0
Research Papers

Efficient Closed-Form Solution of the Kinematics of a Tunnel Digging Machine

[+] Author and Article Information
Paolo Boscariol

DTG,
University of Padova,
Vicenza 36100, Italy
e-mail: paolo.boscariol@unipd.it

Alessandro Gasparetto

DPIA,
University of Udine,
Udine 33100, Italy
e-mail: gasparetto@uniud.it

Lorenzo Scalera

DPIA,
University of Udine,
Udine 33100, Italy
e-mail: scalera.lorenzo@spes.uniud.it

Renato Vidoni

Faculty of Science and Technology,
Free University of Bozen-Bolzano,
Bolzano 39100, Italy
e-mail: renato.vidoni@unibz.it

1Corresponding author.

Manuscript received February 16, 2016; final manuscript received December 26, 2016; published online March 20, 2017. Assoc. Editor: Hai-Jun Su.

J. Mechanisms Robotics 9(3), 031001 (Mar 20, 2017) (13 pages) Paper No: JMR-16-1040; doi: 10.1115/1.4035797 History: Received February 16, 2016; Revised December 26, 2016

In this work, the kinematics of a large size tunnel digging machine is investigated. The closed-loop mechanism is made by 13 links and 13 class 1 couplings, seven of which are actuated. This kind of machines are commonly used to perform ground drilling for the placement of reinforcement elements during the construction of tunnels. The direct kinematic solution is obtained using three methods: the first two are based on the numerical solution of the closure equation written using the Denavit–Hartenberg convention, while the third is based on the definition and solution in closed form of an equivalent spherical mechanism. The procedures have been tested and implemented with reference to a real commercial tunnel digging machine. The use of the proposed method for the closed-form solution of direct kinematics allows to obtain a major reduction of the computation time in comparison with the standard numerical solution of the closure equation.

Copyright © 2017 by ASME
Your Session has timed out. Please sign back in to continue.

References

Mroueh, H. , and Shahrour, I. , 2008, “ A Simplified 3D Model for Tunnel Construction Using Tunnel Boring Machines,” Tunnelling Underground Space Technol., 23(1), pp. 38–45. [CrossRef]
Galli, G. , Grimaldi, A. , and Leonardi, A. , 2004, “ Three-Dimensional Modelling of Tunnel Excavation and Lining,” Comput. Geotech., 31(3), pp. 171–183. [CrossRef]
Pinyol, N. M. , and Alonso, E. E. , 2011, “ Design of Micropiles for Tunnel Face Reinforcement: Undrained Upper Bound Solution,” J. Geotech. Geoenviron. Eng., 138(1), pp. 89–99. [CrossRef]
Coulter, S. , and Martin, C. , 2006, “ Effect of Jet-Grouting on Surface Settlements Above the Aeschertunnel, Switzerland,” Tunnelling Underground Space Technol., 21(5), pp. 542–553. [CrossRef]
Gupta, B. , Sreekumar, A. , and Tripathi, S. , 2012, “ Tunnelling Through Adverse Geological Condition: A Case Study,” Electrical Measuring Instruments and Measurements, Taylor & Francis, London, pp. 31–36.
Coulter, S. , and Martin, C. , 2006, “ Single Fluid Jet-Grout Strength and Deformation Properties,” Tunnelling Underground Space Technol., 21(6), pp. 690–695. [CrossRef]
Tuncdemir, H. , Aksoy, C. , Güçlü, E. , and Özer, S. , 2012, “ Umbrella Arch and Forepoling Support Methods: A Comparison,” ISRM International Symposium (EUROCK), Stockholm, Sweden, May 28–30, pp. 515–527.
Dobashi, H. , Shiratori, A. , Miyama, D. , Nagura, H. , and Miyawaki, T. , 2006, “ Design and Construction of Enlarging Shield Tunnel Sections of Large Dimensional Shield Tunnels for the Non-Open-Cut Method,” Tunnelling Underground Space Technol., 21(3), pp. 249–249. [CrossRef]
Liu, X.-J. , and Wang, J. , 2013, Parallel Kinematics: Type, Kinematics, and Optimal Design, Springer Science & Business Media, Berlin.
Castelli, G. , Ottaviano, E. , and Ceccarelli, M. , 2008, “ A Fairly General Algorithm to Evaluate Workspace Characteristics of Serial and Parallel Manipulators,” Mech. Based Des. Struct. Mach., 36(1), pp. 14–33. [CrossRef]
Jin, Y. , Bi, Z. , Liu, H. , Higgins, C. , Price, M. , Chen, W. , and Huang, T. , 2015, “ Kinematic Analysis and Dimensional Synthesis of Exechon Parallel Kinematic Machine for Large Volume Machining,” ASME J. Mech. Rob., 7(4), pp. 1–8. [CrossRef]
Zhang, J. , Zhao, Y. , and Jin, Y. , 2016, “ Kinetostatic-Model-Based Stiffness Analysis of Exechon PKM,” Rob. Comput.-Integr. Manuf., 37, pp. 208–220. [CrossRef]
Haftka, R. T. , and Gürdal, Z. , 2012, Elements of Structural Optimization, Vol. 11, Springer Science & Business Media, Berlin.
Siciliano, B. , and Khatib, O. , 2008, Springer Handbook of Robotics, Springer Science & Business Media, Berlin.
Hartenberg, R. S. , and Denavit, J. , 1964, Kinematic Synthesis of Linkages, McGraw-Hill, New York.
Siciliano, B. , 1999, “ The Tricept Robot: Inverse Kinematics, Manipulability Analysis and Closed-Loop Direct Kinematics Algorithm,” Robotica, 17(4), pp. 437–445. [CrossRef]
Gough, V. , and Whitehall, S. , 1962, “ Universal Tyre Test Machine,” FISITA 9th International Technical Congress, May, pp. 117–137.
Cleary, K. , and Arai, T. , 1991, “ A Prototype Parallel Manipulator: Kinematics, Construction, Software, Workspace Results, and Singularity Analysis,” IEEE International Conference on Robotics and Automation, Sacramento, CA, Apr. 9–11, pp. 566–571.
Griffis, M. , and Duffy, J. , 1989, “ A Forward Displacement Analysis of a Class of Stewart Platforms,” J. Rob. Syst., 6(6), pp. 703–720. [CrossRef]
Innocenti, C. , and Parenti-Castelli, V. , 1993, “ Forward Kinematics of the General 6–6 Fully Parallel Mechanism: An Exhaustive Numerical Approach Via a Mono-Dimensional-Search Algorithm,” ASME J. Mech. Des., 115(4), pp. 932–937. [CrossRef]
Huang, Z. , Li, Q. , and Ding, H. , 2012, Theory of Parallel Mechanisms, Vol. 6, Springer Science & Business Media, Berlin.
Davidson, J. K. , and Hunt, K. H. , 2004, Robots and Screw Theory: Applications of Kinematics and Statics to Robotics, Oxford University Press, Oxford, UK.
Siciliano, B. , Sciavicco, L. , Villani, L. , and Oriolo, G. , 2009, Robotics: Modelling, Planning and Control, Springer Science & Business Media, Berlin.
Crane, C. D., III , and Duffy, J. , 2008, Kinematic Analysis of Robot Manipulators, Cambridge University Press, Cambridge, UK.
Mckinley, J. R. , Crane, C. , and Dooner, D. B. , 2007, “ Reverse Kinematic Analysis of the Spatial Six Axis Robotic Manipulator With Consecutive Joint Axes Parallel,” ASME Paper No. DETC2007-34433.
Haug, E. J. , 1989, Computer Aided Kinematics and Dynamics of Mechanical Systems, Vol. 1, Allyn and Bacon, Boston, MA.
Wang, D. , 1993, “ An Elimination Method for Polynomial Systems,” J. Symbolic Comput., 16(2), pp. 83–114. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Placement of reinforcement elements for a crown section: umbrella arch method

Grahic Jump Location
Fig. 2

The tunnel digging machine, photo courtesy of Casagrande Group

Grahic Jump Location
Fig. 3

Kinematic model of the tunneling machine

Grahic Jump Location
Fig. 4

Denavit–Hartenberg reference system definitions

Grahic Jump Location
Fig. 5

Reference systems for the manipulator Mp

Grahic Jump Location
Fig. 6

Si and di measures for the manipulator Mp

Grahic Jump Location
Fig. 8

Reference systems in the plane pa

Grahic Jump Location
Fig. 9

Reference systems in the plane pf

Grahic Jump Location
Fig. 10

Equivalent spherical mechanism for the manipulator Mp

Grahic Jump Location
Fig. 11

Planar representation of the spherical five-bar linkage

Grahic Jump Location
Fig. 12

Solutions (a) and (b) to the direct kinematic problem

Grahic Jump Location
Fig. 13

Solutions (c) and (d) to the direct kinematic problem

Grahic Jump Location
Fig. 14

Solutions (e) and (f) to the direct kinematic problem

Grahic Jump Location
Fig. 15

Solutions (g) and (h) to the direct kinematic problem

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In