ti (i = 0, 1 , 2, 3)	Time point of cutting process
h	The maximum depth of cut (μm)
α	Rotation angle of Plane 1 (°)
β	Rotation angle of Plane 2 (°)
γ	The angle between the movement direction of tool on workpiece and the cutting direction (°)
Pi (i = 1, 2, 3)	Position point of cutting process
z, y1, y2	The ideal vibration displacement in Z, Y1 and Y2 directions of tool tip, respectively (μm)
A1, A2, A3	Amplitudes of driving singles in Z, Y1 and Y2 directions, respectively (μm)
ω1, ω2, ω3	Angular frequency in Z, Y1 and Y2 directions, respectively (Hz)
φ1, φ2, φ3	Phase in the driving signals along Z, Y1 and Y2 directions, respectively
t	Time (s)
z’, y1’, y2’	The real displacement of three piezoelectric stacks (μm)
θ	The phase difference between two piezoelectric stacks installed parallel on hinge platform (°)
l1, l2	The vertical distance from the driving point implemented on the flexible hinge along the Y1 and Y2 directions to the plane paralleled to the flexible hinge along the Z direction of diamond tool, respectively (mm)
l	The linear distance from tool tip point to the plane of the two piezoelectric stacks in Y1 and Y2 directions (mm)
xt, yt, zt	Spatial coordinate system
f2D, f3D	Vibration frequency in 2D-EVC and non-resonant 3D-EVC methods, respectively
D, S, F	Depth of cutting, cutting speed and feed rate, respectively
A	Vibration amplitude