Abstract
This paper presents compliance modeling and error compensation for lightweight robotic arms built with parallelogram linkages, i.e., \(\varPi\) joints. The Cartesian stiffness matrix is derived using the virtual joint method. Based on the developed stiffness model, a method to compensate the compliance error is introduced, being illustrated with a 3-parallelogram robot in the application of pick-and-place operation. The results show that this compensation method can effectively improve the operation accuracy.
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References
Ivlev, O., et al.: Rehabilitation robots FRIEND-I and FRIEND-II with the dexterous lightweight manipulator. Technol. Disabil. 17(2), 111–123 (2005)
Bien, Z., et al.: Integration of a rehabilitation robotic system (KARES II) with human-friendly man-machine interaction units. Auto. Robots 16(2), 165–191 (2004)
Zhuang, H.: Self-calibration of parallel mechanisms with a case study on Stewart platforms. IEEE Trans. Robot. Autom. 13(3), 387–397 (1997)
Klimchik, A., et al.: Compliance error compensation technique for parallel robots composed of non-perfect serial chains. Robot. Comput.-Int. Manuf. 29(2), 385–393 (2013)
Salisbury, J.: Active stiffness control of a manipulator in cartesian coordinates. In: 19th IEEE Conference on Decision and Control Including the Symposium on Adaptive Processes, vol. 19 pp. 95–100. New Mexico (1980)
Chen, S.-F., Kao, I.: Conservative congruence transformation for joint and Cartesian stiffness matrices of robotic hands and fingers. Inter. J. Robot. Res. 19, 835–847 (2000)
Alici, G., Shirinzadeh, B.: Enhanced stiffness modeling, identification and characterization for robot manipulators. IEEE T. Robot. 21(4), 554–564 (2005)
Quennouelle, C., et al.: Stiffness matrix of compliant parallel mechanisms. In: Lenarčič, J., Wenger, P. (eds.) Advances in Robot Kinematics: Analysis and Design, pp. 331–341. Springer, Netherlands (2008)
Pashkevich, A., et al.: Enhanced stiffness modeling of manipulators with passive joints. Mech. Mach. Theory 46(5), 662–679 (2011)
Denavit, J., Hartenberg, R.S.: A kinematic notation for lower-pair mechanisms based on matrices, Trans. ASME. J. Appl. Mech. 22, 215–221 (1995)
Wu, G., et. al.: Mobile platform center shift in spherical parallel manipulators with flexible limbs. Mech. Mach. Theory. 75, 12–26 (2014)
International Standard: Manipulating Industrial Robots-Performance Criteria and Related Test Methods ISO 9283: 1998
Acknowledgments
The authors would like to thank Palle Huus, Dennis Andersen, Nikolai Svalebæk, Nikolai Hansen, Mathias Kristensen and Mathias Jungersen for prototyping the robot.
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Appendix
Appendix
The force Jacobian matrix is expressed as
with the unit screws
and
where \({\mathbf{R}}_{n}\) and \({\mathbf{p}}_{n}\), \(n = 1,{\kern 1pt} 2,{\kern 1pt} 3\), respectively, are the rotation matrix and position vector extracted from \(\prod\nolimits_{i = 1}^{n} {^{i - 1} {\mathbf{A}}_{i} }\) of Eq. (1). Moreover, vectors \({\mathbf{i}}\), \({\mathbf{j}}\) and \({\mathbf{k}}\) represent the unit vectors of \(x\)-, \(y\)- and \(z\)-axis, respectively.
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Wu, G., Guo, S., Bai, S. (2015). Compliance Modeling and Error Compensation of a 3-Parallelogram Lightweight Robotic Arm. In: Bai, S., Ceccarelli, M. (eds) Recent Advances in Mechanism Design for Robotics. Mechanisms and Machine Science, vol 33. Springer, Cham. https://doi.org/10.1007/978-3-319-18126-4_31
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DOI: https://doi.org/10.1007/978-3-319-18126-4_31
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