Abstract
Since the very successful application of parallel robots in material handling, many projects attempted to implement the Gough platforms as milling machine manipulators with limited success mainly achieving roughing. The displacement of the milling tool should meet surface finish requirements while increasing tool feedrate in order to improve productivity. This work introduces geometric formalization of surface finish which is more realistic then classic error calculations. This research work also proposes an off-line simulation tool analysing the milling task feasibility using a robot constituted by a general hexapod parallel manipulator, controlled by a typical CNC controller implementing classic position based algorithms where joint space polynomial interpolation is utilized. High and very high speed milling simulation results show the implementation of linear and third order interpolation between the actuator set-points calculated from the CAD/CAM computed end-effector or tool set-points. Linear interpolation is not sufficient for high speed milling and then third order interpolation reach the required surface finish at feasible CNC sampling rates.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Abdellatif H, Heimann B (2005) Adapted time-optimal trajectory planning for parallel manipulators with full dynamic modelling. In: IEEE international conference on robotics and automation. Barcelona, 19–22 April 2005, pp 413–418
Bayaziz OB, Xie D, Anamato NM (2005) Iterative relaxation of constraints: a framework for improving automated motion planning. In: IEEE international conference on robotics and automation. Barcelona, 19–22 April 2005 pp 3433–3440
Bhattacharya S, Hatwal H, Ghosh A (1998) Comparison of an exact and an approximate method of singularity avoidance in platform type parallel manipulators. Mech Mach Theory 33(7):965–974
Bohigas O et al (2012) A singularity-free path planner for closed-chain manipulators. In: IEEE international conference on robotics and automation, Saint Paul, 14–18 May 2012 pp 2128–2134
Bohigas O, Manubens M, Ros L (2012) Planning singularity-free force-feasible paths on the stewart platform. In: ARK. Innsbruck, 25–28 June 2012 pp 245–253
Brady M et al (1982) Robot motion: planning and control. MIT Press, Cambridge
Briot S, Arakelian V (2008) Optimal force generation in parallel manipulators for passing through the singular positions. Int J Robot Res 27(2):967–983
Carbone G, Gmez-Bravo F, Selvi O (2012) An experimental validation of collision-free trajectories for parallel manipulators. Mech Based Des Struct Mach 40(4):414–433
Carbone G et al (1997) An optimum path planning for Cassino parallel manipulator by using inverse dynamics. Robotica 26(02):229–239
Chablat D, Wenger P (1998) Moveability and collision analysis for fully-parallel manipulators. In: 12th RoManSy, Paris, 6–9 July 1998 pp 61–68
Chedmail P, Hascoet JY, Guerin F (1994) Collision detection analysis for milling. Adv Manuf Syst 1:247–252
Chen C-T, Chi H-W (2008) Singularity-free trajectory planning of platform-type parallel manipulators for minimum actuating efforts and reactions. Robotica 26(3):371–384
Chen C-T, Liao TT (2008) Optimal path programming of the Stewart platform manipulator using the Boltzmann-Hamel-d’Alembert dynamics formulation model. Adv Robot 22(6–7):705–730
Chen Y, McInroy JE, Yi Y (2003) Optimal, fault-tolerant mappings to achieve secondary goals without compromising primary performance. IEEE trans robot autom, vol 19(4). University Park, pp 681–691
Coiffet P (1986) Les robots, tome 1, modelisation et commande. Hermes, Paris
Corts J (2003) Motion planning algorithms for general closed-chain mechanisms. Ph.D. Thesis, Institut National Polytechnique de Toulouse, Toulouse, 16 December 2003
Corts J, Simon T, Laumond J-P (2002) A random loop generator for planning the motions of closed kinematic chains using PRM methods. In: IEEE international conference on robotics and automation. Washington, 11–15 May 2002 pp 2141–2146
Corts J, Simon T (2003) Probabilistic motion planning for parallel mechanisms. In: IEEE international conference on robotics and automation Taipei, 14–19 September 2003 pp 4354–4359
Dallefrate D et al (2002) A feed rate optimization technique for high-speed CNC machining with parallel manipulators. In: 3rd Chemnitzer Parallelkinematik Seminar, Chemnitz, 23–25 April 2002 pp 371–388
Daney D (2000) Etalonnage geometric des robots paralleles. Ph.D. thesis, Universite de Nice-Sophia Antipolis
Dasgupta B, Mruthyunjaya TS (1998) Singularity-free path planning for the Stewart platform manipulator. Mech Mach Theory 33(6):711–725
Dash AK et al (2002) Workspace analysis and singularity-free path planning of parallel manipulators. In: International conference on mechatronics technology (ICMT), Fukuoka, 29 September–3 October 2002 pp 457–462
Dash AK et al (2003) Singularity-free path planning of parallel manipulators using clustering algorithm and line geometrie. In: IEEE international conference on robotics and automation, Taipei, 14–19 September 2003 pp 761–766
Dash AK et al (2005) Workspace generation and planning singularity-free path for parallel manipulators. Mech Mach Theory 40(7):778–805
Depince P, Hascoet JY, Furet B (1997) Compensation de trajectoire d’usinage: simulation et experimentation. In: Proceedings of 13e Congrs franais de mcanique, vol 3. pp 293–296
Dombre E, Khalil W (1999) Modelisation, identification et commande des robots, seconde dition. Robotique. Hermes, traite des nouvelles technologies edition
Huang T et al (2007) Time minimum trajectory planning of a 2-DoF translation parallel robot for pick-and-place operations. Ann CIRP 56/1/2007:365–368
Jui CKK, Sun Q (2003) Path trackability and verification for parallel manipulators. In: IEEE international conference on robotics and automation. Taipei, 14–19 September 2003 pp 4336–4341
Khoukhi A, Baron L, Balazinski M (2009) Constrained multi-objective trajectory planning of parallel kinematic machines. Robot Comput-Integr Manuf 25(4–5):756–769
Lahouar S, Zeghloul S, Romdhane L (2008) Singularity free path planning for parallel robots. Analysis and design: advances in robot kinematics, pp 235–242
Latombe JC (1991) Robot motion planning. Kluwer Academic Publisher, Boston
Liegeois A (1984) Les robots, tome 7, analyse des performances et CAO. Hermes, Paris
Liu G, Trinkle JC, Shvalb N (2006) Motion planning for a class of planar closed-chain manipulators. In: IEEE international conference on robotics and automation, Orlando, 16–18 May 2006 pp 133–138
Lozano-Prez T, Wesley M (1979) An algorithm for planning collision-free paths among polyhedral obstacles. In: Communications of ACM, vol 22, pp 560–570
Luh JYS, Lin CS (1981) Optimum path planning for mechanical manipulators. Trans ASME 142–151
Magnin R, et Urso JP (1991) Commande numerique, programmation. Memotech
Marty C, Cassagnes C, La Martin P (1993) pratique de la commande numerique des machines-outils. Technique et documentation. Lavoisier, Paris
Masory O, Xiu D (1998) Contour errors in a new class of CNC machine tools. In: Proceedings of WAC98, vol 1, pp 791–798
Merlet JP (1993) Manipulateurs paralleles, septieme partie: Verification et planification de trajectoire dans l’espace de travail. Technical Report 1940, INRIA, Sophia-Antipolis, June 1993
Merlet J-P (2000) An efficient trajectory verifier for motion planning of parallel machine. In: Parallel kinematic machines international conference, Ann Arbor, 14–15 September 2000
Merlet J-P (2001) A generic trajectory verifier for the motion planning of parallel robots. J Mech Des 123(4):510–515
Merlet J-P (2007) A local motion planner for closed-loop robots. In: IEEE international conference on intelligent robots and systems (IROS), San Diego, 22–26 September 2007 pp 3088–3093
Merlet J-P, Mouly N (1994) Espace de travail et planification de trajectoire des robots parallles plans. Technical Report 2291, INRIA, Sophia-Antipolis, February 1994
Merlet JP, Perng MW, Daney D (2000) Optimal trajectory planning of 5-axis machine-tool based on a 6-axis parallel manipulator. Adv Robot Kinemat 1(1):315–322
Mery B (1997) Machines a commande numerique. Hermes, Paris
Nenchev DN, Uchiyama M (1996) Singularity-consistent path planning and control of parallel robot motion through instantaneous-self-motion type. In: IEEE international conference on robotics and automation. Minneapolis, 24–26 April 1996 pp 1864–1870
Nguyen CC et al (1992) Trajectory planning and control of a Stewart platform-based end-effector with passive compliance for part assembly. J Intell Robot Syst 6(2–3):263–281
Nilsson N (1969) A mobile automaton: an application of artificial intelligence. In: Proceedings of the international joint conference on artificial intelligence, pp 509–520
Oen K-T, Wang L-CT (2007) Optimal dynamic trajectory planning for linearly actuated platform type parallel manipulators having task space redundant degree of freedom. Mech Mach Theory 42(7):727–750
Patel A, Ehmann K (1997) Volumetric error analysis of a Stewart platform based machine tool. In: Annals of the CIRP, vol 46, pp 287–290
Pouyan A et al (2010) Eliminating redundancy and singularity in robot path planning based on masking. Expert Syst Appl 37(9):6213–6217
Pugazhenthi S, Nagarajan T, Singaperumal M (2002) Optimal trajectory planning for a hexapod machine tool during contour machining. Proceed Inst Mech Eng Part C, J Mech Eng Sci A 216(12):1247–1257
Merlet JP (1997) Les Robots Parallel, 2nd edn. Herms, Paris
Dieudonne JE, Parrish RV, Bardusch RE (1972) An actuator extension transformation for a motion simulator and an inverse transformation applying Newton-Raphson’s method, Technical Report D-7067. NASA, Washington
Lazard D (1993) On the representation of rigid-body motions and its application to generalized platform manipulators. J Comput Kinemat 1:175–182
Raghavan M (1993) The Stewart platform of general geometry has 40 configurations. ASME J Mech Des 115:277–282
Raghavan M, Roth B (1995) Solving polynomial systems for the kinematic analysis and synthesis of mechanisms and robot manipulators. Trans ASME 117:71–79
Rolland L (2001) Introduction to algebraic methods for solving the forward kinematics problem of parallel robots applied to high throughput and high accuracy. In: 3rd European-Asian congress on mechatronics, Besancon, 9–11 October 2001
Rolland L (2005) Certified solving of the forward kinematics problem with an exact algebraic method for the general parallel manipulator. Adv Robot 19(9):995–1025
Rolland L (2008) Synthesis on modeling and certified solving of the kinematics problems of Gough-type parallel manipulator with an exact algebraic method. In: Wu H (ed) Parallel manipulators, towards new applications. I-Tech Education and Publishing, Vienna, pp 175–206
Salerni G (1995) The linear delta. Technical report, University of Pisa
Shulz et al (1999) Dynamic stiffness and contouring accuracy of a HSC linear motor machine. In: Proceedings of the 2nd international conference on high speed machining, vol 1. Darmstadt, pp 75–83
Shulz H, Gao H, Stanik B (1999) Analysis and optimization of the dynamic contouring accuracy using the example of a linear motor machine tool. In: Proceedings of the 2nd international conference on high speed machining, vol 1. Darmstadt, pp 107–115
Sen S, Dasgupta B, Mallik AK (2003) Variational approach for singularity-path planning of parallel manipulators. Mech Mach Theory 38(11):1165–1183
Shaw D, Chen Y-S (2001) Cutting path generation of the Stewart platform-based milling machine using an end-mill. Int J Prod Res 39(7):1367–1383
Soni AH, Tanasi GC, Varanasi S (1995) Closed-loop multi-degree freedom mechanisms for surface generation and patching in machining 3d surfaces. In: 9th IFToMM world congress on the theory of machines and mechanisms. Milan, 30 August-2 September pp 2668–2674
Su H-J, Dietmaier P, McCarthy JM (2003) Trajectory planning for constrained parallel manipulators. ASME J Mech Des 125(4):709–716
Takeda Y (2005) Kinematic analysis of parallel mechanisms at singular points at which a connecting chain has local mobility. In: Computational kinematics, Cassino, 4–6 May 2005
Taylor R (1979) Planning and execution of straight line manipulator. IBM J Res Dev 23(4):424–436
Tchon K et al (2012) Motion planning for parallel robots with non-holonomic joints. In: ARK, Innsbruck, 25–28 June 2012 pp 115–122
Tournassoud P (1992) Planification et controle en robotique, application aux robots mobiles et manipulateurs. Robotique. Hermes, Paris, Traité des nouvelles technologies edition
Trinkle JC, Milgram RJ (2002) Complete path planning for closed kinematic chains with spherical joints. Int J Robot Res 21(9):773–789
Udupa SM (1977) Collision detection and avoidance in computer controlled manipulators. In: Proceedings of the international joint conference on artificial intelligence, pp 737–748
Ur-Rehman R, Caro S, Chablat D, Wenger P (2010) Multi-objective path placement of parallel kinematics machines based on energy consumption, shaking forces and maximum actuator torques: application to the Orthoglide. Mech Mach Theory 45(8):1125–1141
Vaca R, Aranda J, Thomas F (2012) Simplified Voronoi diagrams for motion planning of quadratically-solvable Gough-Stewart platforms. In: ARK, Innsbruck, 25–28 June 2012 pp 157–164
Vaishnav RN, Magrab EB (1987) A general procedure to evaluate robot positioning error. Int J Robot Res 6(1):59–74
Yakey JH et al (2001) Randomized path planning for linkages with closed kinematic chains. IEEE Trans Robot Autom 17(6):951–958
Acknowledgments
This research work was produced by the author during his PhD and with special funding from the Lorraine Region, the INRIA and CMW-Marioni. It has helped French hexapod manufacturers to fine-tune their milling machines.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Rolland, L. (2015). Path Planning Kinematics Simulation of CNC Machine Tools Based on Parallel Manipulators. In: Carbone, G., Gomez-Bravo, F. (eds) Motion and Operation Planning of Robotic Systems. Mechanisms and Machine Science, vol 29. Springer, Cham. https://doi.org/10.1007/978-3-319-14705-5_6
Download citation
DOI: https://doi.org/10.1007/978-3-319-14705-5_6
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-14704-8
Online ISBN: 978-3-319-14705-5
eBook Packages: EngineeringEngineering (R0)