**3.4 Instable deformation behaviour of compliant mechanisms: Bifurcation**

Situations with bifurcation of structures are avoided systematically in engineering. The following theoretical analyses reveal some opportunities to apply this behaviour profitably to a technical system.

The best known examples for the loss of stability under static loads are the Eulerian cases of stability. For loads under the critical level, the equilibrium is determinate, whereas at the critical level of loads, bifurcations in the solutions occur to state equations. The solutions are no longer bijective, one load situation may lead to more than one possible geometric configurations of the system. Such structures are shown in Figure 11. Herein, the load is generated by the attraction force of the filaments e.g. SMA-wires or by the low-pressure in cavities. If the wires are uniformly pulled or the cavities possess the same low-pressure, the classical Euler stability problem (bifurcation) is regarded as replacing the named rotationally drive configuration by an axial acting force.

The following statement explains how the bifurcation effect can be used profitably. The response of a systematically designed system with bifurcation behaviour (deformation or displacement in several directions) on external (e.g. temperature change) or on user-defined conditions leads to one preferred direction. The deformation direction is selected "autonomously" whereas the drive regime for each process always remains the same. The sensory and control effort are minimised enormously. The control of the system is partly adopted by "intelligent" mechanics.

Fig. 11. Structures among the influence of an axial load which is generated by the attraction force of the filaments or Shape-Memory-Alloy-wires (a) and by the low-pressure in cavities (b, c)

Figure 12 exemplifies this phenomenon in the case of a half-cycle shaped bending beam subject to loading by a single force with constant direction (conservative force) but with a 2D-free floating location of the site of application under load. Two possible trajectories of this point and two realisations of the equilibrium are illustrated. Solutions have been determined numerically, a current application is the design of compliant grasping devices.

Fig. 12. Equilibrium situations of a half-cycle shaped beam under external load; A force constant in amount and directions traces the free end of the beam
