Some results and characterizations for Mannheim offsets of the ruled surfaces
DOI:
https://doi.org/10.5269/bspm.v34i1.24756Keywords:
Ruled surface, Mannheim offset, E. Study Mapping, integral invariantsAbstract
In this study, we give the dual characterizations of Mannheim offsets of ruled surfaces in terms of their integral invariants and obtain a new characterization of the Mannheim offsets of developable surface, i.e., we show that the striction lines of developable Mannheim offset surfaces are Mannheim partner curves. Furthermore, we obtain the relationships between the area of projections of spherical images for Mannheim offsets of ruled surfaces and their integral invariants.
References
1. Farouki, R.T., The approximation of non-degenerate offset surfaces, Comp. Aided Geom. Design, 3 (1986) 15-43.
2. Gürsoy O., On the integral invariants of a closed ruled surface, Journal of Geometry, 39 (1990) 80-91.
3. Gürsoy O., Some results on closed ruled surface and closed space curves, Mech. Mach. Theory, 27 (2.3) (1992) 323-330.
4. Gürsoy O., Küçük, A., On the invariants of trajectory surfaces, Mech. Mach. Theory, 34 (2.4) (1998) 587-597.
5. Hacisalihoglu. H.H., Hareket Gometrisi ve Kuaterniyonlar Teorisi, Gazi Üniversitesi Fen-Edb. Fakültesi, (1983).
6. Karger, A., Novak, J., Space Kinematics and Lie Groups, STNL Publishers of Technical Lit., Prague, Czechoslovakia (1978).
7. Küçük, A., Gürsoy O., On the invariants of Bertrand trajectory surface offsets, App. Math. and Comp., 151 (2004) 763-773.
8. Liu, H., Wang, F., Mannheim partner curves in 3-space, Journal of Geometry, 88(1-2) (2008) 120-126.
9. Orbay, K., Kasap, E., Aydemir, I, Mannheim Offsets of Ruled Surfaces, Mathematical Problems in Engineering, (2009), Article ID 160917, doi:10.1155/2009/160917.
10. Peternel, M., Pottmann, H., Ravani, B., On the computational geometry of ruled surfaces, Comp. Aided Geom. Design, 31 (1999) 17-32.
11. Papaioannou, S.G., Kiritsis, D., An application of Bertrand curves and surfaces to CAD/CAM, Comp. Aided Design, 17 (2.8) (1985) 348-352.
12. Pottmann, H., Lü, W., Ravani, B., Rational ruled surfaces and their offsets, Graphical Models and Image Processing, 58 (2.6) (1996) 544-552.
13. Ravani, B., Ku, T.S., Bertrand Offsets of ruled and developable surfaces, Comp. Aided Geom. Design, 23 (2.2) (1991) 145-152.
14. Veldkamp, G.R., On the use of dual numbers, vectors and matrices in instantaneous spatial kinematics, Mech. Mach. Theory, 11(2.2) (1976) 141-156.
2. Gürsoy O., On the integral invariants of a closed ruled surface, Journal of Geometry, 39 (1990) 80-91.
3. Gürsoy O., Some results on closed ruled surface and closed space curves, Mech. Mach. Theory, 27 (2.3) (1992) 323-330.
4. Gürsoy O., Küçük, A., On the invariants of trajectory surfaces, Mech. Mach. Theory, 34 (2.4) (1998) 587-597.
5. Hacisalihoglu. H.H., Hareket Gometrisi ve Kuaterniyonlar Teorisi, Gazi Üniversitesi Fen-Edb. Fakültesi, (1983).
6. Karger, A., Novak, J., Space Kinematics and Lie Groups, STNL Publishers of Technical Lit., Prague, Czechoslovakia (1978).
7. Küçük, A., Gürsoy O., On the invariants of Bertrand trajectory surface offsets, App. Math. and Comp., 151 (2004) 763-773.
8. Liu, H., Wang, F., Mannheim partner curves in 3-space, Journal of Geometry, 88(1-2) (2008) 120-126.
9. Orbay, K., Kasap, E., Aydemir, I, Mannheim Offsets of Ruled Surfaces, Mathematical Problems in Engineering, (2009), Article ID 160917, doi:10.1155/2009/160917.
10. Peternel, M., Pottmann, H., Ravani, B., On the computational geometry of ruled surfaces, Comp. Aided Geom. Design, 31 (1999) 17-32.
11. Papaioannou, S.G., Kiritsis, D., An application of Bertrand curves and surfaces to CAD/CAM, Comp. Aided Design, 17 (2.8) (1985) 348-352.
12. Pottmann, H., Lü, W., Ravani, B., Rational ruled surfaces and their offsets, Graphical Models and Image Processing, 58 (2.6) (1996) 544-552.
13. Ravani, B., Ku, T.S., Bertrand Offsets of ruled and developable surfaces, Comp. Aided Geom. Design, 23 (2.2) (1991) 145-152.
14. Veldkamp, G.R., On the use of dual numbers, vectors and matrices in instantaneous spatial kinematics, Mech. Mach. Theory, 11(2.2) (1976) 141-156.
Downloads
Published
2015-01-05
Issue
Section
Research Articles
License
When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).
