Kinematic calibration of precise 6-DOF stewart platform-type positioning systems for radio telescope applications

doi:10.1007/s11465-013-0249-7

Front Mech Eng

2013, Vol. 8

Issue (3) : 252-260 https://doi.org/10.1007/s11465-013-0249-7

RESEARCH ARTICLE

Kinematic calibration of precise 6-DOF stewart platform-type positioning systems for radio telescope applications

Juan Carlos JáUREGUI¹(

), Eusebio E. HERNáNDEZ², Marco CECCARELLI³, Carlos LóPEZ-CAJúN⁴, Alejandro GARCíA⁵

1. División de Estudios de Posgrado, Facultad de Ingeniería, Universidad Autónoma de Quéretaro Quéretaro, Qro. Mexico; 2. National Polytechnic Institute, IPN, Section of Graduate Studies and Research, ESIME-UPT, México D.F., Mexico; 3. Laboratory of Robotics and Mechatronics University of Cassino, Italy; 4. Universidad Autónoma de Quéretaro Querétaro, Qro. México; 5. CIATEQ, A.C. Aguascalientes, Ags. México

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Abstract

The pose accuracy of a parallel robot is a function of the mobile platform posture. Thus, there is no a single value of the robot’s accuracy. In this paper, two novel methods for estimating the accuracy of parallel robots are presented. In the first method, the pose accuracy estimation is calculated by considering the propagation of each error, i.e., error variations are considered as a function of the actuator’s stroke. In the second method, it is considered that each actuator has a constant error at any stroke. Both methods can predict pose accuracy of precise robots at design stages, and/or can reduce calibration time of existing robots. An example of a six degree-of-freedom parallel manipulator is included to show the application of the proposed methods.

Keywords pose errors error estimation parallel robot radio telescopes

Corresponding Author(s): JáUREGUI Juan Carlos,Email:jc.jauregui@uaq.mx

Issue Date: 05 September 2013

Cite this article:

Juan Carlos JáUREGUI,Eusebio E. HERNáNDEZ,Marco CECCARELLI, et al. Kinematic calibration of precise 6-DOF stewart platform-type positioning systems for radio telescope applications[J]. Front Mech Eng, 2013, 8(3): 252-260.

URL:

https://academic.hep.com.cn/fme/EN/10.1007/s11465-013-0249-7
https://academic.hep.com.cn/fme/EN/Y2013/V8/I3/252

Fig.1 A Gough-Stewart platform for positioning the secondary mirror of the millimeter radio-telescope

Fig.2 The actual Gough-Stewart platform. (a) The built prototype; (b) a scheme with kinematic parameters (mm)

Fig.3 Actuator used for the platform

Fig.4 Main parts of the actuator

Fig.5 Calibration equipment RENISHAW ML10 consisting of leg (1), laser (2), and interferometer (3)

Fig.6 Schemes for layout of base (a) and moving (b) platforms

Tab.1 Points along the workspace

Fig.7 Difference between commanded position and actual position for actuator 1

Fig.8 Difference between commanded position and actual position for actuator 2

Fig.9 Difference between commanded position and actual position for actuator 3

Fig.10 Difference between commanded position and actual position for actuator 4

Fig.11 Difference between commanded position and actual position for actuator 5

Fig.12 Difference between commanded position and actual position for actuator 6

Tab.2 RMS values of each actuator

Fig.13 Error comparisons between the Comprehensive and the Simplified Methods

1	Merlet J P. Parallel Robots. Springer , 2006
2	Masory O, Wang J. On the accuracy of a stewart platform-part I: The effect of manufacturing tolerances. In: IEEE Int. Conf. on Robotics and Automation, Atlanta , 1993, 725–731
3	Merlet J P. Parallel Robots: Open Problems. In: ASME Conference DECT , 2002
4	Castillo E, Takeda Y. Improving path accuracy of a crank-type 6-DOF parallel mechanism by stiction compensation. Mechanism and Machine Theory , 2008, 43(1): 104–114 doi: 10.1016/j.mechmachtheory.2006.12.002
5	Zhuang H, Roth Z. Method for kinematic calibration of stewart platforms. Journal of Robotic Systems , 1993, 10(3): 391–405 doi: 10.1002/rob.4620100306
6	Ziegert J C.Volumetric performance of hexapod machine tools, Hexapod Machine Tool Users Group. Internal report 13 , 1996
7	Soons J A. Error Analysis of a hexapod machine tool. In: 3rd International Conference and Exhibition on Laser Metrology and Machine Performance, Lamdamap , 1997, 347–358
8	Rudder F F. Thermal expansion of long slender rods with forced convection cooling along the rod length. Report NISTIR , 1997, 5975: 46
9	Gupta K. Measure of positional error for a rigid body. Journal of Mechanical Design, ASME , 1997, 119(3): 346–348 doi: 10.1115/1.2826354
10	Parenti-Castelli V. Di Gregorio R., Lenarcic J. Sensitivity to geometric parameter variation of a 3 DOF fully-parallel manipulator. In: 3rd International Conference on Advanced Mechatronics JSME , 1998, 364–369
11	Oiwa T, Tamaki M. Study on abbe's principle in parallel kinematics. In: 2nd Chemnitz Parallel Kinematics Seminar, Chemnitz , 354–352 , 2000.
12	Cui H, Zhu Z, Gan Z, Brogangrdh T. Kinematic analysis and error modeling of TAU parallel robot. Robotics and Integrated Manufacturing , 2005, 21(6): 497–505 doi: 10.1016/j.rcim.2004.07.018
13	Brogangrdh T. Device for relative movement of two elements. United States Patent 6425303 , 2002.
14	Oiwa T. Error compensation system for joints, links and machine frame of parallel kinematics machines. International Journal of Robotics Research , 2005, 24(12): 1087–1102 doi: 10.1177/0278364905060149
15	Yu A, Bonev I, Zsombor P. Geometric approach to the accuracy of a class of 3-DOF planar parallel robots. Mechanism and Machine Theory , 2008, 43(3): 364–375 doi: 10.1016/j.mechmachtheory.2007.03.002
16	Briota S, Bonev I. Accuracy analysis of 3-DOF planar parallel robots. Mechanism and Machine Theory , 2008, 43(4): 445–458 doi: 10.1016/j.mechmachtheory.2007.04.002
17	Chebbia A, Affia Z, Romdhaneb L. Prediction of the pose errors produced by joints clearance for a 3-UPU parallel robot. Mechanism and Machine Theory , 2009, 44(9): 1768–1783 doi: 10.1016/j.mechmachtheory.2009.03.006
18	Pashkevich A, Chablat D, Wenger P. Kinematic Calibration of orthoglide-type mechanism from observation of parallel leg motions. Mechatronics , 2009, 19(4): 478–488 doi: 10.1016/j.mechatronics.2008.11.008
19	Ren X, Feng Z, Su C A. New calibration method for parallel kinematic machine tools using orientation constraint. International Journal of Machine Tools & Manufacture , 2009, 49(9): 708–721 doi: 10.1016/j.ijmachtools.2009.03.004
20	Hernandez-Martinez E, Ceccarelli M, Carbone G, Lopez-Cajun C, Jauregui-Correa J C. Characterization of a cable-based parallel mechanism for measurement purposes. Mechanism Based Design of Structures and Machines an International Journal , 2010, 38(1): 25–49 doi: 10.1080/15397730903386101
21	Angeles J. On the Nature of the Cartesian Stifiness Matrix. Ingenieria Mecanica Tecnologia y Desarrollo , 2010, 3(5): 163–170
22	Bohm J, Hefele J, Fritsch D. Towards on-line pose measurement for robots. In: Pattern Recognition, 23rd DAGM Symposium, LCNS-2191 , 2003, 298–303
23	Minor M, Merrel R. Instrumentation and algorithms for posture estimation in compliant framed modular mobile robots. International Journal of Robotics Research , 2007, 26(5): 491–512 doi: 10.1177/0278364907077899
24	Gosselin C, Angeles J. Singularity analysis of closed-loop kinematic chains. IEEE Transactions on Robotics and Automation , 1990, 6(3): 281–290 doi: 10.1109/70.56660

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