| Pitch and Yaw Angular Error Measurement Using a MCV-500 Laser Calibration System I. What is the problem The MCV-500 laser calibration system with the SD-500 sequential step diagonal measurement option can be used to measure the 3 linear displacement errors, 6 straightness errors and 3 squareness errors. However, for many machines, the pitch and yaw angular errors may be large and need to be measured. Instead of using another laser calibration system such as MCV-2002, or add another laser head such as MCV-5000, the existing MCV-500 laser calibration system can be used to measure the pitch and yaw angular errors by repeated measurements with different Abbe offsets and data processing software. II. How to solve this problem Using a dual-beam laser head(MCV-2002) or two laser heads(MCV-5000), the pitch and yaw angular errors of the machine can be measured. For a single laser head(MCV-500), if the machine is repeatable, the angular errors can be determine by2or3 separate measurements along the same axis but at different Abbe offsets [see Ref 1]. For example, for 3 measurements along X-axis at 3 different locations with known Abbe offsets ml, pi; m2, p2; and m3, p3, the measured results, DX1, DX2 and DX3 can be expressed as the followings. DX1 = Dx(x) + m1*Ay(x) + p1*Az(x) DX2 = Dx(x) + m2*Ay(x) + p2*Az(x) DX3 = Dx(x) + m3*Ay(x) + p3*Az(x) Where Dx(x) is the linear displacement error, Ay(x) and Az(x) are pitch and yaw angular errors respectively. There are 3 sets of data DX1, DX2 and DX3 and 3 unknowns Dx(x), Ay(x) and Az(x). The solutions are, Ay(x) = [(m3-m1)*(DX2-DX1)-(m2-m1)*(DX3-DX1)] / [(m3-m1)*(p2-P1) -(m2-m1)*(p3-p1)] Az(x) = [(p3-p1)*(DX2-DX1)-(p2-p1)*(DX3-DX1)] / [(m3-m1)*(p2-P1) -(m2-m1)*(p3-p1)] Dx(x) = DX1*(m2*p3-m3*p2)+DX2*(m3*p1-m1*p3)+DX3*(m1*p2 -m2*p1) / [(m3-m1)*(p2-p1)-(m2-m1)-(p3-p1)]. |