## 1 Introduction  
In recent years, micro coordinate measuring machine (CMM) has become a research hotspot in the field of nanometer-measuring technology. Micro-CMM is a universal and primary tool used in true 3D nano-measurement of micro-devices, such as micro-electro-mechanical systems, ultra-precision mechanical components, and ultra-precision optical devices. The 3D nano-trigger technology is a key point in micro-CMM. As a key element of micro-CMM, nano-probes are being developed on the basis of different operating principles. Rigid contact method is one of the most commonly used methods. For example, the probe based on capacitive sensors developed by NPL [1] has a resolution of 3 nm and probing force of 0.2 mN. The deflections of the flexures are measured by capacitance sensors inside this probe. The probe based on inductive sensors developed by METAS [2; 3] has a resolution of less than 1 nm and probing forces of less than 0.5 mN. The translational motion is separated into its XYZ components, which are measured by three inductive sensors. A silicon-based nano-probe designed by Eindhoven University of Technology [4; 5] has a resolution of about 1 nm and probing force of less than 1 mN. The probe stylus is attached to three silicon elastic elements with embedded piezoresistive strain gauges for sensing the deflection. A tactile-optical fiber probe used by PTB and TU Braunschweig [6; 7; 8] has a resolution of about 1 nm. Different from the previous deflection detection methods, the deflection of the fiber probe in the \(X\) and \(Y\) directions is detected by the camera system. Owing to the low stiffness of the optical fiber and the special detection method, the probing force is approximately 1 uN to 100 uN. This fiber probe can only achieve 2D measurement. The high aspect ratio fiber probe based on a fiber Bragg grating (FBG) developed by the Harbin Institute of Technology can achieve 3D measurement with a radial resolution of 5 nm and an axial resolution of 8 nm [9; 10]. A touch-trigger probe developed by HFUT [11] has a repeatability of better than 5 nm. A long-stroke 3D contact scanning probe developed by HFUT [12; 13] has a contact force gradient within 0.5 mN/um, a measuring range of 20 um, and a measurement standard deviation of 30 nm. In these contact probes mentioned above, the stiffness of the elastic elements should be carefully designed because of the mechanical deformation of the stylus and the damage of the sample surface caused by probing force. To avoid this contradiction, some probes based on non-contact triggering methods have been proposed. Optical method is one of the representatives, but it is easily affected by the characteristics of the sample surface (such as color, roughness, reflectivity, etc.). For example, the ViScan optical probe system--which is composed of a camera sensor and an objective lens--has a measurement repeatability of less than 200 nm [14]. The laser-trapper probe [15; 16; 17] developed by Osaka University has a vertical resolution of about 10 nm. Besides optical methods, many novel probes have also been developed. For example, a probing system based on a spherical capacitive sensor [18] was proposed by Harbin Institute of Technology. This probe can achieve 3D non-contact probing with resolution better than 5 nm. The use of the non-contact method is becoming increasingly popular owing to the fast measurement speed and no contact force. However, non-contact probes are unable to offer high resolution and accessibility to the contact one. To reduce the contact probing force, a vibrating tactile probe [19; 20] consisting of a triskelion device and a micro-stylus was developed by NPL, and has a probing force of nearly zero. A new variable stiffness probing system [21] designed by the University of Nottingham has the overall uncertainty of 58 nm for three-dimensional displacement measurement. This novel probe allows two probe stiffness values to be defined and switched between.