When a force is applied to the output of a conforming mechanism, it causes not only a deformation in the output direction, but also a deformation in the input direction. This deformation at the input has an effect that corresponds to a force that is transmitted to the output, even if no load is applied to the input. Essentially, lemma 1 says that the effective stiffness due to this backward and forward transmission, s32/s1, will always be less than the output stiffness of the input voltage s2. Figure 3.10. Order of the “real” and “virtual” material criteria domains for a compliant mechanism design case that shows the criterion threshold and the quantities of materials to be reorganized. Another example of a conforming mechanism is that of Figure 1.10(a), which represents a piezoelectric displacement gain device. Figure 1.10 b) is the schematic representation of the actual mechanism in which the bending hinges are replaced by conventional point-shaped rotation joints. The diagram shows that the input of the two piezoelectric actuators (PZT) is doubly amplified by means of two lever stages. The mechanism is stretched to the center of the base and moved above it, as shown in Figure 1.10 (a), and can deform and move freely in a plane parallel to the base plane. In the case of a single input-output compliant mechanism, the objective is to maximize the MPE. Therefore, MIMO requires the same process of adding and removing items shown in Fig. 3.10, that is, the elements with the highest elementary criterion value are those that need to be added and removed from the real and virtual design domains.

Nature provides an example of how problems can be solved effectively with small-scale movement. Most moving components in nature are flexible instead of rigid, and the movement comes from bending flexible parts instead of rigid parts. Perhaps the greatest challenge is the relative difficulty of analyzing and designing compliant mechanisms. Knowledge of methods of analyzing the mechanisms and distraction of flexible limbs is required. Combining the two sets of knowledge in conforming mechanisms requires not only an understanding of both, but also an understanding of the interactions of the two in a complex system. The pseudo-rigid body model (see below) helps to bridge this gap. In addition to the somewhat classic examples for the dynamics of technical systems, several applications in the fields of conformal mechanisms and MEMS or NEMS are discussed in this text. This book shows that under normal circumstances, simple applications of conformal mechanisms and MEMS can be reduced to (mostly) linear systems similar to other established examples of system dynamics. Each conforming mechanism has a positive definitive mittance matrix. Therefore, the determinant for each layer is s1kks2−ks32>0. Because each feasible nested actuator contains a finite number of conforming mechanisms, the continuous fractional expansion ends.

Let`s refer to the sequence of continuous fractional extensions for the agglomerated stiffness at the outlet of each layer, starting with the innermost layer, such as zk. The zero term of the sequence, z0, is constant. Since stiffness is derived from a passive elastic material, z0 is positive and all elements of the immitance matrix are positive. We can express the remaining terms of the sequence through the recursive relationship: Conformal mechanisms are monolithic structures that use their flexible structures to transfer the movement or force of an actuator (Ouyang et al., 2008). The conformal mechanism shown in Figure 9 shows that we can design a constrained elastic body that deforms in the desired way in response to the mechanical forces exerted on it. When this conforming mechanism is interpreted as a building block in the microstructure of a material, and when this building block is periodically repeated to create a material, new and unusual properties can be obtained. These are variously called periodic micromechanics (Ananthasuresh 2003, chapter 7), metamaterials or simply custom materials with a constructed periodic microstructure. The associated topological synthesis techniques are similar to those described above, except for periodic boundary conditions and the calculation of the averaged (or homogenized) effects of a repetitive building block. Although this idea of systematic synthesis and fabrication of microstructure may seem rather esoteric in microsystems, there is certainly an opportunity to improve performance.