Crossable surfaces of robotic manipulators with joint limits

Citation
K. Abdel-malek et Hj. Yeh, Crossable surfaces of robotic manipulators with joint limits, J MEC DESIG, 122(1), 2000, pp. 52-60
Citations number
35
Categorie Soggetti
Mechanical Engineering
Journal title
JOURNAL OF MECHANICAL DESIGN
ISSN journal
10500472 → ACNP
Volume
122
Issue
1
Year of publication
2000
Pages
52 - 60
Database
ISI
SICI code
1050-0472(200003)122:1<52:CSORMW>2.0.ZU;2-0
Abstract
A broadly applicable formulation for determining the crossability of singul ar surfaces and curves in the workspace of serial robotic manipulators is p resented. Singular surfaces and curves al-e analytically determined using n ullspace rank-deficiency criteria of the mechanism's constraint position Ja cobian. Imposed joint limits in terms of inequality constraints are taken i nto account in the formulation. Directions of admissible normal movements o n a surface or curve are established from the analysis of the normal curvat ure of singular surfaces. The normal curvature of a parametric surface used in this formulation, is determined from the first and second fundamental f orms adapted from differential geometry. Definiteness properties of a quadr atic form developed from the acceleration analysis determine admissible nor mal movements. For singular surfaces resulting from active joint constraint s, definiteness properties are not enough and supplementary criteria are ne cessary. Two additional criteria are derived. This paper is a complete trea tment of the problem of determining whether a singular surface/curve in the workspace is crossable. Planar and spatial numerical examples are presente d to illustrate the formulation. [S1050-0472(00)01301-5].