Double Matrix Representation Method for the Spatial Rigid Body Transformation

doi:10.3901/JME.2022.13.089

Abstract

Abstract: The representation of the spatial rigid body transformation for the robotic mechanisms is one of the important contents in kinematic analysis. The representation method plays a key role in the performance analysis of such mechanisms and whether or not the formulations and solutions to the kinematic analysis are readily obtained depending on the selective methods. In analogy with the mapping relationship between the double quaternion and the dual quaternion, the double matrix representation method for the spatial rigid body transformation is presented and derived based on the dual-number matrix. The double matrix method operates on lines in space and represents the pose transformation of the rigid body. The relationships among three representation methods such as 4D rotational matrices, double quaternions and double matrices for the spatial rigid body transformation as the limit of four-dimensional rotation transformation are derived in detail. The translation transformation of the rigid body is represented with the rotation transformation in the four-dimensional space by applying the three representation methods. Furthermore, the translational and rotational displacements of the rigid body are scaled and therefore they are compared in a physical scheme.

Key words: spatial rigid body transformation, dual matrices, double matrices, 4D rotational matrices, dual quaternions

CLC Number:

TH112

ZHANG Ying, HUANG Qineng, LIAO Qizheng, WEI Shimin. Double Matrix Representation Method for the Spatial Rigid Body Transformation[J]. Journal of Mechanical Engineering, 2022, 58(13): 89-100.

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