Abstract
This paper introduces a new formation of rotation, which is developed with two non-parallel vectors. A transformation matrix, called extended rotation matrix (ERM), is thus formulated. In particular, the matrix contains two known vectors from one body and their cross product, with which all other vectors or points in the same body can be uniquely described by a set of values associated with the matrix, namely, their alternative coordinates. Using ERM and alternative coordinates, kinematic equations of pointing mechanisms can be formulated uniquely and conveniently, without any redundancy of parametrization. A case study of pointing mechanisms is included to demonstrate the advantage of the new formulation.
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Bai, S. (2022). Extended Rotation Matrix for Kinematics of Pointing Mechanisms. In: Altuzarra, O., Kecskeméthy, A. (eds) Advances in Robot Kinematics 2022. ARK 2022. Springer Proceedings in Advanced Robotics, vol 24. Springer, Cham. https://doi.org/10.1007/978-3-031-08140-8_5
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DOI: https://doi.org/10.1007/978-3-031-08140-8_5
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