Abstract:
A laser measurement system for measuring up to 21 geometric errors, in which a six-degree-of-freedom geometric error simultaneous measurement unit and a beam-turning unit are mounted on either the clamping workpiece or the clamping tool, while an error-sensitive unit is mounted on the remaining one, the beam-turning unit has several switchable working postures and multi-component combinations in its installation state, it can split or turn the laser beam from the six-degree-of-freedom geometric error simultaneous measurement unit to the X, Y, and Z directions in a proper order, or the beam-turning unit can split or turn a beam from the error-sensitive unit to the six-degree-of-freedom geometric error simultaneous measurement unit. The present invention is of simple configuration and convenient operation. Up to 21 geometric errors of three mutual perpendicular linear motion guides are obtained by a single installation and step-by-step measurement.

Description:
FIELD OF THE INVENTION 
       [0001]    The present invention relates to a laser measurement system and method for measuring up to 21 GMEs (geometric motion errors), which is used to an accuracy measurement for precise machining and measuring equipment, such as a numerical control machine tool, a machining center or a coordinate measuring machine. The field of the invention pertains to the dimensional geometric accuracy measurement, particularly to a laser measurement system and method for measuring the 21 GMEs of three mutual perpendicular linear motion guides of the equipment listed above by a single installation and step-by-step measurement. 
         [0002]    The 21 GMEs include the 6 GMEs of the X-axis, the 6 GMEs of the Y-axis, the 6 GMEs of the Z-axis, the perpendicularity error between the X-axis and the Y-axis, the perpendicularity error between the Y-axis and the Z-axis, and the perpendicularity error between the X-axis and the Z-axis. 
       BACKGROUND OF THE INVENTION 
       [0003]    DE10341594A1 discloses a method for directly measuring the geometric errors of the numerical control machine tool, the machining center or the coordinate measuring machine. The beam from the laser interferometer is splitted to be parallel to the three linear motion axes of the equipment listed above. The laser interferometer directly measures the geometric errors of the three linear motion axes. However, the system configuration is complicated, and the assembly and adjustment of the system is difficult. Moreover, the roll error of the three linear motion axes cannot be measured. 
         [0004]    In prior art, there exist no such a measurement system which offers simple configuration and convenient operation, and can directly measure up to 21 GMEs of three mutual perpendicular linear motion axes by a single installation and step-by-step measurement. 
       SUMMARY OF THE INVENTION 
       [0005]    The object of the present invention is to provide a laser measurement system for measuring up to 21 GMEs of three mutual perpendicular linear motion guides of precise machining and measuring equipment, such as a numerical control machine tool, a machining center or a coordinate measuring machine, which is of simple configuration and allows for convenient operation. The 21 GMEs of three mutual perpendicular linear motion guides are directly measured by a single installation and step-by-step measurement. 
         [0006]    Thus, according to one aspect of the present invention, there provides a laser measurement system for measuring up to 21 GMEs, which consists of a 6DOF (six-degree-of-freedom) GME simultaneous measurement unit, a beam-turning unit, and an error-sensitive unit. The 6DOF GME simultaneous measurement unit is combined with the error-sensitive unit to simultaneously measure the 6DOF GME of a single axis, which includes position error, horizontal and vertical straightness errors, yaw, pitch, and roll. There are 18 GMEs for the three axes. The beam-turning unit splits or turns the laser beam from the 6DOF GME simultaneous measurement unit to the X, Y and Z directions in proper order. Similarly, the beam-turning unit splits or turns the beam from the error-sensitive unit to the 6DOF GME simultaneous measurement unit to simultaneously measure the 6DOF GMEs of the corresponding axis. The perpendicularity errors among the three axes are obtained by processing the straightness errors of the three axes. 
         [0007]    Preferably, the error-sensitive unit is composed of three mutual perpendicular 6DOF error-sensitive components, which are sensitive to the 6DOF GMEs of three mutual perpendicular linear motion axes of the equipment listed above. Similarly, the error-sensitive unit is composed of two mutual perpendicular 6DOF error-sensitive components, which are sensitive to the 6DOF GMEs of two mutual perpendicular linear motion axes of the equipment listed above. One of the two 6DOF error-sensitive components is sensitive to the 6DOF GME of the third linear motion axis of the equipment listed above through a 90-degree rotation. 
         [0008]    Preferably, the 6DOF error-sensitive component consists of two retro-reflector elements and one beam-splitting element. The retro-reflector element is sensitive to the position error, horizontal straightness error, and vertical straightness error of a linear motion axis. The beam-splitting element is sensitive to the pitch and yaw of the linear motion axis. The combination of the two retro-reflector elements is sensitive to the roll of the linear motion axis. The cube-corner reflector is used as the retro-reflector element, and the plane beam-splitter is used as the beam-splitting element. 
         [0009]    Preferably, the beam-turning unit consists of the beam-turning prism, or the combination of the beam-splitting prism and the beam-turning prism. Through translation and rotation, the beam-turning prism, which includes a polygon prism or a rectangle prism, turns the measurement beam from the 6DOF GME simultaneous measurement unit to the directions which are parallel to the three linear motion axes of the equipment listed above. The combination of the beam-splitting prism and the beam-turning prism is the combination of two beam-splitting polygon prisms, or the combination of two beam-splitting rectangle prisms. The beam from the 6DOF GME error simultaneous measurement unit is split into three mutual perpendicular beams, which are parallel to the three linear motion axes of the equipment listed above. 
         [0010]    According to another aspect of the present invention, there provides a method for measuring up to 21 geometric errors of the precise machining and measuring equipment, such as a numerical control machine tool, a machining center, and a coordinate measuring machine by single installation and step-by-step measurement. This method includes the following procedures: 
         [0011]    (1) installating the measurement system. The 6DOF GME simultaneous measurement unit and the beam-turning unit are mounted independently or integrally on the clamping workpiece of the equipment listed above. The error-sensitive unit is mounted on the clamping tool of the equipment listed above. 
         [0012]    (2) adjusting the measurement system. The three axes of the equipment listed above are adjusted to the initial positions predetermined by measurement standards such as ISO 230-1. The error-sensitive unit is placed as close as possible to the beam-turning unit, and this predetermined initial position is defined as the start point. By adjusting the 6DOF GME simultaneous measurement unit and the beam-turning unit, the three measurement beams, which are parallel to the X, Y, and Z axes of the equipment listed above, are obtained simultaneously or in separate steps according to the different beam turning structures of the laser beam-turning unit. 
         [0013]    (3) measuring the 6DOF GMEs of the X-axis. The beam-turning unit directs the beam from the six-degree-of-freedom geometric error simultaneous measurement unit to the direction parallel to the X-axis of the equipment listed above. Controlling the motion of the equipment listed above, the laser measurement system for 21 geometric errors is set to the start point. The 6DOF GMEs of the start point, including position error, horizontal and vertical straightness errors, pitch, yaw, and roll, are obtained by the 6DOF GME simultaneous measurement unit combined with the corresponding 6DOF error-sensitive component of the error-sensitive unit. The linear guide moves along the X-axis with the interval predetermined by related measurement standards, such as ISO230-1, and reaches the next measurement point while the Y and Z axes are kept static. The 6DOF GMEs of this point are measured. The measurement is performed point-by-point until the last measurement point, and the errors of all the measurement points on the X-axis are obtained. The linear guide moves along the X-axis in the opposite direction with the same interval. The measurement is performed point-by-point to obtain the errors of all the measurement points. In this way, the errors of all the measurement points in bidirectional movement are obtained through point-by-point static measurement. In another way, the linear guide moves from the start point to the farthest end and returns to the start point in a constant speed, and the continuous measurement is conducted by the 6DOF GME simultaneous measurement unit, combined with the corresponding 6DOF error-sensitive component of the error-sensitive unit. The errors of all the measurement points on the X-axis in bidirectional movement are obtained through dynamic measurement. 
         [0014]    (4) measuring the 6DOG GMEs of the Y-axis. The beam-turning unit directs the beam from the 6DOF GME simultaneous measurement unit to the direction parallel to the Y-axis of the equipment previously listed. The linear guide moves along the Y-axis according to the procedures mentioned in step (3), and the errors of all the measurement points on the Y-axis in bidirectional movement are obtained through point-by-point static measurement or continuous dynamic measurement. 
         [0015]    (5) measuring the 6Ddof GMEs of the Z-axis. The beam-turning unit directs the beam from the 6DOF geometric error simultaneous measurement unit to the direction parallel to the Z-axis of the equipment previously listed. The linear guide moves along the Z-axis according to the procedures mentioned in step (3), and the errors of all the measurement points on the Z-axis in bidirectional movement are obtained through point-by-point static measurement or continuous dynamic measurement. 
         [0016]    (6) Data processing. By performing steps (3), (4), and (5), the invention obtains 6DOF GMEs of each of the measurement points on the X, Y and Z axes of the measured equipment previously listed in bidirectional movement. The total errors are 18. The three perpendicularity errors among the three motion axes are obtained by data processing according to the measurement standards, such as ISO 230-1. Therefore, a total of 21 geometric errors are obtained. 
         [0017]    The order of measuring the X, Y and Z axes according to steps (3), (4), and (5) has no influence on the measurement results. The same results are obtained by performing steps (1) through (6) when the error-sensitive unit is fixed on the clamping workpiece and the 6DOF GMEs simultaneous measurement unit and the beam-turning unit are mounted integrally on the clamping tool of the equipment previously listed. 
         [0018]    The advantages of the present invention are as follows: 
         [0019]    (1) The 6DOF error-sensitive component in the present invention consists of two retro-reflector elements and one beam-splitting element. Only two measurement beams need to simultaneously measure the 6DOF GMEs for one axis. There are fewer beam-splitting elements in the system, which makes the system highly integrated. 
         [0020]    (2) Only a single installation is needed to calibrate the three linear motion axes of the equipment previously listed. The measurement efficiency is highly improved. 
         [0021]    (3) Three mutual perpendicular measurement beams, which are used as the reference datum for the perpendicularity error measurement, are obtained through the beam-turning unit. The three perpendicularity errors are obtained by processing data of the geometric errors of the three linear motion axes. 
         [0022]    Generally speaking, the invention is of simple configuration and allows for high integration with fewer optical elements. The 21 GMEs of three linear motion guides of the equipment previously listed are obtained through single installation and step-by-step measurement. 
         [0023]    A reliable instrument that simultaneously measures the 6DOF GMEs is not available in prior art. The present invention measures not only the 6DOF GMEs of a single axis, but also the 21 GMEs of three axes. The measurement system provided by the invention is of small size, and allows high integration and accuracy. The system is strongly immune from surrounding disturbance because the laser drift can be compensated in real time. 
         [0024]    In conventional measurement methods, three mutual perpendicular datum lines are obtained by mechanical components or optical elements, and several manual installations are needed. Therefore, installation deviation is introduced during the installation process. The beam-turning unit consists of the beam-turning prism or the combination of the beam-splitting prism and the beam-turning prism. The three measurement beams, which are parallel to the three linear motion axes and are used as the measurement reference datum lines for three perpendicularity errors, are obtained simultaneously or step-by-step by the beam-turning unit based on the inherent properties of optical elements and the precision electro-kinetic rotation axis for 90-degree rotation. 
         [0025]    In conventional measurement methods for multi-axes, different installations are needed to realign the measurement unit and the moving unit during the measurement of different axes. The measured parameters are limited, and the measurement efficiency is low. The proposed measurement system contains the beam-turning unit and the error-sensitive unit, which is composed of three mutual perpendicular 6DOF error-sensitive components. Three mutual perpendicular measurement beams are obtained by adjusting the positions and directions of the 6DOF GME simultaneous measurement unit and the beam-turning unit after the system installation and before the actual measurement. The alignment of the three measurement beams and the three 6DOF error-sensitive components is achieved by the movement of linear guide along the three axes. The 21 GMEs are measured through single installation and step-by-step measurement, which greatly improves the measurement efficiency and reduces the potential for manual errors. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0026]      FIG. 1  is a schematic view of the first embodiment of the laser measurement system for 21 GMEs provided by the present invention. 
           [0027]      FIG. 2  is a schematic view of the second embodiment of the laser measurement system for 21 GMEs provided by the present invention. 
           [0028]      FIG. 3  is a schematic view of the first type of beam-turning unit in the present invention. 
           [0029]      FIG. 4  is a schematic view of the second type of beam-turning unit in the present invention. 
           [0030]      FIG. 5  is a schematic view of the third type of beam-turning unit in the present invention. 
           [0031]      FIG. 6  is a schematic view of the fourth type of beam-turning unit in the present invention. 
           [0032]      FIG. 7  is a schematic view of the first type of error-sensitive unit in the present invention. 
           [0033]      FIG. 8  is the schematic view of the second type of error-sensitive unit in the present invention. 
           [0034]      FIG. 9  is a schematic view of the third type of error-sensitive unit in the present invention. 
           [0035]      FIG. 10  is a schematic view of the fourth type of error-sensitive unit in the present invention. 
           [0036]      FIG. 11  is a schematic view of the fifth type of error-sensitive unit in the present invention. 
           [0037]      FIG. 12  is a schematic view of simultaneous measurement for the 6DOF GMEs along the X-axis in the present invention. 
           [0038]      FIG. 13  is a schematic view of simultaneous measurement for the 6DOF GMEs along the Y-axis in the present invention. 
           [0039]      FIG. 14  is a schematic view of the start point for measuring 21 GMEs provided by the present invention. 
           [0040]      FIG. 15  is a schematic view of the measurement along the X-axis in the laser measurement method for 21 GMEs provided by the present invention. 
           [0041]      FIG. 16  is a schematic view of the measurement along the Y-axis in the laser measurement method for 21 GMEs provided by the present invention. 
           [0042]      FIG. 17  is a schematic view of the measurement along the Z-axis in the laser measurement method for 21 GMEs provided by the present invention. 
       
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
       [0043]    As shown in  FIG. 1 , the laser measurement system for the 21 GMEs provided by the present invention consists of the 6DOF GME simultaneous measurement unit  1 , the beam-turning unit  2  and the error-sensitive unit  3 . The error-sensitive unit  3  is fixed on the clamping tool of the measured numerical control machine tool, the machining center, and the coordinate measuring machine. The measurement unit  1  and the beam-turning unit  2  are mounted on the clamping workpiece of the equipment previously listed. 
         [0044]    Referring to  FIG. 2 , the error-sensitive unit  3  can also be fixed on the clamping workpiece, while the measurement unit  1  and the beam-turning unit  2  can also be mounted on the clamping tool of the equipment previously listed. 
         [0045]    As shown in  FIG. 3 , the pentagonal prism  2011  is used in the beam turning  2  to turn the laser beam from the measurement unit  1 . The pentagonal prism  2011  is removed from the light path of measurement unit  1  by manual or electro-kinetic operation. The measurement beam, which is parallel to the X-axis and reaches the 6DOF error-sensitive component  301 , is obtained by adjusting the position and direction of the measurement unit  1 . The pentagonal prism  2011  is then placed into the light path of the measurement unit  1  by manual or electro-kinetic operation. The measurement beam, which is parallel to the Y-axis and reaches the six-degree-of-freedom error-sensitive component  302 , is obtained by adjusting the pentagonal prism  2011  to make the measurement beam enter it perpendicularly. The straight line parallel to X-axis and passing through the center of the incident plane of the pentagonal prism  2011  is used as the rotation axis. The pentagonal prism  2011  is rotated by 90 degrees through the precise rotation component which is fixed with the pentagonal prism  2011 . The measurement beam, which is parallel to the Z-axis and reaches the 6DOF error-sensitive component  303 , is then obtained. In this way, the three measurement beams, which are parallel to the X, Y, and Z axes of the previously listed equipment are obtained step-by-step by the first type of the beam-turning unit  2 . 
         [0046]    Referring to  FIG. 4 , the second type of beam-turning unit  2  is composed of the beam splitting pentagonal prisms  2021  and  2022 . The measurement beam, which is parallel to the X-axis, is obtained by adjusting the position and direction of the measurement unit  1 . The combination of the beam splitting pentagonal prisms  2021  and  2022  is then placed into the light path of the measurement unit  1 . The beam from measurement unit  1  perpendicularly enters onto the beam splitting pentagonal prism  2021 , and the reflected beam from the beam splitting pentagonal prism  2021  perpendicularly enters the beam splitting pentagonal prism  2022  by adjusting the position of the beam splitting pentagonal prisms  2021  and  2022 . The three measurement beams, which are parallel to the X, Y, and Z axes of the measured equipment listed above, are obtained simultaneously by the second type of beam-turning unit  2 . 
         [0047]    As shown in  FIG. 5 , the rectangle prism  2031  is used in the beam-turning unit  2  to turn the laser beam from the measurement unit  1 . The rectangle prism  2031  is removed from the light path of the measurement unit  1  through manual or electro-kinetic operation. The measurement beam, which is parallel to the X-axis and reaches the six-degree-of-freedom error-sensitive component  301 , is obtained by adjusting the position and direction of the measurement unit  1 . The rectangle prism  2031  is then placed into the light path of the measurement unit  1  through manual or electro-kinetic operation. By adjusting the rectangle prism  2031  to make the measurement beam enters it perpendicularly, the measurement beam, which is parallel to the Y-axis and reaches the six-degree-of-freedom error-sensitive component  302 , is obtained. The straight line parallel to the X-axis and passing through the center of the incident plane of the pentagonal prism  2031  is used as the rotation axis. The pentagonal prism  2031  is rotated by 90 degrees through the precise rotation component which is fixed with the pentagonal prism  2031 . The measurement beam, which is parallel to the Z-axis and reaches the six-degree-of-freedom error-sensitive component  303 , is then obtained. In this way, the three measurement beams, which are parallel to the X, Y, and Z axes of the measured equipment previously listed, are obtained step-by-step by the second type of the beam-turning unit  2 . 
         [0048]    Referring to  FIG. 6 , the fourth type of beam-turning unit  2  is composed of the beam splitting prisms  2041  and  2042 . The measurement beam, which is parallel to the X-axis, is obtained by adjusting the position and direction of the measurement unit  1 . The combination of the beam splitting prisms  2041  and  2042  is then placed into the light path of the measurement unit  1 . The beam from the measurement unit  1  perpendicularly enters the beam splitting prism  2041 , and the reflected beam from the beam splitting prism  2041  is directed to perpendicularly enter the beam splitting prism  2042  through adjustment of the position of the beam splitting prisms  2041  and  2042 . The three measurement beams, which are parallel to the X, Y, and Z axes of the measured equipment list above, are obtained simultaneously by the fourth type of the beam-turning unit  2 . 
         [0049]    As shown in  FIG. 3  through  FIG. 6 , the three mutual perpendicular measurement beams, which are parallel to the X, Y, and Z axes of the equipment previously listed, are obtained simultaneously or step-by-step by four different types of the beam-turning unit  2 . The optical property of the beam turning prism and the combination of the beam splitting and turning prisms will result in a difference in the relative order of the two measurement beams, which are from the measurement unit  1  and are turned by the beam-turning unit  2  to the direction perpendicular to the beam transmission direction. Therefore, different types of the error-sensitive unit  3  are needed to cooperate with the different types of beam-turning unit  2 . 
         [0050]    The first type of the error-sensitive unit  3 , which is corresponding to the first type of the beam-turning unit  2 , is shown in  FIG. 7 . The error-sensitive unit  3  consists of three mutual perpendicular 6DOF error-sensitive components  301 ,  302  and  303 , which are sensitive to the six degree-of-freedom geometric errors of the X, Y, and Z axes of the equipment previously listed. 
         [0051]    The 6DOF error sensitive component  301  consists of two retro-reflector elements  3011  and  3012 , and one beam-splitting element  3013 . The retro-reflector element  3011  is sensitive to the position error, horizontal straightness error, and vertical straightness error of the X-axis. The beam-splitting element  3013  is sensitive to the pitch and yaw of the X-axis. The combination of the two retro-reflector elements  3011  and  3012  is sensitive to the roll of the X-axis. 
         [0052]    The 6DOF error sensitive component  302  consists of two retro-reflector elements  3021  and  3022 , and one beam-splitting element  3023 . The retro-reflector element  3021  is sensitive to the positioning error, horizontal and vertical straightness error of the Y-axis. The beam-splitting element  3023  is sensitive to the pitch and yaw of the Y-axis. The combination of the two retro-reflector elements  3021  and  3022  is sensitive to the roll of the Y-axis. 
         [0053]    The 6DOF error sensitive component  303  consists of two retro-reflector elements  3031  and  3032 , and one beam-splitting element  3033 . The retro-reflector element  3031  is sensitive to the positioning error, horizontal and vertical straightness error of the Z-axis. The beam-splitting element  3033  is sensitive to the pitch and yaw of the Z-axis. The combination of the two retro-reflector elements  3031  and  3032  is sensitive to the roll of the Z-axis. 
         [0054]    The second, third and fourth types of the error sensitive unit  3 , which correspond to the second, third and fourth types of the beam-turning unit  2 , respectively, are shown in  FIG. 8 ,  FIG. 9  and  FIG. 10 . Each type of the error sensitive unit  3  is composed of three mutual perpendicular 6DOF error sensitive components  301 ,  302 , and  303 , which are sensitive to the 6DOF GMEs of the X, Y, and Z axes of the measured equipment previously listed. The positions of the retro-reflector elements and the beam-splitting elements in 6DOF error sensitive components  301 ,  302 , and  303  correspond to the positions of the two measurement beams, from the measurement unit  1  to the 6DOF error sensitive components  301 ,  302 , and  303 , after the transmission from the beam turning unit  2 . 
         [0055]    As shown in  FIG. 11 , the fifth type of the error sensitive unit  3  consists of two mutual perpendicular 6DOF error-sensitive components  301  and  302 , which are sensitive to the 6DOF GMEs of the X and Z axes of the equipment to be measured previously listed. The 6DOF error sensitive component  301  is sensitive to the 6DOF GMEs of the Y-axis after 90-degree rotation around the Z axis. 
         [0056]    The cube-corner reflectors are used as the retro-reflector elements  3011 ,  3012 ,  3021 ,  3022 ,  3031 , and  3032 , shown in  FIG. 7  through  FIG. 11 . The plane beam-splitter or the beam-splitting film which is coated on the corresponding position of the retro-reflector element is used as the beam-splitting elements  3013 ,  3023 , and  3033 . 
         [0057]    As shown in  FIG. 3 , the pentagonal prism  2011  is used in the first type of the beam-turning unit  2  to obtain step-by-step the measurement beams, which are parallel to the X, Y, and Z axes of the equipment previously listed. The pentagonal prism  2011  has no influence on the relative order of the two measurement beams emitted from the measurement unit  1  in the transmission directions. It also does not change the relative positions between the reference datum line for angle measurement and the angle measurement beams, which are reflected by the beam-splitting elements  3013 ,  3023 , and  3033 . Therefore, the first type of beam-turning unit  2  is used in the preferred embodiment of the present invention to simultaneously measure the 6DOF GMEs of each linear motion axis. 
         [0058]    As shown in  FIG. 12 , the 6DOF GMEs of the X-axis of the equipment to be measured previously listed are simultaneously measured by the measurement unit  1  in cooperation with the 6DOF error-sensitive component  301 . The measurement unit  1  consists of the dual frequency laser  101 ; the quarter-wave plates  102  and  107 ; the polarization beam-splitters  103  and  106 ; the beam-splitters  104 ,  108 , and  109 ; the retro-reflector element  105 ; the beam-reflecting elements  110  and  114 ; the detectors  111 ,  112 ,  113 ,  116  and  118 ; the lens  115  and  117 . The six-degree-of-freedom error-sensitive component  301  consists of the retro-reflector elements  3011  and  3012 , and the beam-splitting element  3013 . 
         [0059]    As shown in  FIG. 12 , the error-sensitive unit  3  and the 6DOF error-sensitive component  301  move along the X-axis to a certain measurement point. During the measurement process of the X-axis, the pentagonal prism  2011  in the beam-turning unit  2  is moved out of the light path of the measurement unit  1 . 
         [0060]    The beam from the dual frequency laser  101  passes through the quarter-wave plate  102  and is split by the polarization beam-splitter  103 . The reflected beam from  103  is split again by the beam-splitter  104 , and the transmitted beam from  104  is used as the reference beam for interferometric length measurement. The transmitted beam from the polarization beam-splitter  103  is reflected by the retro-reflector element  3011  and split by the beam-splitter  108 . The transmitted beam from beam-splitter  108  and the reflected beam from the retro-reflector element  105  interfere on the detector  111 , and the position error of the measurement point on the X-axis is obtained. 
         [0061]    The reflected beam from the beam-splitter  108  is split by the beam-splitter  109 . The reflected beam from the beam-splitter  109  reaches the detector  112 . The horizontal and vertical straightness errors of the measurement point on the X-axis are obtained. 
         [0062]    The transmitted beam from the beam-splitter  109  is reflected by the beam-reflecting element  110  and is focused onto the detector  118  by lens  117 . The angular drift of the measurement beam is measured in this way. 
         [0063]    The reflected beam from the beam-splitter  104  passes through the polarization beam-splitter  106  and the quarter-wave plate  107 , and is partially reflected by the beam-splitting element  3013 . The reflected beam from  3013  passes through the quarter-wave plate  107 , and is totally reflected by the polarization beam-splitter  106 . The reflected beam from the beam-splitter  106  is reflected by the beam-reflecting element  114  and is focused onto the detector  116  by lens  115 . The pitch and yaw of the measurement point on the X-axis are obtained. 
         [0064]    The transmitted beam from the beam-splitting element  3013  is reflected by the retro-reflector element  3012  and is directed onto the detector  113 . The horizontal and vertical straightness errors of the measurement point on the X-axis are obtained. 
         [0065]    The vertical straightness errors of two different measurement points on the X-axis with the same horizontal position are measured by the detectors  112  and  113 . The roll of the measurement point on the X-axis is calculated using these two straightness errors. 
         [0066]    As shown in  FIG. 13 , the 6DOF GMEs of the Y and Z axes of the measured equipment previously listed are simultaneously measured by the measurement unit  1  in cooperation with the beam-turning unit  2  and the error-sensitive unit  3 . 
         [0067]    The error-sensitive unit  3  and the 6DOF error-sensitive component  302  move along the Y-axis to a certain measurement point. The transmitted beam from the polarization beam-splitter  103  and the reflected beam from the beam-splitter  104 , which are parallel to the X-axis, are used as the measurement beams. The measurement beams are turned in the directions parallel to the Y-axis by the pentagonal prism  2011  in the beam-turning unit  2  and reach the 6DOF error-sensitive component  302 . The reflected beam from the beam-splitting element  3023  and the reflected beam from the retro-reflector elements  3021  and  3022  are then turned back to the measurement unit  1  by the beam-turning unit  2 . The 6DOF GMEs of the Y-axis are measured in this way. 
         [0068]    Similarly, the beam from the measurement unit  1  is turned in the direction parallel to the Z-axis by the beam-turning unit  2 . The 6DOF GMEs of the Z-axis are obtained by the measurement unit  1  in cooperation with the beam-turning unit  2  and the 6DOF error-sensitive component  303 . 
         [0069]    A method for measuring 21 GMEs through single installation and step-by-step measurement is provided and used in the present system. The 21 GMEs of the numerical control machine tool, the machining center, or the coordinate measuring machine are obtained according to the following procedures: 
         [0070]    1) installating the measurement system. As shown in  FIG. 1 , the 6DOF GME simultaneous measurement unit  1  and the beam-turning unit  2  are mounted on the clamping workpiece of the equipment to be measured listed above. The error-sensitive unit  3  is fixed on the clamping tool. 
         [0071]    2) adjusting the measurement system. As shown in  FIG. 14 , the three axes of the precise machining and measuring equipment listed above are adjusted to the initial position predetermined by related measurement standards, such as ISO 230-1, and the error-sensitive unit  3  is placed as close as possible to the beam-turning unit  2 . This predetermined initial position is defined as the start point. The positions and directions of the measurement unit  1  and the beam-turning unit  2  are adjusted simultaneously or in separate steps to obtain the three measurement beams, which are parallel to the X, Y, and Z axes of the equipment listed above, according to the different laser turning structures of the beam-turning unit  2 . The three measurement beams are mutually perpendicular, according to the inherent property of the beam-turning unit  2 , and are used as the reference datum lines for perpendicularity error measurement. 
         [0072]    3) measuring the 6DOF GMEs of the X-axis. As shown in  FIG. 15 , the beam from the measurement unit  1  is directed to be parallel to the X-axis of the equipment by the beam-turning unit  2 . By controlling the motion of the equipment, the laser measurement system for 21 GMEs is set at the start point. The 6DOF GMEs of the start point of the X-axis, including the position error, the horizontal and vertical straightness errors, and pitch, yaw, and roll, are obtained by the measurement unit  1  combined with the corresponding six-degree-of-freedom error-sensitive component  301  on the error-sensitive unit  3 . The linear guide moves along the X-axis with the interval predetermined by related measurement standards, such as ISO 230-1, and reaches the next measurement point while the Y and Z axes are kept static. The six degree-of-freedom geometric errors of this point are measured by the measurement unit  1 . The measurement of the X-axis is performed point-by-point to the last measurement point and the six degree-of-freedom geometric errors of each of the measurement points on the X-axis are obtained. The linear guide moves along the X-axis in the opposite direction with the same interval, and the measurement is performed point-by-point to obtain the errors of all of the measurement points. In this way, the 6DOF GMEs of each of the measurement points in bidirectional movement are obtained through point-to-point static measurement. The errors of all the measurement points in bidirectional movement are obtained more than once by repeating the mentioned procedures. In another usage option, the linear guide moves from the start point to the farthest end and returns to the start point in constant speed, and continuous measurements are obtained by the measurement unit  1 , combined with the corresponding 6DOF error-sensitive component on the error-sensitive unit  3 . The errors of all the measurement points on the X-axis in bidirectional movement are obtained through dynamic measurement. 
         [0073]    4) measuring the 6DOF GMEs of the Y-axis. As shown in  FIG. 16 , the beam-turning unit  2  points the beam from the measurement unit  1  in the direction parallel to the Y-axis of the equipment previously listed. The Y-axis linear guide moves according to the procedures mentioned in step 3), and the 6DOF GMEs of each of the measurement points on the Y-axis in bidirectional movement are obtained through point-by-point static measurement or continuous dynamic measurement. 
         [0074]    5) measuring the 6DOF GMEs of Z-axis. As shown in  FIG. 17 , the beam-turning unit  2  points the beam from the measurement unit  1  in the direction parallel to the Z-axis of the equipment previously listed. The Z-axis linear guide moves according to the procedures mentioned in steps 3) or 4), and the 6DOF GMEs of each of the measurement points on the Z-axis in bidirectional movement are obtained through point-by-point static measurement or continuous dynamic measurement. 
         [0075]    6) Data processing. The 18 geometric errors are obtained through point-by-point static measurement or continuous dynamic measurement by performing steps (3), (4) and (5). The angle between the motion trajectory along the three axes and the measurement beam for corresponding axes, which is the reference datum for perpendicularity error measurement, can be calculated by processing the straightness errors of the three axes. The perpendicularity errors among the three motion axes can then be obtained. Therefore, a total of 21 GMEs are obtained.