Projective Differential Geometry of Curves and Ruled Surfaces. By E. J. Wilczynski Pp. viii, 298. (Chelsea Publishing Co., New York)

1963 ◽  
Vol 47 (360) ◽  
pp. 181
Keyword(s):  
Differential Geometry ◽  
New York ◽  
Ruled Surfaces ◽  
Projective Differential Geometry

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.

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