Abstract
This chapter presents an introduction to the kinematics and dynamics of parallel mechanisms, also referred to as parallel robots. As opposed to classical serial manipulators, the kinematic architecture of parallel robots includes closed-loop kinematic chains. As a consequence, their analysis differs considerably from that of their serial counterparts. This chapter aims at presenting the fundamental formulations and techniques used in their analysis.
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- 3-D:
-
three-dimensional
- CCT:
-
conservative congruence transformation
- DOF:
-
degree of freedom
References
J.E. Gwinnett: Amusement device, US Patent 1789680 (1931)
V.E. Gough: Contribution to discussion of papers on research in automobile stability, control and tyre performance, 1956--1957. Proc. Auto Div. Inst. Mech. Eng. (1956)
D. Stewart: A platform with 6 degrees of freedom, Proc. Inst. Mech. Eng. Part 1 15 (1965) pp. 371–386
I.A. Bonev: The true origins of parallel robots, http://www.parallemic.org/Reviews/Review007.html (2003)
S. Briot, I.A. Bonev: Are parallel robots more accurate than serial robots?, CSME Transactions 31(4), 445–456 (2007)
G. Aridon, D. Rémond, F. Morestin, L. Blanchard, R. Dufour: Self-deployment of a tape-spring hexapod: experimental and numerical investigation, ASME J. Mech. Des. 131(2), 0210031–0210037 (2009)
M. Hafez, M.D. Lichter, S. Dubowsky: Optimized binary modular reconfigurable robotic devices, IEEE Trans. Mechatron. 8(1), 152–162 (2003)
J. Albus, R. Bostelman, N. Dagalakis: The NIST robocrane, J. Robotic Syst. 10(5), 709–724 (1993)
R. Clavel: DELTA, a fast robot with parallel geometry, 18th Int. Symp.Ind. Robots (ISIR), Lausanne (1988) pp. 91–100
K.H. Hunt: Structural kinematics of in parallel actuated robot arms, J. Mech. Transm. Autom. Des. 105(4), 705–712 (1983)
K.E. Neumann: Robot: Neos Product HB Norrtalje Suède. US Patent 4732525, (1988)
Q. Li, J.M. Hervè: Parallel mechanisms with bifurcation of Schoenflies motion, IEEE Trans. Robotics 25(1), 158–164 (2009)
J.M. Hervé: Group mathematics and parallel link mechanisms, 9th IFToMM World Congr.TheoryMach.Mech., Milan (1995) pp. 2079–2082
C.-C. Lee, J.M. Hervè: Type synthesis of primitive Schönflies-motion generators, Mech.Mach. Theory 44(10), 1980–1997 (2009)
J. Meng, G.F. Liu, Z. Li: A geometric theory for analysis and synthesis of sub-6 DOF parallel manipulators, IEEE Trans. Robotics 23(4), 625–649 (2007)
X. Kong, C.M. Gosselin: Type Synthesis of Parallel Mechanisms, Springer Tracts in Advanced Robotics, Vol. 33 (Springer, Berlin, Heidelberg 2007)
J.P. Merlet: http://www.sop.inria.fr/members/Jean-Pierre.Merlet//Archi/archi_robot.html (INRIA, France)
F. Pierrot, V. Nabat, O. Company, S. Krut, P. Poignet: Optimal design of a 4-DOF parallel manipulator: From academia to industry, IEEE Trans.Robotics 25(2), 213–224 (2009)
C. Gosselin, T. Lalibertè, A. Veillette: Singularity-free kinematically redundant planar parallel mechanisms with unlimited rotational capability, IEEE Trans. Robotics 31(2), 457–467 (2015)
G. Gogu: Structural Synthesis of Parallel Robots (Kluwer, Dordrecht 2007)
P. Dietmaier: The Stewart Gough platform of general geometry can have 40 real postures. In: Advances in Robot Kinematics: AnalysisControl, ed. by J. Lenarčič, M.L. Husty (Kluwer, Dordrecht 1998) pp. 7–16
M.L. Husty: An algorithm for solving the direct kinematic of Stewart Gough-type platforms, Mech.Mach. Theory 31(4), 365–380 (1996)
M. Raghavan: The Stewart platform of general geometry has 40 configurations, ASME J. Mech. Des. 115(2), 277–282 (1993)
J.C. Faugère, D. Lazard: The combinatorial classes of parallel manipulators, Mech.Mach. Theory 30(6), 765–776 (1995)
T.-Y. Lee, J.-K. Shim: Improved dyalitic elimination algorithm for the forward kinematics of the general Stewart Gough platform, Mech.Mach. Theory 38(6), 563–577 (2003)
F. Rouillier: Real roots counting for some robotics problems. In: Computational Kinematics, ed. by J.-P. Merlet, B. Ravani (Kluwer, Dordrecht 1995) pp. 73–82
J.-P. Merlet: Solving the forward kinematics of a Gough-type parallel manipulator with interval analysis, Int. J. Robotics Res. 23(3), 221–236 (2004)
D. Manocha: Algebraic and Numeric Techniques for Modeling and Robotics, Ph.D. Thesis (University of California, Berkeley 1992)
A.J. Sommese, C.W. Wampler: The Numerical Solution of Systems of Polynomials: Arising in Engineering And Science (World Scientific, Singapore 2005)
C. Gosselin, J. Sefrioui, M.J. Richard: Solution polynomiale au problème de la cinématique directe des manipulateurs parallèles plans à 3 degrés de liberté, Mech.Mach. Theory 27(2), 107–119 (1992)
P. Wenger, D. Chablat, M. Zein: Degeneracy study of the forward kinematics of planar $3-R\underline{P}R$ parallel manipulators, ASME J. Mech. Des. 129(12), 1265–1268 (2007)
L. Baron, J. Angeles: The direct kinematics of parallel manipulators under joint-sensor redundancy, IEEE Trans.RoboticsAutom. 16(1), 12–19 (2000)
J.-P. Merlet: Closed-form resolution of the direct kinematics of parallel manipulators using extra sensors data, IEEE Int. Conf.RoboticsAutom. (ICRA), Atlanta (1993) pp. 200–204
R. Vertechy, V. Parenti-Castelli: Robust, fast and accurate solution of the direct position analysis of parallel manipulators by using extra-sensors. In: Parallel Manipulators: Towards New Applications, ed. by H. Wu (InTech, Rijeka 2008) pp. 133–154
R. Stoughton, T. Arai: Kinematic optimization of a chopsticks-type micro-manipulator, Jpn. Symp.Flex. Autom., San Fransisco (1993) pp. 151–157
J.-P. Merlet, D. Daney: Dimensional synthesis of parallel robots with a guaranteed given accuracy over a specific workspace, IEEE Int. Conf.RoboticsAutom. (ICRA), Barcelona (2005)
J.-P. Merlet: Jacobian, manipulability, condition number, and accuracy of parallel robots, ASME J. Mech. Des. 128(1), 199–206 (2006)
F.-T. Niaritsiry, N. Fazenda, R. Clavel: Study of the source of inaccuracy of a 3 DOF flexure hinge-based parallel manipulator, IEEE Int. Conf.RoboticsAutom. (ICRA), New Orleans (2004) pp. 4091–4096
G. Pritschow, C. Eppler, T. Garber: Influence of the dynamic stiffness on the accuracy of PKM, 3rd Chemnitzer Parallelkinematik Semin. Chemnitz (2002) pp. 313–333
V. Parenti-Castelli, S. Venanzi: On the joint clearance effects in serial and parallel manipulators, WorkshopFundam. IssuesFuture Res. Dir.Parallel Mech.Manip. Québec (2002) pp. 215–223
A. Pott, M. Hiller: A new approach to error analysis in parallel kinematic structures, Adv. Robot Kinemat., Sestri-Levante (2004)
K. Wohlhart: Degrees of shakiness, Mech.Mach. Theory 34(7), 1103–1126 (1999)
K. Tönshoff, B. Denkena, G. Günther, H.C. Möhring: Modelling of error effects on the new hybrid kinematic DUMBO structure, 3rd Chemnitzer Parallelkinematik Semin. Chemnitz (2002) pp. 639–653
U. Sellgren: Modeling of mechanical interfaces in a systems context, Int. ANSYS Conf., Pittsburgh (2002)
S. Eastwood, P. Webbb: Compensation of thermal deformation of a hybrid parallel kinematic machine, RoboticsComput. Manuf. 25(1), 81–90 (2009)
W. Khalil, S. Besnard: Identificable parameters for the geometric calibration of parallel robots, Arch.Control Sci. 11(3/4), 263–277 (2001)
C.W. Wampler, J.M. Hollerbach, T. Arai: An implicit loop method for kinematic calibration and its application to closed-chain mechanisms, IEEE Trans.RoboticsAutom. 11(5), 710–724 (1995)
D. Daney, Y. Papegay, A. Neumaier: Interval methods for certification of the kinematic calibration of parallel robots, IEEE Int. Conf.RoboticsAutom. (ICRA), New Orleans (2004) pp. 1913–1918
D. Daney, N. Andreff, G. Chabert, Y. Papegay: Interval method for calibration of parallel robots: a vision-based experimentation, Mech.Mach. Theory 41(8), 929–944 (2006)
A. Nahvi, J.M. Hollerbach: The noise amplification index for optimal pose selection in robot calibration, IEEE Int. Conf.RoboticsAutom. (ICRA), Minneapolis (1996) pp. 647–654
G. Meng, L. Tiemin, Y. Wensheng: Calibration method and experiment of Stewart platform using a laser tracker, Int. ConfSyst. ManCybern., Hague (2003) pp. 2797–2802
D. Daney: Optimal measurement configurations for Gough platform calibration, IEEE Int. Conf.RoboticsAutom. (ICRA), Washington (2002) pp. 147–152
P. Renaud, N. Andreff, P. Martinet, G. Gogu: Kinematic calibration of parallel mechanisms: A novel approach using legs observation, IEEE Trans. Robotics 21(4), 529–538 (2005)
C. Gosselin, J. Angeles: Singularity analysis of closed-loop kinematic chains, IEEE Trans.RoboticsAutom. 6(3), 281–290 (1990)
D. Zlatanov, R.G. Fenton, B. Benhabib: A unifying framework for classification and interpretation of mechanism singularities, ASME J. Mech. Des. 117(4), 566–572 (1995)
D. Zlatanov, I.A. Bonev, C.M. Gosselin: Constraint singularities of parallel mechanisms, IEEE Int. Conf.RoboticsAutom. (ICRA), Washington (2002) pp. 496–502
M. Conconi, M. Carricato: A new assessment of singularities of parallel kinematic chains, IEEE Trans. Robotics 25(4), 757–770 (2009)
G. Liu, Y. Lou, Z. Li: Singularities of parallel manipulators: A geometric treatment, IEEE Trans. RoboticsAutom. 19(4), 579–594 (2003)
I.A. Bonev, D. Zlatanov: The mystery of the singular SNUtranslational parallel robot, http://www.parallemic.org/Reviews/Review004.html (2001)
H. Li, C.M. Gosselin, M.J. Richard, B. Mayer St-Onge: Analytic form of the six-dimensional singularity locus of the general Gough-Stewart platform, ASME J. Mech. Des. 128(1), 279–287 (2006)
B. Mayer St-Onge, C.M. Gosselin: Singularity analysis and representation of the general Gough-Stewart platform, Int. J. Robotics Res. 19(3), 271–288 (2000)
J.-P. Merlet: Singular configurations of parallel manipulators and Grassmann geometry, Int. J. Robotics Res. 8(5), 45–56 (1989)
R. Ben-Horin, M. Shoham: Application of Grassmann Cayley algebra to geometrical interpretation of parallel robot singularities, Int. J. Robotics Res. 28(1), 127–141 (2009)
H. Pottmann, M. Peternell, B. Ravani: Approximation in line space. Applications in robot kinematics, Adv. Robot Kinemat., Strobl (1998) pp. 403–412
P.A. Voglewede, I. Ebert-Uphoff: Measuring closeness to singularities for parallel manipulators, IEEE Int. Conf.RoboticsAutom. (ICRA), New Orleans (2004) pp. 4539–4544
G. Nawratil: New performance indices for 6-DOF UPS and 3-DOF RPR parallel manipulators, Mech.Mach. Theory 44(1), 208–221 (2009)
J. Hubert, J.-P. Merlet: Static of parallel manipulators and closeness to singularity, J. Mech.Robotics 1(1), 1–6 (2009)
P. Cardou, S. Bouchard, C. Gosselin: Kinematic-sensitivity indices for dimensionally nonhomogeneous jacobian matrices, IEEE Trans. Robotics 26(1), 166–173 (2010)
J.-P. Merlet, D. Daney: A formal-numerical approach to determine the presence of singularity within the workspace of a parallel robot. In: Computational Kinematics, ed. by F.C. Park, C.C. Iurascu (EJCK, Seoul 2001) pp. 167–176
S. Bhattacharya, H. Hatwal, A. Ghosh: Comparison of an exact and an approximate method of singularity avoidance in platform type parallel manipulators, Mech.Mach. Theory 33(7), 965–974 (1998)
D.N. Nenchev, M. Uchiyama: Singularity-consistent path planning and control of parallel robot motion through instantaneous-self-motion type, IEEE Int. Conf.RoboticsAutom. (ICRA), Minneapolis (1996) pp. 1864–1870
C. Innocenti, V. Parenti-Castelli: Singularity-free evolution from one configuration to another in serial and fully-parallel manipulators, 22nd Bienn. Mech. Conf., Scottsdale (1992) pp. 553–560
M. Husty: Non-singular assembly mode change in 3-RPR parallel manipulators. In: Computational Kinematics, ed. by A. Kecskeméthy, A. Müller (Springer, Berlin, Heidelberg 2009) pp. 51–60
S. Caro, P. Wenger, D. Chablat: Non-singular assembly mode changing trajectories of a 6-DOF parallel robot, ASME Int. Des. Eng. Techn. Conf. Comput. Inform. Eng. Conf., Chicago (2012)
R. Ranganath, P.S. Nair, T.S. Mruthyunjaya, A. Ghosal: A force-torque sensor based on a Stewart platform in a near-singular configuration, Mech.Mach. Theory 39(9), 971–998 (2004)
M.L. Husty, A. Karger: Architecture singular parallel manipulators and their self-motions. In: Adv.Robot Kinematics: AnalysisControl, ed. by J. Lenarčič, M.L. Husty (Springer, Dordrecht 2000) pp. 355–364
A. Karger: Architecture singular planar parallel manipulators, Mech.Mach. Theory 38(11), 1149–1164 (2003)
K. Wohlhart: Mobile 6-SPS parallel manipulators, J. Robotic Syst. 20(8), 509–516 (2003)
C. Innocenti, V. Parenti-Castelli: Direct kinematics of the 6-4 fully parallel manipulator with position and orientation uncoupled, Eur. RoboticsIntell. Syst. Conf., Corfou (1991)
G. Gogu: Mobility of mechanisms: A critical review, Mech.Mach. Theory 40(10), 1068–1097 (2005)
I. Zabalza, J. Ros, J.J. Gil, J.M. Pintor, J.M. Jimenez: Tri-Scott a new kinematic structure for a 6-DOF decoupled parallel manipulator, WorkshopFundam. IssuesFuture Res. Dir.Parallel Mech.Manip., Québec (2002) pp. 12–15
C. Gosselin: Determination of the workspace of 6-DOF parallel manipulators, ASME J. Mech. Des. 11(3), 331–336 (1990)
J.-P. Merlet: Geometrical determination of the workspace of a constrained parallel manipulator, Adv. Robot Kinemat., Ferrare (1992) pp. 326–329
F.A. Adkins, E.J. Haug: Operational envelope of a spatial Stewart platform, ASME J. Mech. Des. 119(2), 330–332 (1997)
E.J. Haugh, F.A. Adkins, C.M. Luh: Operational envelopes for working bodies of mechanisms and manipulators, ASME J. Mech. Des. 120(1), 84–91 (1998)
O. Bohigas, L. Ros, M. Manubens: A complete method for workspace boundary determination, Adv. Robot Kinemat., Piran (2010) pp. 329–338
J.-P. Merlet: Determination of 6D workspaces of Gough-type parallel manipulator and comparison between different geometries, Int. J. Robotics Res. 18(9), 902–916 (1999)
P. Wenger, D. Chablat: Workspace and assembly modes in fully parallel manipulators: A descriptive study. In: Advances in Robot Kinematics: AnalysisControl, ed. by J. Lenarčič, M.L. Husty (Springer, Dordrecht 1998) pp. 117–126
G. Moroz, F. Rouiller, D. Chablat, P. Wenger: On the determination of cusp points of 3-$R\underline{P}R$ parallel manipulators, Mech.Mach. Theory 45(11), 1555–1567 (2010)
S. Briot, V. Arakelian: Optimal force generation in parallel manipulators for passing through the singular positions, Int. J. Robotics Res. 27(2), 967–983 (2008)
J. Hesselbach, C. Bier, C. Budde, P. Last, J. Maaß, M. Bruhn: Parallel robot specific control fonctionalities, 2nd Int. Colloquium, Collab. Res. Centre, Braunschweig (2005) pp. 93–108
J.-P. Merlet: An efficient trajectory verifier for motion planning of parallel machine, Parallel Kinemat. Mach. Int. Conf., Ann Arbor (2000)
R. Ur-Rehman, S. Caro, D. Chablat, P. Wenger: 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 (2010)
J. Cortés, T. Siméon: Probabilistic motion planning for parallel mechanisms, IEEE Int. Conf.RoboticsAutom. (ICRA), Taipei (2003) pp. 4354–4359
J.H. Yakey, S.M. LaValle, L.E. Kavraki: Randomized path planning for linkages with closed kinematic chains, IEEE Trans.RoboticsAutom. 17(6), 951–958 (2001)
J.-P. Merlet, M.-W. Perng, D. Daney: Optimal trajectory planning of a 5-axis machine tool based on a 6-axis parallel manipulator. In: Advances in Robot Kinematics, ed. by J. Lenarčič, M.L. Husty (Kluwer, Dordrecht 2000) pp. 315–322
D. Shaw, Y.-S. Chen: Cutting path generation of the Stewart platform-based milling machine using an end-mill, Int. J. Prod. Res. 39(7), 1367–1383 (2001)
Z. Wang, Z. Wang, W. Liu, Y. Lei: A study on workspace, boundary workspace analysis and workpiece positioning for parallel machine tools, Mech.Mach. Theory 36(6), 605–622 (2001)
D.R. Kerr: Analysis, properties, and design of a Stewart-platform transducer, J. Mech. Transm.Autom.Des. 111(1), 25–28 (1989)
C.C. Nguyen, S.S. Antrazi, Z.L. Zhou, C.E. Campbell: Analysis and experimentation of a Stewart platform-based force/torque sensor, Int. J. RoboticsAutom. 7(3), 133–141 (1992)
C. Reboulet, A. Robert: Hybrid control of a manipulator with an active compliant wrist, 3rd Int. Symp. Robotics Res., Gouvieux (1985) pp. 76–80
J. Duffy: Statics and Kinematics with Applications to Robotics (Cambridge Univ. Press, New York 1996)
C. Huang, W.-H. Hung, I. Kao: New conservative stiffness mapping for the Stewart Gough platform, IEEE Int. Conf.RoboticsAutom. (ICRA), Washington (2002) pp. 823–828
J.L. Herder: Energy-free systems: Theory, Conception and Design of Statically Balanced Spring Mechanisms, Ph.D. Thesis (Delft University of Technology, Delft 2001)
G.R. Dunlop, T.P. Jones: Gravity counter balancing of a parallel robot for antenna aiming, 6th Int. Symp. Robotics Manuf., Montpellier (1996) pp. 153–158
M. Jean, C. Gosselin: Static balancing of planar parallel manipulators, IEEE Int. Conf.RoboticsAutom. (ICRA), Minneapolis (1996) pp. 3732–3737
I. Ebert-Uphoff, C.M. Gosselin, T. Laliberté: Static balancing of spatial parallel platform-revisited, ASME J. Mech. Des. 122(1), 43–51 (2000)
C.M. Gosselin, J. Wang: Static balancing of spatial six-degree-of-freedom parallel mechanisms with revolute actuators, J. Robotic Syst. 17(3), 159–170 (2000)
M. Leblond, C.M. Gosselin: Static balancing of spatial and planar parallel manipulators with prismatic actuators, ASME Des. Eng. Tech. Conf., Atlanta (1998) pp. 5187–5193
B. Monsarrat, C.M. Gosselin: Workspace analysis and optimal design of a 3-leg 6-DOF parallel platform mechanism, IEEE Trans.RoboticsAutom. 19(6), 954–966 (2003)
J. Wang, C.M. Gosselin: Static balancing of spatial three-degree-of-freedom parallel mechanisms, Mech.Mach. Theory 34(3), 437–452 (1999)
Y. Wu, C.M. Gosselin: Synthesis of reactionless spatial 3-DOF and 6-DOF mechanisms without separate counter-rotations, Int. J. Robotics Res. 23(6), 625–642 (2004)
M. Ait-Ahmed: Contribution à la Modélisation Géométrique et Dynamique des Robots Parallèles, Ph.D. Thesis (Univ. Paul Sabatier, Toulouse 1993)
G.F. Liu, X.Z. Wu, Z.X. Li: Inertial equivalence principle and adaptive control of redundant parallel manipulators, IEEE Int. Conf.RoboticsAutom. (ICRA), Washington (2002) pp. 835–840
R. Clavel: Conception d'un robot parallèle rapide à 4 degrés de liberté, Ph.D. Thesis (EPFL, Lausanne, 1991), No. 925.
J. Gallardo, J.M. Rico, A. Frisoli, D. Checcacci, M. Bergamasco: Dynamics of parallel manipulators by means of screw theory, Mech.Mach. Theory 38(11), 1113–1131 (2003)
L.-W. Tsai: Solving the inverse dynamics of a Stewart Gough manipulator by the principle of virtual work, ASME J. Mech. Des. 122(1), 3–9 (2000)
J. Wang, C.M. Gosselin: A new approach for the dynamic analysis of parallel manipulators, Multibody Syst. Dyn. 2(3), 317–334 (1998)
Z. Geng, L.S. Haynes: On the dynamic model and kinematic analysis of a class of Stewart platforms, RoboticsAuton. Syst. 9(4), 237–254 (1992)
K. Liu, F. Lewis, G. Lebret, D. Taylor: The singularities and dynamics of a Stewart platform manipulator, J. Intell.Robotic Syst. 8(3), 287–308 (1993)
K. Miller, R. Clavel: The Lagrange-based model of Delta-4 robot dynamics, Robotersysteme 8(1), 49–54 (1992)
H. Abdellatif, B. Heimann: Computational efficient inverse dynamics of 6-DOF fully parallel manipulators by using the Lagrangian formalism, Mech.Mach. Theory 44(1), 192–207 (2009)
K. Miller: Optimal design and modeling of spatial parallel manipulators, Int. J. Robotics Res. 23(2), 127–140 (2004)
A. Codourey, E. Burdet: A body oriented method for finding a linear form of the dynamic equations of fully parallel robot, IEEE Int. Conf.RoboticsAutom. (ICRA), Albuquerque (1997) pp. 1612–1618
B. Dasgupta, P. Choudhury: A general strategy based on the Newton Euler approach for the dynamic formulation of parallel manipulators, Mech.Mach. Theory 34(6), 801–824 (1999)
P. Guglielmetti: Model-Based Control of Fast Parallel Robots: a Global Approach in Operational Space, Ph.D. Thesis (EPFL, Lausanne, 1994)
K. Harib, K. Srinivasan: Kinematic and dynamic analysis of Stewart platform-based machine tool structures, Robotica 21(5), 541–554 (2003)
W. Khalil, O. Ibrahim: General solution for the dynamic modeling of parallel robots, IEEE Int. Conf.RoboticsAutom. (ICRA), New Orleans (2004) pp. 3665–3670
C. Reboulet, T. Berthomieu: Dynamic model of a six degree of freedom parallel manipulator, Int. Conf. Adv. Robotics, Pise (1991) pp. 1153–1157
H. Abdellatif, B. Heimann: Experimental identification of the dynamics model for 6-DOF parallel manipulators, Robotica 28(3), 359–368 (2010)
H. Abdellatif, B. Heimann: Model based control for industrial robots: Uniform approaches for serial and parallel structures. In: Industrial Robotics: Theory, Modelling and Control, ed. by S. Cubero (pro literatur Verlag, Augsburg 2007) pp. 523–556
S. Tadokoro: Control of parallel mechanisms, Adv. Robotics 8(6), 559–571 (1994)
M. Honegger, A. Codourey, E. Burdet: Adaptive control of the Hexaglide, a 6 DOF parallel manipulator, IEEE Int. Conf. RoboticsAutom. (ICRA), Albuquerque (1997) pp. 543–548
S. Bhattacharya, H. Hatwal, A. Ghosh: An on-line estimation scheme for generalized Stewart platform type parallel manipulators, Mech.Mach. Theory 32(1), 79–89 (1997)
P. Guglielmetti, R. Longchamp: A closed-form inverse dynamics model of the Delta parallel robot, 4th IFAC Symp.Robot Control, Syroco, Capri (1994) pp. 51–56
K. Miller: Modeling of dynamics and model-based control of DELTA direct-drive parallel robot, J. RoboticsMechatron. 17(4), 344–352 (1995)
E. Burdet, M. Honegger, A. Codourey: Controllers with desired dynamic compensation and their implementation on a 6 DOF parallel manipulator, IEEE Int. Conf.Intell. RobotsSyst. (IROS), Takamatsu (2000)
K. Yamane, Y. Nakamura, M. Okada, N. Komine, K.I. Yoshimoto: Parallel dynamics computation and $h_{{\infty}}$ acceleration control of parallel manipulators for acceleration display, ASME J. Dyn. Syst. Meas.Control 127(2), 185–191 (2005)
J.E. McInroy: Modeling and design of flexure jointed Stewart platforms for control purposes, IEEE/ASME Trans.Mechatron. 7(1), 95–99 (2002)
F. Paccot, N. Andreff, P. Martinet: A review on the dynamic control of parallel kinematic machines: theory and experiments, Int. J. Robotics Res. 28(3), 395–416 (2009)
D. Corbel, M. Gouttefarde, O. Company, F. Pierrot: Towards 100G with PKM is actuation redundancy a good solution for pick-and-place?, IEEE Int. Conf. RoboticsAutom. (ICRA), Anchorage (2010) pp. 4675–4682
F. Xi: Dynamic balancing of hexapods for high-speed applications, Robotica 17(3), 335–342 (1999)
J. Angeles: The robust design of parallel manipulators, 1st Int. Colloquium, Collab. Res. Centre, Braunschweig (2002) pp. 9–30
S. Bhattacharya, H. Hatwal, A. Ghosh: On the optimum design of a Stewart platform type parallel manipulators, Robotica 13(2), 133–140 (1995)
K.E. Zanganeh, J. Angeles: Kinematic isotropy and the optimum design of parallel manipulators, Int. J. Robotics Res. 16(2), 185–197 (1997)
H. Fang, J.-P. Merlet: Multi-criteria optimal design of parallel manipulators based on interval analysis, Mech.Mach. Theory 40(2), 151–171 (2005)
S. Kamamura, W. Choe, S. Tanaka, S.R. Pandian: Development of an Ultrahigh Speed Robot FALCON using Wire Drive System, IEEE Int. Conf.RoboticsAutom. (ICRA) (1995) pp. 215–220
L.L. Cone: Skycam: An Aerial Robotic Camera System, Byte 10(10), 122–132 (1985)
J. Pusey, A. Farrah, S.K. Agrawal, E. Messina: Design and workspace analysis of a 6-6 cable-suspended parallel robot, Mech. Mach. Theory 39, 761–778 (2004)
C. Gosselin, S. Bouchard: A gravity-powered mechanism for extending the workspace of a cable-driven parallel mechanism: Application to the appearance modelling of objects, Int. J. Autom. Technol. 4(4), 372–379 (2010)
J. Lamaury, M. Gouttefarde: A tension distribution method with improved computational efficiency. In: Cable-Driven Parallel Robots, ed. by T. Bruckmann, A. Pott (Springer, Berlin, Heidelberg 2012) pp. 71–85
A.T. Riechel, I. Ebert-Uphoff: Force-feasible workspace analysis for underconstrained,point-mass cable robots, IEEE Int. Conf.RoboticsAutom. (ICRA) (2004) pp. 4956–4962
D. Cunningham, H. Asada: The Winch-Bot: A cable-suspended, under-actuated robot utilizing parametric self-excitation, IEEE Int. Conf.RoboticsAutom. (ICRA) (2009) pp. 1844–1850
S. Lefrançois, C. Gosselin: Point-to-point motion control of a pendulum-like 3-DOF underactuated cable-driven robot, IEEE Int. Conf.RoboticsAutom. (ICRA) (2010) pp. 5187–5193
D. Zanotto, G. Rosati, S.K. Agrawal: Modeling and control of a 3-DOF pendulum-like manipulator, IEEE Int. Conf.RoboticsAutom. (ICRA) (2011) pp. 3964–3969
C. Gosselin, P. Ren, S. Foucault: Dynamic trajectory planning of a two-DOF cable-suspended parallel robot, IEEE Int. Conf.RoboticsAutom. (ICRA) (2012) pp. 1476–1481
G. Barrette, C. Gosselin: Determination of the dynamic workspace of cable-driven planar parallel mechanisms, ASME J. Mech. Des. 127(2), 242–248 (2005)
M. Carricato, J.-P. Merlet: Direct geometrico-static problem of under-constrained cable-driven parallel robots with three cables, IEEE Int. Conf.RoboticsAutom. (ICRA) (2011) pp. 3011–3017
J.-F. Collard, P. Cardou: Computing the lowest equilibrium pose of a cable-suspended rigid body, Optim.Eng. 14, 457–476 (2013)
S. Behzadipour, A. Khajepour: Trajectory planning in cable-based high-speed parallel robots, IEEE Trans.Robotics 22(3), 559–563 (2006)
M. Gouttefarde, C. Gosselin: Analysis of the wrench-closure workspace of planar parallel cable-driven mechanisms, IEEE Trans.Robotics 22(3), 434–445 (2006)
E. Stump, V. Kumar: Workspace delienation of cable-actuated parallel manipulators, ASME Int. Des. Eng. Tech. Conf. (2004)
M. Gouttefarde, D. Daney, J.-P. Merlet: Interval-analysis-based determination of the wrench-feasible workspace of parallel cable-driven robots, IEEE Trans.Robotics 27(1), 1–13 (2011)
K. Azizian, P. Cardou: The dimensional synthesis of planar parallel cable-driven mechanisms through convex relaxations, ASME J. Mech. Des. 4(3), 0310111–03101113 (2012)
S. Perreault, P. Cardou, C. Gosselin, M.J.D. Otis: Geometric determination of the interference-free constant-orientation workspace of parallel cable-driven mechanisms, ASME J. Mech.Robotics 2(3), 031016 (2010)
J.-P. Merlet: MARIONET, a family of modular wire-driven parallel robots, Adv.Robot Kinemat.: MotionManMach. (2010) pp. 53–61
The National Advanced Driving Simulator, The University of Iowa: http://www.nads-sc.uiowa.edu
M. Girone, G. Burdea, M. Bouzit, V. Popescu, J.E. Deutsch: A Stewart platform-based system for ankle telerehabilitation, Auton. Robots 10(2), 203–212 (2001)
T. Nakano, M. Sugita, T. Ueta, Y. Tamaki, M. Mitsuishi: A parallel robot to assist vitreoretinal surgery, Int. J. Comput. Assist. Radiol. Surg. 4(6), 517–526 (2009)
M. Wu, T.G. Hornby, J.M. Landry, H. Roth, B.D. Schmit: A cable-driven locomotor training system for restoration of gait in human SCI, Gait Posture 33(2), 256–260 (2011)
J. Fink, N. Michael, S. Kim, V. Kumar: Planning and control for cooperative manipulation and transportation with aerial robots, Proc. Intl. Sym.Robot. Res., Luzern (2009)
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3-DOF high-speed 3-RPS parallel robot available from http://handbookofrobotics.org/view-chapter/18/videodetails/43
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6-DOF cable-suspended robot available from http://handbookofrobotics.org/view-chapter/18/videodetails/44
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CoGiRo available from http://handbookofrobotics.org/view-chapter/18/videodetails/45
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Parallel 5R robot available from http://handbookofrobotics.org/view-chapter/18/videodetails/46
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Diamond available from http://handbookofrobotics.org/view-chapter/18/videodetails/47
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6-DOF statically balanced parallel robot available from http://handbookofrobotics.org/view-chapter/18/videodetails/48
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3-DOF dynamically balanced parallel robot available from http://handbookofrobotics.org/view-chapter/18/videodetails/49
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IPAnema available from http://handbookofrobotics.org/view-chapter/18/videodetails/50
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Par2 robot available from http://handbookofrobotics.org/view-chapter/18/videodetails/51
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Quadrupteron robot available from http://handbookofrobotics.org/view-chapter/18/videodetails/52
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R4 robot available from http://handbookofrobotics.org/view-chapter/18/videodetails/53
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Tripteron robot available from http://handbookofrobotics.org/view-chapter/18/videodetails/54
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Merlet, JP., Gosselin, C., Huang, T. (2016). Parallel Mechanisms. In: Siciliano, B., Khatib, O. (eds) Springer Handbook of Robotics. Springer Handbooks. Springer, Cham. https://doi.org/10.1007/978-3-319-32552-1_18
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