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Calibration of Coordinate Measuring Arms

Coordinate measuring arms (CMA) provide a special class of portable 3D coordinate measuring machines. Due to their redundant characteristic, they are able to reach each point in their workspace using an infinite number of joint configurations.


As shown in Figure 1, our CMA, a ROMER Infinite 2.0, comprises seven rotary joints linked by carbon fiber arm elements. Each joint is equipped with a high precise rotary encoder providing the joint displacement as observations. The calculation of the 3D coordinate is based on a kinematic chain in accordance to the conventions of Denavit and Hartenberg (1955). Consequently, the mathematical model of the CMA is described by 31 parameters representing the geometrical construction of the arm. 

Romer Arm Arm_Side_View


Figure 1: Left: ROMER Infinite 2.0 combined with a Perceptron-V5 laser line scanner. Right: Technical drawing of the CMA including the coordinate frames of the Denavit & Hartenberg transformation (ROMER Inc. modified)


In order to obtain a complete stochastic model of a coordinate measuring arm, a calibration approach is developed using measurements of a high precision length gage with conical sockets. The calibration procedure uses the redundant characteristic of the CMA as well as the certified lengths of the gage in a least-squares optimization approach (Gauß-Helmert model).  Therefore, the length gage is place in different orientations in the workspace of the CMA (Figure 2).

Arm Calibration

Figure 2: Positioning of the length gage using the example of one quadrant of the workspace


The result is a set of 31 kinematic parameters and parameter accuracies that can be used to calculate 3D coordinates and their accuracy using error propagation.



  • Hartenberg, R. S., & Denavit, J. (1955) A kinematic notation for lower-pair mechanisms based on metrics , Transactions of the ASME, Journal of Applied Mechanics, 22, 215–221.


  • Dupuis, J., Holst, Ch., Kuhlmann, H. (2017) Improving the Kinematic Calibration of a Coordinate Measuring Arm using Configuration Analysis, Precision Engineering, Available online 5 May 2017, doi:10.1016/j.precisioneng.2017.05.004.