## 2 Basic Structure and Key Technologies  
### Basic Structure  
The schematic structure of the developed micro CMM is shown in Figure 1a. The measuring probe (1) is located under a granite column which is fixed on the granite base (5). The tip-ball of the stylus probe is placed at the center of the \(XYZ\) three-dimensional (3D) stage (2) and kept still after assembly. The sample is mounted on a moving table of the 3D stage and can be moved in \(X\), \(Y\) and \(Z\) directions together with the stage. Two deadweight balance systems (4) are connected to the 3D stage and the granite base. They can transfer the deadweight of the 3D stage to the granite base. The position of each axis is measured by the corresponding laser interferometer (3). The reflection mirrors (7) and (8) of \(X\)- and \(Y\)-interferometers are fixed on two of the lateral sides of \(Y\)-stage. The reflection mirror of \(Z\)-interferometer is mounted on the bottom of \(Z\)-stage. The \(Z\)-interferometer and its reflection mirror are concealed and invisible in Figure 1. Figure 1b shows the photography of the main mechanical assembly of the developed micro CMM which is located in a thermostatic chamber isolated on an anti-vibration base.  
Abbe principle is the basis for all linear instrument designs. It is easy to obey the Abbe principle in a one-dimensional measurement but difficult to satisfy in all directions for a multi-dimensional measurement system. In conventional CMMs, measuring scales are always mounted on one side of each stage so that their metrological systems do not follow the Abbe principle. Abbe errors in conventional CMMs have to be reduced by well manufacture, fine adjustment in fabrication and error correction after assembly. However, limited by these efforts, the metrological systems of the  
Figure 1: (**a**) schematic structure of the micro CMM (Coordinating Measuring Machines). (**b**) the photography of the mechanical assembly of the developed micro CMM. 1: Measuring probe, 2: \(XYZ\) stage, 3: \(Y\)-interferometer, 4: Deadweight balance, 5: Granite base, 6: \(X\)-interferometer, 7: Reflection mirror of \(X\)-interferometer, 8: Reflection mirror of \(Y\)-interferometer.  
conventional CMMs have difficulty achieving measurement accuracy better than 100 nm due to Abbe errors.  
In order to follow the Abbe principle, a special structural design different from conventional CMMs is identified, as shown in Figure 2. The reflection mirrors (10) and (11) of \(X\)- and \(Y\)-interferometers are fixed on two of the vertical sides of the \(Y\)-stage (8). The reflection mirror of \(Z\)-interferometer (9) is mounted under the bottom of \(Z\)-stage (9). It can be seen that the length reference lines (represented by laser beams) of three axes (\(X\), \(Y\), \(Z\)) are perpendicular to each other and intersect at one fixed point, which is corresponding to the measuring point of the CMM. In addition, the \(X\)-guideway (5) and \(Y\)-guideway (7) are placed at the same height level and coincident with the reference plane (common plane) which is constructed by \(X\)-\(Y\) reference lines. All the guideways use roller bearing. The \(X\)-stage (6) and \(Y\)-stage (8) constitute a co-planar structure. These key components will be described in detail as follows.