Abstract
Direct kinematics (DK) of parallel robots is most of the time a difficult problem. This is true for cable-driven parallel robots (CDPR) especially if cable deformations are taken into account. If the cable model, whatever it is, is introduced in the kinematic equations we always end up with a square system of equations that is usually very difficult to solve. We first show that with minimal assumptions we are able to give an upper bound on the number of the solutions of the DK whatever is the cable model. We then propose a generic method, based on non-linear continuation, to solve the DK for any cable model, that is illustrated with a practical example of sagging cables.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Abbasnejad, G., Carricato, M.: Real solutions of the direct geometrico-static problem of underconstrained cable-driven parallel robot with 3 cables: a numerical investigation. Meccanica 473(7), 1761–1773 (2012)
Berti, A.: Kinematics and statics of cable-driven parallel robots by interval-analysis-based methods. Ph.D. thesis, University of Bologna, Bologna, 21 Apr 2015
Berti, A., Merlet, J.P., Carricato, M.: Solving the direct geometrico-static problem of the 3-3 cable-driven parallel robots by interval analysis: preliminary results. In: 1st International Conference on Cable-Driven Parallel Robots (CableCon), pp. 251–268. Stuttgart, 3–4 September 2012
Bruckman, T., et al.: Parallel manipulators, New Developments, Chap. Wire robot part I, kinematics, analysis and design, pp. 109–132. ITECH (2008)
Carricato, M., Abbasnejad, G.: Direct geometrico-static analysis of under-constrained cable-driven parallel robots with 4 cables. In: 1st International Conference on cable-driven parallel robots (CableCon), pp. 269–286. Stuttgart, 3–4 Sept 2012
Carricato, M., Merlet, J.P.: Stability analysis of underconstrained cable-driven parallel robots. IEEE Trans. Robot. 29(1), 288–296 (2013)
Carricato, M., Merlet, J.P.: Direct geometrico-static problem of under-constrained cable-driven parallel robots with three cables. In: IEEE International Conference on Robotics and Automation, pp. 3011–3017. Shangai, 9–13 May 2011
Gouttefarde, M., et al.: Simplified static analysis of large-dimension parallel cable-driven robots. In: IEEE International Conference on Robotics and Automation, pp. 2299–2305 (2012)
Irvine, H.M.: Cable Structures. MIT Press (1981)
Jiang, Q., Kumar, V.: The inverse kinematics of 3-d towing. In: ARK (2010)
Kozak, K., et al.: Static analysis of cable-driven manipulators with non-negligible cable mass. IEEE Trans. Robot. 22(3), 425–433 (2006)
Merlet, J.P.: The forward kinematics of cable-driven parallel robots with sagging cables. In: 2nd International Conference on cable-driven parallel robots (CableCon), pp. 3–16. Duisburg (2014)
Merlet, J.P.: The kinematics of cable-driven parallel robots with sagging cables: preliminary results. In: IEEE International Conference on Robotics and Automation, pp. 1593–1598. Seattle (2015)
Merlet, J.P.: MARIONET, a family of modular wire-driven parallel robots. In: ARK, pp. 53–62. Piran, 28 Jun–1 Jul 2010
Merlet, J.P., Daney, D.: A portable, modular parallel wire crane for rescue operations. In: IEEE International Conference on Robotics and Automation, pp. 2834–2839. Anchorage, 3–8 May 2010
Nguyen, D., et al.: On the simplification of cable model in static analysis of large dimension cable-driven parallel robots. In: IEEE International Conference on Intelligent Robots and Systems (IROS), pp. 928–934. Tokyo, 3–7 Nov 2013
Pott, A.: An algorithm for real-time forward kinematics of cable-driven parallel robots. In: ARK, pp. 529–538. Piran, 28 Jun–1 Jul 2010
Pott, A., et al.: IPAnema: a family of cable-driven parallel robots for industrial applications. In: 1st International Conference on Cable-Driven Parallel Robots (CableCon), pp. 119–134. Stuttgart (2012)
Riehl, N., et al.: Effects of non-negligible cable mass on the static behavior of large workspace cable-driven parallel mechanisms. In: IEEE International Conference on Robotics and Automation, pp. 2193–2198. Kobe, 14–16 May 2009
Tadokoro, S., et al.: A portable parallel manipulator for search and rescue at large-scale urban earthquakes and an identification algorithm for the installation in unstructured environments. In: IEEE International Conference on Intelligent Robots and Systems (IROS) (1999)
Tapia, R.: The Kantorovitch theorem for Newton’s method. American Mathematic Monthly 78(1.ea), 389–392 (1971)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing Switzerland
About this paper
Cite this paper
Merlet, JP. (2017). Preliminaries of a New Approach for the Direct Kinematics of Suspended Cable-Driven Parallel Robot with Deformable Cables. In: Wenger, P., Flores, P. (eds) New Trends in Mechanism and Machine Science. Mechanisms and Machine Science, vol 43. Springer, Cham. https://doi.org/10.1007/978-3-319-44156-6_36
Download citation
DOI: https://doi.org/10.1007/978-3-319-44156-6_36
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-44155-9
Online ISBN: 978-3-319-44156-6
eBook Packages: EngineeringEngineering (R0)