On Singularity of Polar Surface Associated to a Regular Space Curve

2016 ◽  
Vol 13 (11) ◽  
pp. 8633-8637
Author(s):  
Azeb Alghanemi
Keyword(s):  
Space Curve ◽  
Regular Space ◽  
Polar Surface

A pair of kinematically related space curves

2018 ◽  
Vol 15 (10) ◽  
pp. 1850180 ◽  
Author(s):  
Vishesh S. Bhat ◽  
R. Haribaskar
Keyword(s):  
Space Curve ◽  
Regular Space ◽  
Motion Trajectory ◽  
Space Curves ◽  
Related Space ◽  
Constant Pitch ◽  
Mannheim Curve ◽  
Special Case ◽  
Radius Function ◽  
Geometric Nature

We investigate the relation between two types of space curves, the Mannheim curves and constant-pitch curves and primarily explicate a method of deriving Mannheim curves and constant-pitch curves from each other by means of a suitable deformation of a space curve. We define a “radius” function and a “pitch” function for any arbitrary regular space curve and use these to characterize the two classes of curves. A few non-trivial examples of both Mannheim and constant pitch curves are discussed. The geometric nature of Mannheim curves is established by using the notion of osculating helices. The Frenet–Serret motion of a rigid body in theoretical kinematics is studied for the special case of a Mannheim curve and the axodes in this case are deduced. In particular, we show that the fixed axode is developable if and only if the motion trajectory is a Mannheim curve.

scholarly journals On geometry of the midlocus associated to a smooth curve in plane and space

Filomat ◽  
2018 ◽  
Vol 32 (8) ◽  
pp. 2977-2990
Author(s):  
Azeb Alghanemi ◽  
Peter Giblin
Keyword(s):  
Plane Curve ◽  
Smooth Curve ◽  
Space Curve ◽  
Regular Space ◽  
Geometric Conditions ◽  
Special Cases ◽  
Smooth Plane ◽  
Surface Singularities

The singularities of the midpoint map associated to a smooth plane curve, which is a map from the plane to the plane, are classified. The midlocus associated to a regular space curve is introduced. The geometric conditions for the midlocus of a space curve to have a crosscap or an S?1 singularities are investigated. A more general map, the ?-point map, associated to a space curve is introduced and many known surface singularities are realized as a special cases of this construction.

scholarly journals A Different View on Dynamics of Space Curves Geometry

2021 ◽  
Author(s):  
Yılmaz Tunçer
Keyword(s):  
Space Curve ◽  
Regular Space ◽  
Position Vector ◽  
Space Curves

AbstractIn this study, we define the X-torque curves, $$X-$$ X - equilibrium curves, X-moment conservative curves, $$X-$$ X - gyroscopic curves as new curves derived from a regular space curve by using the Frenet vectors of a space curve and its position vector, where $$X\in \left\{ T\left( s\right) , N\left( s\right) , B\left( s\right) \right\} $$ X ∈ T s , N s , B s and we examine these curves and we give their properties.

Geometry Design and Contact Ratio Analysis for Circular Arc Parallel-Axis Helical Gears

2016 ◽  
Author(s):  
Z. Chen ◽  
B. Lei ◽  
Q. Zhao
Keyword(s):  
Rolling Process ◽  
Helical Gear ◽  
Space Curve ◽  
Impact Factors ◽  
Contact Ratio ◽  
Circular Arc ◽  
Practical Applications ◽  
Geometry Design ◽  
Gear Mechanism ◽  
The Impact

Based on space curve meshing theory, in this paper, we present a novel geometric design of a circular arc helical gear mechanism for parallel transmission with convex-concave circular arc profiles. The parameter equations describing the contact curves for both the driving gear and the driven gear were deduced from the space curve meshing equations, and parameter equations for calculating the convex-concave circular arc profiles were established both for internal meshing and external meshing. Furthermore, a formula for the contact ratio was deduced, and the impact factors influencing the contact ratio are discussed. Using the deduced equations, several numerical examples were considered to validate the contact ratio equation. The circular arc helical gear mechanism investigated in this study showed a high gear transmission performance when considering practical applications, such as a pure rolling process, a high contact ratio, and a large comprehensive strength.

scholarly journals Polar-surface-driven growth of ZnS microsprings with novel optoelectronic properties

2015 ◽  
Vol 7 (9) ◽  
pp. e213-e213 ◽  
Author(s):  
Qi Zhang ◽  
Cong Wei ◽  
Xing Li ◽  
Muhammad Hafeez ◽  
Lin Gan ◽  
...  
Keyword(s):  
Optoelectronic Properties ◽  
Polar Surface
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