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Research Papers

Application of Hyper-Dual Numbers to Multibody Kinematics

[+] Author and Article Information
Avraham Cohen

Robotics Laboratory,
Department of Mechanical Engineering,
Technion–Israel Institute of Technology,
Technion City, Haifa 32000, Israel
e-mail: avico@tx.technion.ac.il

Moshe Shoham

Robotics Laboratory,
Department of Mechanical Engineering,
Technion–Israel Institute of Technology,
Technion City, Haifa 32000, Israel
e-mail: shoham@technion.ac.il

Manuscript received January 30, 2015; final manuscript received May 1, 2015; published online August 18, 2015. Assoc. Editor: J. M. Selig.

J. Mechanisms Robotics 8(1), 011015 (Aug 18, 2015) (4 pages) Paper No: JMR-15-1019; doi: 10.1115/1.4030588 History: Received January 30, 2015

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.

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References

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Grahic Jump Location
Fig. 1

Two cylindrical, four degrees-of-freedom robot

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