Chapter 9 - Design for low sensitivity

High-precision 3D coordinate measuring machine according to Abbe and Bryan principle


In Precision Engineering components are getting smaller and tolerances become tighter, so demands for accuracy are increasing. To improve the precision of Coordinate Measuring Machines (CMMs) an alternative high precision 3D-CMM was developed with measuring uncertainty beneath 0.1 μm in a measurement volume of 1 dm3. The machine design is based on the Abbe and Bryan principle, thus smaller measuring errors are feasible with less effort on software compensation. Application of a light and stiff construction, compensated air bearings and well-positioned linear motors result in high stiffness and favorable dynamic behavior. A statically determined design, extensive use of aluminum and mechanical thermal length compensation make the machine less sensitive to temperature changes. To prevent mechanical disturbances an active vibration isolation system was designed.


Conventional large CMMs have good accessibility but relatively large measurement uncertainty due to large Abbe-offsets, scaling down is preferred. Measurement uncertainty U3 scales with the dimensions of the CMM according to U3 = 0.7 + L/600 [μm] (L in [mm]), so scaling down is preferred for a large class of small products to be measured. A new concept was conceived based on both the Abbe and Bryan principle (see Figure 1 and 2), as a result of which, only 13 out of 21 error contributions remain. Closed box structures are used for the moving platform that are made out of aluminum. In addition to high specific stiffness, low density, and relatively low cost, aluminum has fast thermal response, i.e. high volumetric thermal diffusivity λ⁄ ρCp [m2/s], which expresses the response time towards quasi-static deformation from heat load. Based on the first prototype developed at TU/e, Carl Zeiss has developed the F25 series product with a measuring uncertainty of 250 nm at a resolution of 7.5 nm.

Figure 1a. Abbe principle (1890): A straightness error in a guide way causes a measurement error, which is linear proportional to the offset h between the probe and the scale.Figure 1b. Bryan principle (1979): A straightness error that is being measured at an offset h gives a measurement error, which is linear proportional to the offset between probe and scale.
Figure 2a. Schematic representation of the small scale 3D CMM. Top view: 3 bodies (platform PL and intermediate bodies A and B) each with separate vertical bearings on table, measurement systems (X, Y) remain pointed towards probe P at all times.Figure 2b. Realized prototype of the 3D CMM according to the Abbe and Bryan principle. The design is statically determined, and is based on extensive use of aluminum and mechanical thermal length compensation, which make the machine less sensitive to temperature changes.

High-precision coordinate measurement machine (CMM)

Prototype CMM, which was further developed into a series product F25 by Carl Zeiss.

Abbe and Bryan principle, closed box design, high volumetric diffusivity through application of aluminum


Marc Vermeulen, TU/e (1999)


[1] Vermeulen, M.M.P.A., High-precision 3D-coordinate measuring machine, PhD Thesis, Eindhoven University of Technology, September 28, 1999.

[2] Schellekens, P., et al, Design for precision: Current status and trends, Annals of the CIRP, Vol. 47/2, 1998.

[3] Vermeulen, M.M.P.A., Rosielle, P.C.J.N., Schellekens, P.H.J., Design of a High-precision 3D-Coordinate Measuring Machine, Annals of the CIRP, Vol. 47/1, pp. 447-450, 1998.


Design principles