This article proposes a new algorithm of quaternion and dual quaternion in matrix form. It applies quaternion in special cases of rotated plane, transforming the sine and cosine of the rotation angle into matrix form, then exporting flat quaternions base in two matrix form. It establishes serial 6R manipulator kinematic equations in the form of quaternion matrix. Then five variables are eliminated through linear elimination and application of lexicographic Groebner base. Thus, upper bound of the degree of the equation is determined, which is 16. In this way, a 16-degree equation with single variable is obtained without any extraneous root. This is the first time that quaternion matrix modeling has been used in 6R robot inverse kinematics analysis.
References
[1]
Liao, Q.Z. and Liang, C.G. (1993) Synthesizing Spatial 7R Mechanism with 16-Assembly Configurations. Mechanisms and Machine Theory, 28, 715-720. https://doi.org/10.1016/0094-114X(93)90010-S
[2]
Qiao, S., Liao, Q., Wei, S. and Su, H.J. (2010) Inverse Kinematic Analysis of the General 6R Serial Manipulators Based on Double Quaternions. Mechanism and Machine Theory, 45, 193-197. https://doi.org/10.1016/j.mechmachtheory.2009.05.013
[3]
Huang, X.G. and Liao, Q.Z. (2010) New Algorithm for Inverse Kinematics of 6R Serial Robot Mechanism. Journal of Beijing University of Aeronautics and Astronautics, 36, 295-298.
[4]
Gan, D., Liao, Q., Wei, S., Dai, J.S. and Qiao, S. (2008) Dual Quaternion-Based Inverse Kinematics of the General Spatial 7R Mechanism. Journal of Mechanical Engineering Science, 222, 1593-1598. https://doi.org/10.1243/09544062JMES1082
[5]
Goodson, G.R. (1997) The Inverse-Similarity Problem for Real Orthogonal Matrices. American Mathematical Monthly, 104, 223-230. https://doi.org/10.2307/2974787
[6]
Stephen, J., Wine, S. and Le Bihan, N. (2006) Quaternion Singular Value Decomposition Based on Bidiagonalization to a Real or Complex Matrix Using Quaternion Householder Transformations. Applied Mathematics and Computation, 128, 727-738.
[7]
Ni, Z.S., Liao, Q.Z., Wei, S.M. and Li, R.H. (2009) Dual Four Element Method for Inverse Kinematics Analysis of Spatial 6R Manipulator. Journal of Mechanical Engineering, 45, 25-29. https://doi.org/10.3901/JME.2009.11.025
[8]
Ni, Z.S. (2010) A Study of Geometric Algebro Method on Some Issues for Kinematrics of Mechanisms. Beijing University of Posts and Telecommunications, Beijing.
