*3.1.1 A hybrid flexure hinge EVC vibrator actuated by parallel piezoelectric actuator configuration*

## *3.1.1.1 Orthogonal type*

In this work, a hybrid flexure hinge EVC vibrator actuated by parallel piezoelectric actuators was proposed [8]. The mechanical structure of the vibrator is shown in **Figure 2(a)**. The coordinate system *O*out*-xyz* is fixed on the end-effector. The mechanical structure has mirror symmetry about the *y*-axis. Two piezoelectric actuators, which are placed in parallel from top to bottom and directly preloaded by two screws, are used to actuate the motion of the cutting tool. There are four motion guidance components in the mechanical structure, i.e. two double parallel four-bar linkage mechanisms and two

#### **Figure 2.**

*Illustration of the proposed hybrid flexure hinge EVC actuated by a parallel piezoelectric actuator. (a) Mechanical structure. (b) Working principle. (c) Two types of flexure hinge. (d) Deformation schematic of flexure-based mechanism. (e) FEM simulation [8].*

right circular flexure hinges. The double parallel four-bar linkage mechanism is connected in series with the right circular flexure hinges. The upper component and bottom component are connected in parallel with the end-effector beam. The working principle is shown in **Figure 2(b)**. The elliptical locus will be obtained when two electric sinusoidal signals with phase different are applied to the piezoelectric actuators.

The characteristics of the two types of flexure hinge and deformation schematic of flexure-based mechanism are shown in **Figure 2(c)** and **(d)**, respectively. Sixty-five Mn was adopted as the material of main structural components. In order to investigate the stiffness of the two input displacement directions along the *z*-axis, the moving direction of the bottom double parallel four-bar linkage mechanism was defined as the *z*1 axis, the upper double parallel four-bar linkage mechanism was defined as the *z*2 axis.
