**2.5 Numerical results and structural design**

**Figure 2** shows that the design domain is divided into 64 48 square four node elements, the side length of the element is 1, and the structural dimensions and material units are dimensionless. Based on the practical engineering experiments, the parameters in topology optimization model are chosen as follows: the volume fraction *V <sup>f</sup>* is set to 0.2, *τ* <sup>∗</sup> is set to 104, and the input stiffness *kin* and output stiffness *kout* in Eq. (6) are chosen as 10 and 0.001, respectively. and the input force is a unit force. For more details, we refer readers to Refs. [25, 40].

**Figure 4** shows that the evaluation indicator *τ* decrease significantly with the increase of iteration number. Therefore, the first constraint restriction in Eq. (4) markedly eliminates the effect of parasitic displacement *uy out* on the output displacement *ux out*. As shown in **Figure 5**, the displacement magnification factor *λ* raises with the increases of iteration number. With the continuous updating of design variables, the related topology optimization results are gradually converged.

**Figure 4.**

*The relationship between the iteration number and evaluation indicator τ.*

*Topology Optimization Methods for Flexure Hinge Type Piezoelectric Actuators DOI: http://dx.doi.org/10.5772/intechopen.103983*

**Figure 6** shows the topology optimization result, which is similar to the traditional four-bar mechanism, and the positions of the four flexure hinges and the tilt angles of the beams will be the main consideration in the mechanism design. Due to the gray unit in the topology image and the inaccurate contour extraction, the details of the hinges and boundaries of the structure are modified. **Figure 7** showns the main parameters of the driving mechanism, the overall dimension of the flexure hinge mechanism is 32 mm 32 mm 9 mm, and an indenter with radius of 2.5 mm is

**Figure 7.** *Structural parameters of the driving mechanism. (unit: mm).*

selected to ensure that the driving mechanism can provide sufficient contact. The thicknesses of the four special-shaped flexure hinges are 0.3 mm, 0.3 mm, 0.4 mm and 0.4 mm, respectively.
