Precision-point synthesis problems for design of four-bar linkages have typically been formulated using two approaches. The exclusive use of path-points is known as “path synthesis,” whereas the use of poses, i.e., path-points with orientation, is called “rigid-body guidance” or the “Burmester problem.” We consider the family of “Alt–Burmester” synthesis problems, in which some combination of path-points and poses is specified, with the extreme cases corresponding to the classical problems. The Alt–Burmester problems that have, in general, a finite number of solutions include Burmester's original five-pose problem and also Alt's problem for nine path-points. The elimination of one path-point increases the dimension of the solution set by one, while the elimination of a pose increases it by two. Using techniques from numerical algebraic geometry, we tabulate the dimension and degree of all problems in this Alt–Burmester family, and provide more details concerning all the zero- and one-dimensional cases.
Computing the real solutions to a system of polynomial equations is a challenging problem, particularly verifying that all solutions have been computed. We describe an approach that combines numerical algebraic geometry and sums of squares programming to test whether a given set is "complete" with respect to the real solution set. Specifically, we test whether the Zariski closure of that given set is indeed equal to the solution set of the real radical of the ideal generated by the given polynomials. Examples with finitely and infinitely many real solutions are provided, along with an example having polynomial inequalities.
Surface acoustic wave band gaps in a diamond-based two-dimensional locally resonant phononic crystal for high frequency applicationsWe present a complete analysis on the possibility of exciting and observing the intrinsic localized modes (ILMs) in a crystalline linear array of nano pillars. We discuss the nano-fabrication techniques for these arrays and visualization procedures to observe the real-time dynamics. As a consequence, we extend previous models to the study of two dimensional vibrations to be consistent with these restrictions. For these pillars, the elastic properties and hence the dynamics depend on the pillar's shape and the orientation of the crystal axes. We show that ILMs do form in the system, but their stability, defect pinning, and reaction to friction strongly depend on the crystals properties, with the optimal dynamics only achieved in a rather small region of the parameter space. We also demonstrate fabrication techniques for these pillars and discuss the applications of these pillar arrays to sensing. V C 2012 American Institute of Physics. [http://dx.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.