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.

References

References
1.
Shabana
,
A. A.
, 2001,
Computational Dynamics
,
Wiley
,
New York
.
2.
Shuster
,
M. D.
, 1993, “
A Survey of Attitude Representations
,”
J. Astronaut. Sci.
,
41
(
4
), pp.
439
517
.
3.
Nikravesh
,
P. E.
, 1988,
Computer-Aided Analysis of Mechanical Systems
,
Prentice-Hall, Englewood Cliffs
,
New Jersey
.
4.
Duffy
,
J.
, 1978, “
Displacement Analysis of the Generalized RSSR Mechanism
,”
Mech. Mach. Theory
,
13
, pp.
533
541
.
5.
Chaudhary
,
H.
, and
Saha
,
S. K.
, 2007, “
Constraint Wrench Formulation for Closed-Loop Systems Using Two-Level Recursions
,”
ASME J. Mech. Des.
,
129
, pp.
1234
1242
.
6.
Denavit
,
J.
, and
Hartenberg
,
R. S.
, 1955, “
A Kinematic Notation for Lower-Pair Mechanisms Based on Matrices
,”
J. Appl. Mech.
,
22
, pp.
215
221
.
7.
Wittenburg
,
J.
, 2008,
Dynamics of Multibody systems
,
Springer
,
Berlin
.
8.
Shuster
,
M. D.
, and
Oh
,
S. D.
, 1981, “
Three-Axis Attitude Determination From Vector Observation
,”
J. Guid. Control Dyn.
,
4
(
1
), pp.
70
77
.
9.
Singla
,
P.
,
Mortari
,
D.
, and
Junkins
,
J. L.
, 2004, “
How to Avoid Singularity for Euler Angle Set?
,” Proceedings of the AAS Space Flight Mechanics Conference, Hawaii.
10.
Craig
,
J. J.
, 2006,
Introduction to Robotics, Mechanics and Control
,
Pearson Education
,
Delhi
.
11.
Khalil
,
W.
,
Kleinfinger
,
J.
, 1986, “
A New Geometric Notation for Open and Closed-Loop Robots
,”
IEEE Int. Conf. Rob. Autom.
,
3
, pp.
1174
1179
.
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