J. A. Thornby 1,2 , R. J. Sanders 2,3 , R. Hyde-Moxon 3 1 Mathematics Institute, University of Warwick, CV4 7AL 2 WMG, University of Warwick, CV4 7AL 3 METRIS, Argosy Road, Derby, DE74 2SA Acknowledgements The authors wish to thank METRIS UK. Work supported by the UK Technology Strategy Board under the EPSRC-managed scheme “Gathering Data in Complex Introduction In partnership with Metris UK we present the modelling and development of a revolutionary Robot Coordinate-measuring Arm (RCA). The RCA combines the automation capability of traditional Coordinate Measurement Machine (CMM) methods with the mobility and part accessibility of an articulated arm, resulting in a versatile and powerful tool for coordinate measuring applications with a target accuracy of sub-100µm. The RCA exploits novel, patented technology to accelerate repetitive 3D inspection jobs. A highly accurate 7-axis articulated arm is housed within a robotized exoskeleton driven by electromotors. Figure 1: The Metris RCA schematic and (inset) prototype performing a typical car cockpit scan. Dataset Model Parameters Calibratio n Residual (μm) original kinematic 65.4 original kin + others 53.4 reduced kinematic 46.5 reduced kin + others 33.4 J 1 J 3 J 2 (Shoulder) J 7 J 6 (Wrist) J 4 (Elbow) J 5 0.9m 0.9m Axis n+1 Axis n Axis n- 1 z n-1 y n-1 x n-1 α n-1 a n- 1 d n x n y n z n a n θ n d (length) a (offset) θ (joint angle) α (twist) Kinematic Modelling We utilise Denavit-Hartenberg parameters to model the robot links and investigate the accessible configurations of the exoskeleton under the effects of arbitrary offsets and twists. Error correction algorithms are less effective in the singular positions; evidenced by smaller calibration residuals in the reduced dataset. It would therefore be advantageous to somehow manipulate or avoid singular regions. At present two approaches are being investigated in parallel; one to better understand singularities, the other to avoid them by mechanical design. The latter has been modelled to test its suitability for a range of tasks and to verify that it will pass a series of standard engineering tests. Figure 6: Third generation RCA demonstrating compatibility with industry standard “VDI” tests. 1 0 0 0 cos sin 0 sin sin cos cos cos sin cos sin sin cos sin cos 1 n n n n n n n n n n n n n n n n n n n d a a A Calibration Calibration is performed by positioning the RCA in 300 unique poses and comparing the deviation of the measured position to that predicted by the nominal kinematic model. An error correction algorithm attempts to reduce the error. Figure 4: RCA Calibration residuals from February 2009 (above) and May 2009 (below). Spikes occur in so-called “singular” poses. Calibration residuals have improved by a factor of two due to improvements in error correction. The reduced dataset disregards singular poses. Pose # Pose # Figure 2: Denavit-Hartenberg Parameters and associated transformation matrix. Figure 3: Accessible workspace surface for an odd/even axis pair with arbitrary offsets. Singular Poses When consecutive links become parallel the RCA passes through a singular pose. In such situations the supporting structure subjects the internal measurement arm to extreme contact forces, resulting in deformation. This is verified by Finite Element Analysis (FEA). Figure 5: FEA simulation result demonstrating deformation of the internal measurement arm. (a = 0) (α = 0) (a = 0) (α ≠ 0) (a ≠ 0) (α = 0) (a ≠ 0) (α ≠ 0)

J. A. Thornby 1,2, R. J. Sanders 2,3, R. Hyde-Moxon 3 1 Mathematics Institute, University of Warwick, CV4 7AL 2 WMG, University of Warwick, CV4 7AL 3 METRIS,

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J. A. Thornby 1,2, R. J. Sanders 2,3, R. Hyde-Moxon 3

1 Mathematics Institute, University of Warwick, CV4 7AL2 WMG, University of Warwick, CV4 7AL

3 METRIS, Argosy Road, Derby, DE74 2SA

Acknowledgements

The authors wish to thank METRIS UK.

Work supported by the UK Technology Strategy Board under the EPSRC-managed scheme “Gathering Data in Complex Environments”.

Introduction

In partnership with Metris UK we present the modelling and development of a revolutionary Robot Coordinate-measuring Arm (RCA). The RCA combines the automation capability of traditional Coordinate Measurement Machine (CMM) methods with the mobility and part accessibility of an articulated arm, resulting in a versatile and powerful tool for coordinate measuring applications with a target accuracy of sub-100µm.

The RCA exploits novel, patented technology to accelerate repetitive 3D inspection jobs. A highly accurate 7-axis articulated arm is housed within a robotized exoskeleton driven by electromotors.

Figure 1: The Metris RCA schematic and (inset) prototype performing a typical car cockpit scan.

Dataset ModelParameters

CalibrationResidual (μm)

original kinematic 65.4original kin + others 53.4reduced kinematic 46.5reduced kin + others 33.4

J2 (Shoulder)

J6 (Wrist)

J4 (Elbow)

0.9m

Axis n+1Axis n

Axis n-1

zn-1yn-1

xn-1

αn-1

an-1

xnyn

θn

d (length)a (offset)θ (joint angle) α (twist)

Kinematic Modelling

We utilise Denavit-Hartenberg parameters to model the robot links and investigate the accessible configurations of the exoskeleton under the effects of arbitrary offsets and twists.

Error correction algorithms are less effective in the singular positions; evidenced by smaller calibration residuals in the reduced dataset. It would therefore be advantageous to somehow manipulate or avoid singular regions.

At present two approaches are being investigated in parallel; one to better understand singularities, the other to avoid them by mechanical design. The latter has been modelled to test its suitability for a range of tasks and to verify that it will pass a series of standard engineering tests.

Figure 6: Third generation RCA demonstrating compatibility with industry standard “VDI” tests.

1000

cossin0

sinsincoscoscossin

cossinsincossincos

nnn

nnnnnnn

nn d

Calibration

Calibration is performed by positioning the RCA in 300 unique poses and comparing the deviation of the measured position to that predicted by the nominal kinematic model. An error correction algorithm attempts to reduce the error.

Figure 4: RCA Calibration residuals from February 2009 (above) and May 2009 (below). Spikes occur in so-called “singular” poses.

Calibration residuals have improved by a factor of two due to improvements in error correction. The reduced dataset disregards singular poses.

Pose #

Figure 2: Denavit-Hartenberg Parameters and associated transformation matrix.

Figure 3: Accessible workspace surface for an odd/even axis pair with arbitrary offsets.

Singular Poses

When consecutive links become parallel the RCA passes through a singular pose. In such situations the supporting structure subjects the internal measurement arm to extreme contact forces, resulting in deformation. This is verified by Finite Element Analysis (FEA).

Figure 5: FEA simulation result demonstrating deformation of the internal measurement arm.

(a = 0)

(α = 0)

(a = 0)

(α ≠ 0)

(a ≠ 0)

(α = 0)

(a ≠ 0)

(α ≠ 0)