Freedom and constraint analysis and optimization

Many mathematical and intuitive methods for constraint analysis of mechanisms have been proposed. In this article we compare three methods. Method one is based on Grüblers equation. Method two uses an intuitive analysis method based on opening kinematic loops and evaluating the constraints at the intersection. Method three uses a flexible multibody modeling approach which facilitates the analysis of complex systems. We demonstrate a visualization method using generalized von Mises stress to show overconstraint modes. A four bar mechanism and a two-degree-of- freedom (DOF) flexure-based mechanism serve as a case study. Briefly the optimization of the location and orientation of releases is discussed. The implementation of the releases in the flexure-based two DOF mechanism is presented.\u

A two-node superelement description for modelling of flexible complex-shared beam-like components

In this paper, a two-node superelement description is proposed for use in multibody models which is capable of modelling flexible complex-shaped beam-like components. Assuming that the deformations with respect to a co-rotational frame remain small, substructuring methods may be used to obtain a dynamical model with reduced mass and stiffness matrices from a linear finite element model. The development of a two-node superelement is established by linking a reduced linear finite element model with a non-linear finite beam element capable of describing large rigid body motion and small elastic deformations. This is achieved by equating their potential and kinetic energies. Two examples are included. A simulation of the spin-up motion of a flexible beam with uniform cross-section and a similar simulation in which the beam is simultaneously excited in the out-of-plane direction. Both examples show good\ud agreement with simulations obtained using non-linear finite beam elements

Langevin description of speckle dynamics in nonlinear disordered media

We formulate a Langevin description of dynamics of a speckle pattern resulting from the multiple scattering of a coherent wave in a nonlinear disordered medium. The speckle pattern exhibits instability with respect to periodic excitations at frequencies $\Omega$ below some $\Omega_{\mathrm{max}}$, provided that the nonlinearity exceeds some $\Omega$-dependent threshold. A transition of the speckle pattern from a stationary state to the chaotic evolution is predicted upon increasing nonlinearity. The shortest typical time scale of chaotic intensity fluctuations is of the order of $1/\Omega_\mathrm {max}$.Comment: 6 pages, 3 figure

Seasonal diet changes in elephant and impala in mopane woodland

Elephant and impala as intermediate feeders, having a mixed diet of grass and browse, respond to seasonal fluctuations of forage quality by changing their diet composition. We tested the hypotheses that (1) the decrease in forage quality is accompanied by a change in diet from more monocots in the wet season to more dicots in the dry season and that that change is more pronounced and faster in impala than in elephant; (2) mopane (Colophospermum mopane), the most abundant dicot species, is the most important species in the elephant diet in mopane woodland, whereas impala feed relatively less on mopane due to the high condensed tannin concentration; and (3) impala on nutrient-rich soils have a diet consisting of more grass and change later to diet of more browse than impala on nutrient-poor soils. The phosphorus content and in vitro digestibility of monocots decreased and the NDF content increased significantly towards the end of the wet season, whereas in dicots no significant trend could be detected. We argue that this decreasing monocot quality caused elephant and impala to consume more dicots in the dry season. Elephant changed their diet gradually over a 16-week period from 70% to 25% monocots, whereas impala changed diets rapidly (2-4 weeks) from 95% to 70% monocots. For both elephants and impala, there was a positive correlation between percentage of monocots and dicots in the diet and the in vitro digestibility of these forage items. Mopane was the most important dicot species in the elephant diet and its contribution to the diet increased significantly in the dry season, whereas impala selected other dicot species. On nutrient-rich gabbroic soils, impala ate significantly more monocots than impala from nutrient-poor granitic soils, which was related to the higher in vitro digestibility of the monocots on gabbroic soil. Digestibility of food items appears to be an important determinant of diet change from the wet to the dry season in impala and elephants

Temporal fluctuations of waves in weakly nonlinear disordered media

We consider the multiple scattering of a scalar wave in a disordered medium with a weak nonlinearity of Kerr type. The perturbation theory, developed to calculate the temporal autocorrelation function of scattered wave, fails at short correlation times. A self-consistent calculation shows that for nonlinearities exceeding a certain threshold value, the multiple-scattering speckle pattern becomes unstable and exhibits spontaneous fluctuations even in the absence of scatterer motion. The instability is due to a distributed feedback in the system "coherent wave + nonlinear disordered medium". The feedback is provided by the multiple scattering. The development of instability is independent of the sign of nonlinearity.Comment: RevTeX, 15 pages (including 5 figures), accepted for publication in Phys. Rev.