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Research Papers

Denavit-Hartenberg Parameterization of Euler Angles

[+] Author and Article Information
S. V. Shah

Department of Mechanical Engineering,  Indian Institute of Technology Delhi, New Delhi 110016, Indiasurilvshah@gmail.com

S. K. Saha

Department of Mechanical Engineering,  Indian Institute of Technology Delhi, New Delhi 110016, Indiasaha@mech.iitd.ac.in

J. K. Dutt

Department of Mechanical Engineering,  Indian Institute of Technology Delhi, New Delhi 110016, Indiajkdutt@mech.iitd.ac.in

J. Comput. Nonlinear Dynam 7(2), 021006 (Jan 06, 2012) (10 pages) doi:10.1115/1.4005467 History: Received May 23, 2011; Accepted November 18, 2011; Revised November 18, 2011; Published January 06, 2012; Online January 06, 2012

Euler angles describe rotations of a rigid body in three-dimensional Cartesian space, as can be obtained by, say, a spherical joint. The rotation carried out by a spherical joint can also be expressed by using three intersecting revolute joints that can be described using the popular Denavit-Hartenberg (DH) parameters. However, the motions of these revolute joints do not necessarily correspond to any set of the Euler angles. This paper attempts to correlate the Euler angles and DH parameters by introducing a concept of DH parameterization of Euler angels. A systematic approach is presented in order to obtain the DH parameters for any Euler angles set. This gives rise to the concept of Euler-angle-joints (EAJs), which provide rotations equivalent to a particular set of Euler angles. Such EAJs can be conveniently used for the modeling of multibody systems having multiple-degrees-of-freedom joints.

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Copyright © 2012 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Rotation about the Y axis

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Figure 2

Equivalent transformations

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Figure 3

A universal joint represented by two intersecting revolute joints

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Figure 4

Representation of DH frames for YZ EAJs

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Figure 5

A spherical joint represented by three intersecting revolute joints

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Figure 6

Representation of DH frames for ZYZ EAJs

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Figure 7

Representation of DH frames for XYZ EAJs

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Figure 8

ZYZ Euler angles

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Figure 9

The Denavit and Hartenberg (DH) parameters and frames

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