modeling to simulate the surface geometry of such a mechanism before and after machining. The result of this work is necessary for the task of computer-aided design and manufacturing of the variable pitch lead screw transmission mechanisms for industrial applications, e.g., in shuttleless weaving looms.

Computer-Aided Geometry Design of Trapezoidal Threaded Variable Pitch Conical Lead Screws

1991 ◽  
Author(s):  
Jen-Yu Liu ◽  
Hong-Sen Yan
Keyword(s):  
Computer Aided Design ◽  
Solid Modeling ◽  
Design Code ◽  
Surface Geometry ◽  
Variable Pitch ◽  
Screw Motion ◽  
Lead Screw ◽  
Geometry Design ◽  
Computer Aided ◽  
Aided Design

Abstract Based on conical screw matrix transformation, equations of variable pitch conical helix and helicoid are derived. The surface geometry of a trapezoidal threaded variable pitch conical lead screw is generated by a trapezoid with a variable pitch conical screw motion. A computer-aided design code is developed with Patran Plus solid modeling. The result of this work is necessary for the computer-aided machining of trapezoidal threaded variable pitch conical lead screws.

CURVATURE ANALYSIS OF VARIABLE PITCH LEAD SCREWS WITH CYLINDRICAL MESHING ELEMENTS

1996 ◽  
Vol 20 (2) ◽  
pp. 139-157 ◽  
Author(s):  
Yaw-Hong Kang ◽  
Hong-Sen Yan
Keyword(s):  
Contact Point ◽  
Tangential Direction ◽  
Radius Of Curvature ◽  
Principal Curvatures ◽  
Surface Geometry ◽  
Variable Pitch ◽  
Transformation Matrices ◽  
Mathematical Expressions ◽  
Screw Surface ◽  
Principal Directions

Based on coordinate transformation matrices and theory of gearing, we derive the mathematical expressions of surface geometry and the location of contact point of variable pitch lead screws. According to curvature theory, we obtain the principal curvatures, the principal directions, and the orientation of the contacting line at any contact point. Furthermore, the condition of avoiding undercutting of the screw surface, the reduced radius of curvature along any tangential direction, and the angle between the normal of contact line and the relative velocity are also derived. The result of this work is necessary for the tasks of contact stress analysis and wear/lubrication analysis for variable pitch lead screws with cylindrical meshing elements.

Edges of Regression and Limit Normal Point of Conjugate Surfaces1

1998 ◽  
Vol 122 (4) ◽  
pp. 419-425 ◽  
Author(s):  
Ningxin Chen
Keyword(s):  
Differential Geometry ◽  
Contact Boundary ◽  
Boundary Line ◽  
Tangent Point ◽  
Common Tangent ◽  
Numerical Examples ◽  
Envelope Surface ◽  
The Common ◽  
Conjugate Surfaces ◽  
Definition Of

The presented paper utilizes the basic theory of the envelope surface in differential geometry to investigate the undercutting line, the contact boundary line and the limit normal point of conjugate surfaces in gearing. It is proved that (1) the edges of regression of the envelope surfaces are the undercutting line and the contact boundary line in theory of gearing respectively, and (2) the limit normal point is the common tangent point of the two edges of regression of the conjugate surfaces. New equations for the undercutting line, the contact boundary line and the limit normal point of the conjugate surfaces are developed based on the definition of the edges of regression. Numerical examples are taken for illustration of the above-mentioned concepts and equations. [S1050-0472(00)00104-5]

scholarly journals Input-Output Models and Derived Indicators: A Critical Review

2019 ◽  
Vol 66 (3) ◽  
pp. 267-308 ◽  
Author(s):  
Argyrios D. Kolokontes ◽  
Achilleas Kontogeorgos ◽  
Efstratios Loizou ◽  
Fotios Chatzitheodoridis
Keyword(s):  
Critical Review ◽  
Input Output ◽  
Developmental Patterns ◽  
Actual Computation ◽  
Mathematical Expressions

Input-Output literature can be characterized as complicated and chaotic. The complications concern the nomenclature of concepts for the derived indices from the multipliers’ models, their mathematical expressions and computable applications. The terminologies’ inconsistencies often end up to a deviation between the description for these indices and their actual computation, or/and to a misunderstanding as for their usefulness and outcomes. The aim of the paper is to help the readers to face the weaknesses in the literature. In this way, the paper provide an overview with a critical look to the constructed multipliers’ matrices and their derived indicators from the I-O models, and elaborate the causes for the scrutinized confusions. The paper proposes both terminological and computational adjustments and differentiated approaches for the models and their indices, in order to ameliorate their capabilities and to exploit their peculiarities for the developmental patterns. Alternative interpretative ways and applicable expansions are suggested.

Unified Mobility Identification and Rectification of Six-Bar Linkages

2009 ◽  
Author(s):  
Kwun-Lon Ting ◽  
Jun Wang ◽  
Changyu Xue
Keyword(s):  
Special Form ◽  
Simple Explanation ◽  
Input Output ◽  
Mobility Analysis ◽  
Joint Rotation ◽  
Input Condition ◽  
Computer Aided ◽  
Unified Method

This paper offers a unified method for a complete and unified treatment on the mobility identification and rectification of any planar and spherical six-bar linkages regardless the linkage type and the choice of the input, output, or fixed links. The method is based on how the joint rotation spaces of the four-bar loop and a five-bar loop in a Stephenson six-bar linkage interact each other. A Watt six-bar linkage is regarded as a special form of Stephenson six-bar linkage via the stretch and rotation of a four-bar loop. The paper offers simple explanation and geometric insights for the formation of branch (circuit), sub-branch, and order of motion of six-bar linkages. All typical mobility issues, including branch, sub-branch, and type of motion under any input condition can be identified and rectified with the proposed method. The method is suitable for automated computer-aided mobility identification. The applicability of the results to the mobility analysis of serially connected multiloop linkages is also discussed.

Over-Constrained Mechanisms Derived From RPRP Loops

2018 ◽  
Author(s):  
Kwun-Lon Ting ◽  
Kuan-Lun Hsu
Keyword(s):  
Computer Aided Design ◽  
Random Search ◽  
Modular Approach ◽  
Input Output ◽  
Assembly Strategy ◽  
Revolute Joints ◽  
Computer Aided ◽  
Prismatic Joints ◽  
Aided Design ◽  
Four Bar Linkage

This paper addresses the assembly strategy capable of deriving a family of over-constrained mechanisms systematically. The modular approach is proposed. It treats the topological synthesis of over-constrained mechanisms as a systematical derivation rather than a random search. The result indicates that a family of over-constrained mechanisms can be constructed by combining legitimate modules. A spatial four-bar linkage containing two revolute joints (R) and two prismatic joints (P) is selected as the source-module for the purpose of demonstration. All mechanisms discovered in this paper were modeled and animated with computer aided design (CAD) software and their mobility were validated with input-output equations as well as computer simulations. The assembly strategy can serve as a self-contained library of over-constrained mechanisms.

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