×
Li, Z.; Schicho, Josef; Schröcker, Hans-Peter

The rational motion of minimal dual quaternion degree with prescribed trajectory. (English) Zbl 1417.53012

Comput. Aided Geom. Des. 41, 1-9 (2016).
Summary: We give a constructive proof for the existence of a unique rational motion of minimal degree in the dual quaternion model of Euclidean displacements with a given rational parametric curve as trajectory. The minimal motion degree equals the trajectory’s degree minus its circularity. Hence, it is lower than the degree of a trivial curvilinear translation for circular curves.

Cited in 8 Documents

MSC:

53A17 Differential geometric aspects in kinematics
70B10 Kinematics of a rigid body
70B15 Kinematics of mechanisms and robots
65D17 Computer-aided design (modeling of curves and surfaces)

Keywords:

motion polynomial; rational curve; factorisation; circularity; dual quaternion
PDF BibTeX XML Cite
\textit{Z. Li} et al., Comput. Aided Geom. Des. 41, 1--9 (2016; Zbl 1417.53012)
Full Text: DOI arXiv
  • logo of hbz
  • logo of WorldCat

References:

[1] Abbott, T. G., Generalizations of Kempe’s universality theorem, (2008), Massachusetts Institute of Technology, Master’s thesis
[2] Bottema, O.; Roth, B., Theoretical kinematics, (1990), Dover Publications · Zbl 0747.70001
[3] Demaine, E. D.; O’Rourke, J., Geometric folding algorithms: linkages, origami, polyhedra, (2007), Cambridge University Press · Zbl 1135.52009
[4] Hamann, M., Line-symmetric motions with respect to reguli, Mech. Mach. Theory, 46, 7, 960-974, (2011) · Zbl 1337.70003
[5] Hegedüs, G.; Schicho, J.; Schröcker, H.-P., Factorization of rational curves in the study quadric and revolute linkages, Mech. Mach. Theory, 69, 1, 142-152, (2013)
[6] Jüttler, B., Über zwangläufige rationale bewegungsvorgänge, Sitz.ber. - Österr. Akad. Wiss. Math.-Nat.wiss. Kl., II Math. Astron. Phys. Meteorol. Tech., 202, 117-132, (1993) · Zbl 0806.53011
[7] Li, Z.; Schicho, J.; Schröcker, H.-P., 7R Darboux linkages by factorization of motion polynomials, (Chang, Shuo-Hung, Proceedings of the 14th IFToMM World Congress 2015, (2015)), ISBN 979-986-04-6098-8. In press
[8] Li, Z., Schicho, J., Schröcker, H.-P., 2015b. Factorization of motion polynomials. Submitted for publication. arXiv:1502.07600 [cs.SC].
[9] Li, Z.; Schicho, J.; Schröcker, H.-P., Spatial straight-line linkages by factorization of motion polynomials, ASME J. Mech. Robot, (2015), In press
[10] Ore, O., Theory of non-commutative polynomials, Ann. Math. (2), 34, 3, 480-508, (1933) · Zbl 0007.15101
[11] Peternell, M.; Gruber, D.; Sendra, J., Conchoid surfaces of spheres, Comput. Aided Geom. Des., 30, 1, 35-44, (2013) · Zbl 1255.65055
[12] Selig, J., Geometric fundamentals of robotics, Comput. Sci. Monogr, (2005), Springer · Zbl 1062.93002
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.