The set of all points in space that are occupied by points in the working body of a mechanism or manipulator, for some kinematically admissible configuration, is defined as its operational envelope. Criteria for points on the boundary of the operational envelope of working bodies with smooth boundaries are developed, for both parametric and equation representations of domains and boundaries of working bodies, in two-and three-dimensional space. The criteria derived involve kinematic constraint equations for the underlying mechanism and equations that characterize the shape of the working body. A row rank deficiency condition is derived as a criterion for the boundary of the operational envelope, and numerical methods based on this condition for mapping the boundary are presented. Examples involving a planar Stewart platform with a dome attached and the wheel assembly of a vehicle suspension system in three dimensions are analyzed numerically.

1.
Allgower, E. L., and Georg, K., 1990, Numerical Continuation Methods, Springer-Verlag, Berlin,
2.
Dongarra, J. J., Moler, C. B., Bunch, J. R., and Stewart, G. W., 1979, LINPACK Users’ Guide, SIAM, Philadelphia.
3.
Freudenstein
F.
, and
Primrose
E. J.
,
1984
, “
On the Analysis and Synthesis of the Workspace of a Three-Link, Turning-Pair Connected Robot Arm
,”
ASME JOURNAL OF MECHANISMS, TRANSMISSIONS, AND AUTOMATION IN DESIGN
, Vol.
106
, pp.
365
370
.
4.
Haug, E. J., 1989, Computer Aided Kinematics and Dynamics of Mechanical Systems, Allyn and Bacon, Boston.
5.
Haug
E. J.
,
Luh
C. M.
,
Adkins
F. A.
, and
Wang
J. Y.
,
1996
, “
Numerical Algorithms for Mapping Boundaries of Manipulator Workspaces
,”
ASME JOURNAL OF MECHANICAL DESIGN
, Vol.
118
, pp.
228
234
.
6.
Jo
D. Y.
, and
Haug
E. J.
,
1989
, “
Workspace Analysis of Multibody Mechanical Systems Using Continuation Methods
,”
ASME JOURNAL OF MECHANISMS, TRANSMISSIONS, AND AUTOMATION IN DESIGN
, Vol.
3
, No.
4
, pp.
581
589
.
7.
Kumar
A.
, and
Waldron
K. J.
,
1981
, “
The Workspaces of a Mechanical Manipulator
,”
ASME JOURNAL OF MECHANICAL DESIGN
, Vol.
103
, pp.
665
672
.
8.
Luh, C. M., Haug, E. J., and Wang, J. Y., 1995, Operational Envelope of a Vehicle Suspension System, Technical Report R-196, The University of Iowa, Iowa City,
9.
Spanos
J.
, and
Kohli
D.
,
1985
, “
Workspace Analysis of Regional Structures of Manipulators
,”
ASME JOURNAL OF MECHANISMS, TRANSMISSIONS, AND AUTOMATION IN DESIGN
, Vol.
107
, pp.
216
222
.
10.
Tsai
Y. C.
, and
Soni
A. H.
,
1981
, “
Accessible Region and Synthesis of Robot Arms
,”
ASME JOURNAL OF MECHANICAL DESIGN
, Vol.
103
, pp.
803
811
.
11.
Yang
D. C. H.
, and
Lee
T. W.
,
1983
, “
On the Workspace of Mechanical Manipulators
,”
ASME JOURNAL OF MECHANISMS, TRANSMISSIONS, AND AUTOMATION IN DESIGN
, Vol.
105
, pp.
62
69
.
12.
Yang
F. C.
, and
Haug
E. J.
,
1994
, “
Numerical Analysis of the Kinematic Working Capability of Mechanisms
,”
ASME JOURNAL OF MECHANICAL DESIGN
, Vol.
116
, pp.
119
125
.
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