Forward position analysis of 6-3 Linapod parallel manipulators. (English) Zbl 1293.70013
Summary: In this study closed-form solutions to the forward kinematic problems are obtained for a particular type of six degree-of-freedom parallel manipulator called 6-3 Linapod. The 6-3 Linapod parallel manipulators have a 6-3 PSS (or PUS) structure, and forward kinematic solutions are obtained by using the solution procedure for 6-3 SPS (or UPS) manipulators. In this procedure, a 6-3 Linapod is first transformed into its equivalent mechanism, namely an inclined 3RS manipulator, and then the condition that the three spherical joints on the moving platform form an equilateral triangle leads us to obtain three polynomial equations in three unknowns. These equations are solved by using Sylvester dialytic elimination method. Each set of real roots corresponds to a particular configuration of the manipulator. Solutions so obtained are verified by performing inverse position analysis. A method to identify configurations containing crossed links is presented in this study, which is based on the interpretation of link crossing as intersection of a link with a triangle, whose vertices are positions of joints on the corresponding links.
MSC:
| 70B15 | Kinematics of mechanisms and robots |
Keywords:
Linapod; hexaglide; hexaslide; parallel manipulators; parallel robots; kinematics of machineryReferences:
| [1] | Merlet J-P (2006) Parallel robots, 2nd edn. Springer, Dordrecht · Zbl 1110.70002 |
| [2] | Wiegand A, Hebsacker M, Honegger M (1996) Parallele Kinematik und Linearmotoren: Hexaglide–ein neues, hochdynamisches Werkzeugmaschinenkonzept, Technische Rundschau Transfer Nr 25 |
| [3] | Shibukawa T, Toyama T, Hattori K (1997) Parallel mechanism based milling machine. Int. J. Jpn. Soc. Precis. Eng. 63:1671–1675 · doi:10.2493/jjspe.63.1671 |
| [4] | http://www.isw.uni-stuttgart.de/veroeffent/aufwtds6.htm |
| [5] | Boye T, Pritschow G (2005) New transformation and analysis of a N-DOF LINAPOD with six struts for higher accuracy. Robotica 23:555–560 · doi:10.1017/S0263574704001249 |
| [6] | Honegger M, Brega R, Schweitzer G (2000) Application of a nonlinear adaptive controller to a 6 dof parallel manipulator. In: Proceedings of the 2000 IEEE international conference on robotics and automation, San Francisco, April 2000, pp 1930–1935 |
| [7] | Honegger M, Codourey A, Burdet E (1997) Adaptive control of the hexaglide, a 6 dof parallel manipulator. In: Proceedings of the 1997 IEEE international conference on robotics and automation, Albuquerque, New Mexico, April 1997, pp 543–548 |
| [8] | Burdet E, Honegger M, Codourey A (2000) Controllers with desired dynamic compensation and their implementation on a 6dof parallel manipulator. In: Proceedings of the 2000 IEEE/RSJ international conference on intelligent robots and systems, Takamatsu, Oct 31–Nov 5, 2000, pp 39–45 |
| [9] | Yen P-L, Ke Z-W, Lu T-S, Lu C-W (2004) Development of a new safety-enhanced surgical robot using the hexaglide structure. In: Proceedings of the 2004 IEEE international conference on systems, man and cybernetics, Taipei, Taiwan, pp 2162–2167 |
| [10] | Rao ABK, Rao PVM, Saha SK (2003) Workspace and dexterity analyses of hexaslide machine tools. In: Proceedings of the 2003 IEEE international conference on robotics and automation, Taipei, Taiwan, September 14–19, 2003, pp 4104–4109 |
| [11] | Rao ABK, Rao PVM, Saha SK (2005) Dimensional design of hexaslides for optimal workspace and dexterity. IEEE Trans Robot 21(3):444–449 · doi:10.1109/TRO.2004.842353 |
| [12] | Ryu J, Cha J (2001) Optimal architecture design of parallel manipulators for best accuracy. In: Proceedings of the 2001 IEEE/RSJ international conference on intelligent robots systems, Maui, Hawaii, USA, Oct 29–Nov 03, 2001, pp 1281–1286 |
| [13] | Ryu J, Cha J (2003) Volumetric error analysis and architecture optimization for accuracy of HexaSlide type parallel manipulators. Mech Mach Theory 38:227–240 · Zbl 1062.70538 · doi:10.1016/S0094-114X(02)00126-X |
| [14] | Ruaf A, Kim SG, Ryu J (2004) Complete parameter identification of parallel manipulators with partial pose information using a new measurement device. Robotica 22:689–695 · doi:10.1017/S0263574704000359 |
| [15] | Chang KS (2003) Position analysis of 6-dof slider platform-hexaglide. Master Thesis, Department of Mechanical and Electro-mechanical Engineering, Tamkang University, Taiwan (in Chinese) |
| [16] | Innocenti C, Parenti-Castelli V (1990) Direct position analysis of the Stewart platform mechanism. Mech Mach Theory 25:611–621 · doi:10.1016/0094-114X(90)90004-4 |
| [17] | Nanua P, Waldron KJ, Murthy V (1990) Direct solutions of a Stewart platform. IEEE Trans Robot Autom 6:438–444 · doi:10.1109/70.59354 |
| [18] | Zhang C-D, Song S-M (1994) Forward position analysis of nearly general Stewart platforms. J Mech Des 116:54–60 · doi:10.1115/1.2919376 |
| [19] | Wen F, Liang C (1994) Displacement analysis of the 6-6 Stewart platform mechanisms. Mech Mach Theory 29:547–557 · doi:10.1016/0094-114X(94)90094-9 |
| [20] | Song S-K, Kwon D-S (2001) New methodology for the forward kinematics of 6-dof parallel manipulators using tetrahedron configurations. In: Proceedings of the 2001 international conference on robotics and automation, Seoul, Korea, pp 1307–1312 |
| [21] | Song S-K, Kwon D-S (2002) A tetrahedron approach for a unique closed-form solution of the forward kinematics of six-dof parallel mechanisms with multiconnected joints. Journal of Robotic Systems 19(6), 269–281 · Zbl 1073.70003 · doi:10.1002/rob.10040 |
| [22] | 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 · doi:10.1163/156855305774307004 |
| [23] | Huang KC (2006) Forward position analysis of HexaSlide parallel manipulators. Master Thesis, Department of Mechanical and Electro-mechanical Engineering, Tamkang University, Taiwan (in Chinese) |
| [24] | Tsai LW (1999) Robot analysis–the mechanics of serial and parallel manipulators. Wiley, New York |
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