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The paper study the curvature theory of a line-trajectory of constant Disteli-axis, according to the invariants of the axodes of moving body in spatial motion. A necessary and sufficient condition for a line-trajectory to be a constant Disteli-axis is derived. From which new proofs of the Disteli's formulae and concise explicit expressions of the inflection line congruence are directly obtained. The obtained explicit equations degenerate into a quadratic form, which can easily give a clear insight into the geometric properties of a line-trajectory of constant Disteli-axis with the theory of line congruence. The degenerated cases of the Burmester lines are discussed according to dual points having specific trajectories.
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참고문헌 (17)
참고문헌 신청
R. A. Abdel-Baky / 2007 / In ection and torsion line congruences / J. Geom. Graph 11(1):1~14
R. A. Abdel-Baky / 2011 / On the one-parameter dual spherical motions / Computer Aided Geometric Design 28:23~37
R. A. Abdel-Baky / 2008 / A new geometrical approach to one-parameter spatial motion / J. Eng. Maths 60:149~172
Reem A. Al-Ghefari / 2015 / Kinematic geometry of a line trajectory in spatial motion / Journal of Mechanical Science and Technology 29(9):3597~3608
O. Bottema / 1979 / Theoretical Kinematics / North-Holland Press
R. A. Abdel-Baky / 2011 / On the one-parameter dual spherical motions / Computer Aided Geometric Design 28:23~37
R. A. Abdel-Baky / 2008 / A new geometrical approach to one-parameter spatial motion / J. Eng. Maths 60:149~172
Reem A. Al-Ghefari / 2015 / Kinematic geometry of a line trajectory in spatial motion / Journal of Mechanical Science and Technology 29(9):3597~3608
O. Bottema / 1979 / Theoretical Kinematics / North-Holland Press
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