The theory of dual quaternion and its use in serial mechanisms are described in this paper. A closed-form solution to the inverse kinematic analysis of the general 7-link 7R mechanism is presented. Dixon's resultant is used and the input—output equation is expressed in the form of a 6×6 determinant equated to zero, and the formulae to determine other angular displacements are expressed in the closed form. Numerical example confirms these theoretical results. The whole process is very simple and easy to program, which supplies a new method for the real use of the 7R mechanism.
FreudensteinF.Kinematics: Past, present and future. Mech. Mach. Theory19738(2)151–161.
2.
DuffyJ.CraneC.A displacement analysis of the general 7-link 7R mechanism. Mech. Mach. Theory198015(2)153–169.
3.
DenavitJ.HartenbergR. S.A kinematic notation for lower-pair mechanisms based on matrices. ASME J. Appl. Mech.195522215–221.
4.
YangA. T.Displacement analysis of spatial five-link mechanisms using (3 × 3) matrices with dual-number elements. ASME J. Eng. Ind.196991152–157.
5.
LiaoQ. Z.LiangC. G.ZhangQ. X.A novel approach to the displacement analysis of general spatial 7R mechanism. Chinese J. Mech. Eng.198622(3)1–9.
6.
LeeH. Y.LiangC. G.Displacement analysis of the general spatial 7-link 7R mechanism. Mech. Mach. Theory198823(3)219–226.
7.
RaghavanM.RothB.Inverse kinematics of the general 6R manipulator and related linkages. ASME J. Mech. Des.1993115(3)502–508.
8.
KohliD.OsvaticM.Inverse kinematics of general 6R and 5R, P serial manipulators. ASME J. Mech. Des.1993115(4)922–931.
9.
HangL. B.WangY.YangT. L.Inverse kinematic analysis of the general 6R serial robot mechanism based on Gröbner basis. J. Shanghai Jiaotong Univ.200438(6)853–856.
10.
ManfredL. H.Martin PfurnerH.-P. S.A new and efficient algorithm for the inverse kinematics of a general serial 6R manipulator. Mech. Mach. Theory20074266–81.
11.
RavaniB.RothB.Mapping of spatial kinematics. ASME J. Mech. Transm. Autom. Des.1984106(3)341–347.
12.
McCarthyJ. M.EtzelK.Spatial motion polation in an image space of SO(4). In Proceedings of the 1996 ASME Design Technical Conference, Number 96-DETC/MECH-1164, Irvine, California, USA, 18–22 August 1996.
13.
DanillidisK.Hand-Eye calibration using dual quaternions. Int. J. Robot. Res.199918(3)286–298.
14.
GeQ. J.VarshneyA.MenonJ.ChangC.On the use of quaternions, dual quaternions, and double quaternions for freeform Motion synthesis. Mech. Des. Res.2004Z1147–150.
15.
HamiltonW. R.Elements of quaternions1860 (Reprinted by Chelsea Pub, New York in 1969).
16.
DonaldB. R.KapurD.MundyJ. L. (Ed.) Symbolic and numerical computation for artificial intelligence1992, pp. 52–55 (Academic PressOrlando, Florida).
17.
SuH. J.LiaoQ. Z.LiangC. G.Direct positional analysis for a kind of 5-5 platform in-parallel robotic mechanism. Mech. Mach. Theory199934285–301.
