A sequential design procedure is explained, whereby two arms are designed first to satisfy workspace requirements, then the third arm is designed to provide a singularity-free workspace.
We illustrate the added value and the complementary information provided by singularity theory with one distinguished parameter.
Of particular interest is the S1IS2 configuration, as it provides "sharp" singularity at eV = Δ1(T) + Δ2(T), which is almost temperature independent in the low-T limit T << T c1,2.
However, even though the shift value is an eigenvalue of the system, the proposed method provides non-singularity, and that is analytically proved.
It has been proposed that the unfolding of this singularity could provide a minimal model to understand neuronal excitability and its modulation [30, 31], or a qualitative model for a cortical mass [32].
This paper extends previous studies made for sectorial plates having re-entrant (i.e., interior) corners causing stress singularities, to provide accurate frequencies when the circular edge is either clamped or simply-supported.
The results provide algebraic expressions for the singularity conditions, in terms of some bracket monomials obtained from the superbracket decomposition.
Different from the equation studied in [6, 16], which is only singular at (x=0), equation (1.4) is provided with both singularities at (x=+infty) and at (x=0).
Among all these approaches, the shearlet transform stands out because it is related to group theory, and it has a flexible enough extension to precisely detect the position and orientation of singularities and to provide optimally sparse representations.
Moreover, the continuous and accurate computation of the mechanism configuration in the vicinity of singularities provides detailed information about the kinematic behavior of the mechanism in its extreme positions.
