Elastic motion

Tirion, M. (1996) Large Amplitude Elastic Motions in Proteins from a Single-Parameter, Atomic Analysis. Phys. Rev. Lett. 77,1905-1908. 

Tirion, M.M. (1996) Large amplitude elastic motions in proteins from a single-parameter, atomic analysis. Physical Review Letters, 77 (9), 1905-1908. 

A typical AE sensor of PZT element transforms elastic motions of 1 pm displacement into electrical signals of 1 pV voltage. As an example, frequency responses of AE sensors commercially available are given in Fig. 3.8. 

The. motion equation of gel (as an elastic motion) (Equation 22.1 in Landau and Lifshitz, 1987) comprises an additional term owing to the friction forces ari.sing when liquid moves over the elements of a polymer framework (Tanaka et al., 1973)... 

Elastic motion implies that the atoms of the matrix fluctuate about their... 

We follow Debye s approach [51], suggested many years ago for analyzing the thermal vibrations in solids, and approximate W( A ) by the assumption of isotro elastic motion in the following form [ ]... 

Of course, the elastic motion of the chain molecules is anisotropic and a refinement might be to consider a 3N x 3N smearing tensor which describes the elastic fluctuations of the atomic positions. Nevertheless, we tend to think that the simple approximation of Eq. (11) is enough in order to study the fundamentals involved in the transport of gas molecules through solid polymers. 

A Guest Molecule in a Matrix with Isotropic Elastic Motion... 

The isotropic approximation to elastic motion makes the treatment remarkably simple by converting the evaluation of the solute distribution function p(r) to a trivial multiplication of independent terms describing the pair interaction between the solute molecule and the polymer atoms localized at their average positions . A set of mean positions describes the structure of the... 

The isotropic elastic motion of the polymer matrix is specified by the spectrum of the . In the homogeiKous apjHoximation we n ect the differences between the amplitudes of elastic motkm of different polymer atoms and describe the elastic motion of all polymer atoms with an identical smearing factor . One would expect to assume a value similar to the... 

The smearing factor . To start the TSA simulation one needs to specify the smearing factor . We can surmise that, at ambient conditions, tte value rf A > should be some fractions of an A and should not be very sensith to the chemical details of the polymer matrix. On the other hand, pven tte abo approximations involved in describing the elastic motion erf polyn r atoms, a universal method for evaluating can hardly be expected tte re icher should rather rely on intuition and experience in order to specify a suitable value of for the problem at hand. Two possibilities are reviewed in the following. 

Living animals show elastic motions with flexible bodies [1, 2, 3, 4]. Cheetah runs at full speed after the prey, bending its backbones like an arch. Dolphins flip over while fl3dng out of the water. These vertebrates are elastic while invertebrates like mollusks have more flexible bodies. Starfishes fold their bodies for turning over. Octopus twists objects with their tentacles. Jell3dishes swim in the... 

The elastic motions of each link are referred to the position of the undeformed corresponding link. 

The variational equations of motion are developed for flexible serial manipulators with rotary joints which account for full coupling between the rigid body motion and link deformation. Velocity and acceleration transformation equations are developed to conveniently transform Cartesian space equations into Joint space. Small deformation is assxamed such that vibration modal coordinates and mode shapes can represent the elastic motion of the flexible links. Flexibility and mass properties of the links are obtained by finite element method. A case study of an industrial robot is presented to show the effect of bending and torsional vibrations on end-effector motion. 

In this paper an approximate method to find out the kineto-elastodynamic acceleration of an elastic coupler of a four-bar linkage produced due to elastic motion of the coupler is explained. A comparison of rigid body acceleration with the resultant acceleration of the elastic link is also made. The results (in MKS units) clearly indicate the importance of considering KED effects while designing high-speed linkages with elastic links. 

The elastic motion in the transverse direction of any point on the coupler as given in Eq. (1) above, is rewritten as... 

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