Research Papers: Design of Mechanisms and Robotic Systems

Designing Multi-Axis Force–Torque Sensors by Minimizing the Amplitudes of Their Nonlinear Displacements

[+] Author and Article Information
R. Bekhti

Control and Robotics Laboratory,
Department of Automated Manufacturing Engineering,
École de Technologie Supérieure,
Montreal, QC H3C 1K3, Canada
e-mail: rachid.bekhti.1@ens.etsmtl.ca

P. Cardou

Department of Mechanical Engineering,
Laval University,
Quebec, QC G1V 0A6, Canada
e-mail: pcardou@gmc.ulaval.ca

V. Duchaine

Control and Robotics Laboratory,
Department of Automated Manufacturing Engineering,
École de Technologie Supérieure,
Montreal, QC H3C 1K3, Canada
e-mail: vincent.duchaine@etsmtl.ca

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received July 19, 2015; final manuscript received December 17, 2015; published online January 20, 2016. Assoc. Editor: Oscar Altuzarra.

J. Mech. Des 138(3), 032302 (Jan 20, 2016) (10 pages) Paper No: MD-15-1513; doi: 10.1115/1.4032401 History: Received July 19, 2015; Revised December 17, 2015

Compliant multi-axis force–torque sensors play a crucial role in many emerging robotic applications, such as telemanipulation, haptic devices and human-robot physical interaction. In order to synthesize the compliant architectures at the core of these sensors, several researchers have devised performance indices from mechanism theory. This paper follows the same approach, but includes the innovation of using the changes in the compliant mechanism geometry as a new performance index. Once external forces are applied, the compliant mechanism deviates from its unloaded configuration, and thus, changes in geometry prevent the sensor from exhibiting a linear response. In order to minimize this nonlinear behavior, the potential sources of error are analyzed by applying linear algebra techniques to the expression of the Cartesian force mapping. Two performance indices are then presented and combined. The first index measures the variations of the Jacobian matrix about the unloaded configuration. The second index measures the amplification of the error arising from the joint displacements measurement. The resulting indices can be expressed symbolically, making them easier to evaluate and synthesize. Finally, we apply the performance indices we have developed to simple compliant mechanisms, and discuss the results.

Copyright © 2016 by ASME
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Fig. 1

Generic rigid-link mechanism with lumped elastic springs at its joints

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Fig. 2

The nonlinear relationship between w¯i and q̂, and its linear approximation

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Fig. 3

Two-link planar compliant serial mechanism

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Fig. 4

Comparison between the global and local indices of structural error

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Fig. 5

Results of Pareto optimization for the two-link planar mechanism

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Fig. 6

A 2-PRR planar biaxial force sensor mechanism

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Fig. 7

Comparison of the contour plots of the GSEI for the 2-PRR mechanism: (a)dq̂ = 0.3 mm, (b) dq̂ = 0.6 mm, and (c) dq̂ = 0.9 mm

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Fig. 8

Contour plots in Cartesian space of the performance indices for the 2-PRR mechanism: (a) GSEI, (b) LSEI, and (c) MEAI

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Fig. 9

Pareto optimization for the 2-PRR planar mechanism: close-up view of the concentration of solutions at the Pareto front




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