The Kinematics, statics and dynamics of singular configurations of mechanisms are analysed. Using Lie group theory, the tangent cone at such a configuration is defined and calculated. It is clear that the structure of the cone is directly linked with one of Lie algebra. The statics and dynamics of singularity analysis are addressed, making it possible to apply the concept of the transitory degree of mobility.
ChevallierD. P.Lie Algebras, Modules, Dual Quaternions and Algebraic Methods in KinematicsMech. Mach. Theory, 1991, 26 (6), 613–627.
4.
KargerA.Classification of robot-manipulators with only singular configurationsMech. Mach. Theory, 1995, 30 (5), 727–736.
5.
KargerA.Geometry of the motion of robot-manipulatorsManuscripta Math., 1989, 62, 115–328.
6.
HerveJ. M.Intrinsic formulation of problems of geometry and kinematics of mechanismsMech. Mach. Theory, 1982, 17 (3), 179–184.
7.
GibsonC. G.HuntK. H.Geometry of screw systems. Parts I and IIMech. Mach. Theory, 1990, 25 (1), 1–10 and 11–27.
8.
SugimotoK.DuffyJ.Application of linear algebra to screw systemsMech. Mach. Theory, 1982, 17 (1), 73–83.
9.
DaviesH.Mechanical network I, II, IIIMech. Mach. Theory, 1983, 18 (2), 95–112.
10.
LerbetJ.HaoK.Kinematics of mechanisms to the second order—application to the closed mechanismsActa Applic. Math., 1999, 59, 1–19.
11.
LerbetJ.Analytic geometry and singularities of mechanismZAMM, 1998, 78 (10), 687–694.
12.
WhitneyH.Tangents to an analytic varietyAnn. Math., 1965, 81, 496–549.
13.
HuntK. H.Kinematic Geometry of Mechanisms, 1978, p. 38 (Clarendon Press, Oxford).
14.
KuznetsovE. N.Systems with infinitesimal mobility: Parts I-II Matrix analysis and first-order infinitesimal mobilityJ. Appl. Mechanics, June 1991, 58, 513–519 and 520–526.
