Hyper-dual numbers (HDNs) are applied in this paper to multibody kinematics. First, the hyper-dual angle that encompasses a body's position, orientation, as well as its velocity, is defined as an element of the hyper-dual transformation matrix. Then, the “automatic differentiation” feature of the dual numbers is used to obtain the second derivative of a body pose. The body's velocity and acceleration are obtained from the elements of the hyper-dual transformation matrix by algebraic manipulations only, with no need for further time derivatives of the body pose. A robot manipulator is presented as an exemplary application of HDNs to multibody kinematics.
Application of Hyper-Dual Numbers to Multibody Kinematics
Manuscript received January 30, 2015; final manuscript received May 1, 2015; published online August 18, 2015. Assoc. Editor: J. M. Selig.
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Cohen, A., and Shoham, M. (August 18, 2015). "Application of Hyper-Dual Numbers to Multibody Kinematics." ASME. J. Mechanisms Robotics. February 2016; 8(1): 011015. https://doi.org/10.1115/1.4030588
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