Rigid-body analysis

Fig. 5. Rigid-body analysis of citrate synthase, using two X-ray structures (after Hayward and Berendsen, Proteins 30 (1998) 144). The decomposition of the protein into two domains (dark gray and white) and two interconnecting regions (light gray) is shown, together with the hinge axis for the closing/opening motion between them.

Ghose S., Schomaker V., and McMullan R.K., "Enstatite, Mg2Si20g A Neutron Diffraction Refinement of the Crystal Structure and a Rigid-Body Analysis of the Thermal Vibration," Z. Kristallogr., 176, 159-75 (1986). 

Most of the work in mechanism deformation analysis is based on the linear theory of elasticity [1-5]. In most of these, a kinematics and rigid body analysis is used to solve for the gross body motion and the inertial forces. By employing different techniques, the elastic deformations are then found by applying these inertial forces as externally applied forces to the linear elasticity problem. The small elastic deformations are superimposed onto the gross motion in order to predict the total motion of each link in the system. 

Figure 3 shows the results of the rigid body analysis. The slip path ABCD is elliptical and has maximum interference at point A. There is no contact possible along the path BCD because the surfaces are separated. It is noted that the displacements depend only on the orientation of the tooth with respect to its local pressure angle and of the instantaneous misalignment vector. Therefore, all teeth in the coupling experience the same displacement history as the shaft rotates under a constant misalignment. 

Hayward et al. 1994] Hayward, S., Kitao, A., Go, N. Harmonic and anharmonic aspects in the dynamics of BPTI A normal mode analysis and principal component analysis. Prot. Sci. 3 (1994) 936-943 [Head-Gordon and Brooks 1991] Head-Gordon, T., Brooks, C.L. Virtual rigid body dynamics. Biopol. 31 (1991) 77-100... 

These operations do not occur separately and in any particular sequence but are simply a convenient way to conceptualize the transformation as a series of operations, each of which can be analyzed separately, but which working together produce a martensitic structure containing an invariant plane. As such, they can be imagined to occur in any sequence. For purposes of analysis, it is convenient to imagine that the lattice-invariant deformation occurs first, followed by the lattice deformation, followed finally by the rigid-body rotation. We now show that a lattice-invariant shear by slip followed by the lattice deformation analyzed above can produce an undistorted plane. 

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