Differential geometry of the ruled surfaces optically generated by mirror-scanning devices I Intrinsic and extrinsic properties of the scan field

2011 ◽  
Vol 28 (4) ◽  
pp. 667 ◽  
Author(s):  
Yajun Li
Keyword(s):  
Differential Geometry ◽  
Ruled Surfaces ◽  
Extrinsic Properties

scholarly journals Characteristics of the double-cycled motion-ruled surface of the Schatz linkage based on differential geometry

2014 ◽  
Vol 229 (5) ◽  
pp. 957-964 ◽  
Author(s):  
Lei Cui ◽  
Jian S Dai ◽  
Chung-Ching Lee
Keyword(s):  
Differential Geometry ◽  
Ruled Surface ◽  
Ruled Surfaces ◽  
Full Rotation ◽  
Kinematic Properties

This paper applies Euclidean invariants from differential geometry to kinematic properties of the ruled surfaces generated by the coupler link and the constraint-screw axes. Starting from investigating the assembly configuration, the work reveals two cycle phases of the coupler link when the input link finishes a full rotation. This leads to analysis of the motion ruled surface generated by the directrix along the coupler link, where Euclidean invariants are obtained and singularities are identified. This work further presents the constraint ruled surface that is generated by the constraint screw axes and unveils its intrinsic characteristics.

The Differential Geometry of Ruled Surfaces

1948 ◽  
Vol 32 (301) ◽  
pp. 270
Author(s):  
A. G. Walker ◽  
Ram Behari
Keyword(s):  
Differential Geometry ◽  
Ruled Surfaces

On the Scalar and Dual Formulations of the Curvature Theory of Line Trajectories

1987 ◽  
Vol 109 (1) ◽  
pp. 101-106 ◽  
Author(s):  
J. M. McCarthy
Keyword(s):  
Differential Geometry ◽  
Ruled Surface ◽  
The Other ◽  
Ruled Surfaces ◽  
Vector Representation ◽  
Dual Vector ◽  
Vector Algebra ◽  
Distribution Parameters ◽  
Local Properties ◽  
Curvature Theory

The curvature theory of ruled surfaces has been studied in two different ways. The scalar formulation proceeds by defining a seqeunce of ruled surfaces associated with the trajectory ruled surface. The relative positions of these surfaces and their distribution parameters characterize the local properties of the original ruled surface. The other formulation uses dual vector algebra to transform the differential geometry of ruled surfaces into that of spherical curves. In each theory functions are obtained which characterize the shape of the ruled surface. This paper unites these formulations by deriving formulas relating the scalar and dual curvature functions. This provides the ability to compute either set of curvature properties from either the scalar or dual vector representation of the ruled surface. The ruled surface generated by a line fixed in a body undergoing a screw displacement is examined in detail.

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