Abstract
In this paper, a novel methodology based on screw theory to study the singularity of spatial hybrid mechanisms is presented. According to the physical meaning of inverse screws, we introduce the equivalent kinematic screws to replace the function of those of the parallel limbs, and therefore the hybrid branch can be transformed into a pure series kinematic chain which can facilitate the whole analytical process of the singularity of complex spatial hybrid mechanisms. In fact, this methodology can be widely used to solve the singularity problems of spatial hybrid mechanisms based on the analysis of their kinematic characters.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Sugimoto K, Duffy J, Hunt KH (1982) Special configuration of spatial mechanisms and robot arms. Mechanism Mach Theory 17(2):119–132
Sugimoto K, Duffy J (1981) Determination of extreme distances of a robot hand. Part 1: A general theory. J Mech Des 103(7):631–636
Burdick JW (1995) A classification of 3R regional manipulator singularities and geometries. Mechanism Mach Theory 30(1):71–89
Wazwaz A-M (1999) A comparative study on a singular perturbation problem with two singular boundary points. Appl Math Comput 99(2–3):179–193
Bhattacharya S, Hatwal H, Ghosh A (1998) Comparison of an exact and an approximate methodology of singularity avoidance in platform type parallel manipulators. Mechanism Mach Theory 33(7):965–974
Mattson KG, Pennock GR (1996) The velocity problems of two 3-R robots manipulating a four-bar linkage payload. Mechanism Mach Theory 31(8):1019–1032
Collins CL, McCarthy JM (1998) The quartic singularity surfaces of planar platforms in the Clifford algebra of the projective plane. Mechanism Mach Theory 33(7):931–944
Sefrioui J, Gosselin CM (1993) Singularity analysis and representation of planar parallel manipulators. Robot Auton Sys 10(4):209–224
Sefrioui J, Gosselin CM (1995) On the quadratic nature of the singularity curves of planar three-degree-of-freedom parallel manipulators. Mechanism Mach Theory 30(4):533–551
Mlynarski T, Romaniak K (2001) The methodologyization of examination of the mechanisms of high structural complexity. Mechanism Mach Theory 36(6):709–715
Karger A (2001) Singularities and self-motions of equiform platforms. Mechanism Mach Theory 36(7):801–815
Ball RS (1900) A treatise on the theory of screws. Cambridge University Press, Cambridge
Phillips JR, Hunt KH (1964) On the theorem of three axes in the spatial motion of three bodies. Austral J Appl Sci 15:267–287
Hunt KH (1978) Kinematic geometry of mechanisms. Oxford University Press, Oxford
Nokleby SB, Podhorodeski RP (2001) Reciprocity-based resolution of velocity degeneracies (singularities) for redundant manipulators. Mechanism Mach Theory 36(3):397–409
Jia S-H (1987) Dynamics of rigid body. Advanced Education Press, China
Zhao J-S, Zhou K, Mao D-Z, Gao Y-F, Fang Y, A new method to study the DoF of spatial parallel mechanism. Int J Adv Manuf Technol (in press)
Author information
Authors and Affiliations
Corresponding author
Additional information
An erratum to this article can be found at http://dx.doi.org/10.1007/s00170-004-2228-y
Rights and permissions
About this article
Cite this article
Zhao, JS., Zhou, K., Feng, ZJ. et al. The singularity study of spatial hybrid mechanisms based on screw theory. Int J Adv Manuf Technol 25, 1053–1059 (2005). https://doi.org/10.1007/s00170-003-1934-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00170-003-1934-1