Hostname: page-component-7bb8b95d7b-l4ctd Total loading time: 0 Render date: 2024-09-12T22:24:52.189Z Has data issue: false hasContentIssue false
  • English
  • Français

Tri-pyramid Robot: stiffness modeling of a 3-DOF translational parallel manipulator

Published online by Cambridge University Press:  20 June 2014

Qiang Zeng ,
Kornel F. Ehmann  and
Jian Cao
Qiang Zeng*
Affiliation:
Department of Mechanical Engineering, Northwestern University, 2145 Sheridan Road, Evanston, IL 60208-3111, USA
Kornel F. Ehmann
Affiliation:
Department of Mechanical Engineering, Northwestern University, 2145 Sheridan Road, Evanston, IL 60208-3111, USA
Jian Cao
Affiliation:
Department of Mechanical Engineering, Northwestern University, 2145 Sheridan Road, Evanston, IL 60208-3111, USA
*
*Corresponding author. E-mail address: qiangzengnu@gmail.com
Get access Rights & Permissions [Opens in a new window]

Summary

This paper presents a 3-DOF (degree of freedom) translational parallel manipulator named the Tri-pyramid Robot. Compared to the developed 3-DOF translational parallel manipulators, the Tri-pyramid Robot is designed based on conical displacement subset to exhibit better kinematic characteristic. The inverse position solution is obtained through closed-loop constraint analysis and used to formulate the overall Jacobian matrix of constraints and actuations based on the theory of reciprocal screws. Furthermore, by considering the stiffness of all links, joints, actuators, fixed, and moving platforms, the output stiffness matrix of the Tri-pyramid Robot is derived by the transformations of loads and deformations in the closed-loop form. The relations between the virtual input-output displacements are analyzed by the overall Jacobian matrix and used to build the manipulator's stiffness model. Stiffness performance is evaluated by the extreme eigenvalues of the output stiffness matrix in the reachable workspace. By considering the variations of the structural parameters and the distribution of the output stiffness, the maximal stiffness workspace is obtained through numerical optimization, providing, thereby, basic constraints for the parametric design of the Tri-pyramid Robot.

Keywords

Parallel manipulatorMechanism designStiffness matrixTheory of reciprocal screws
Type
Articles
Information
Robotica , Volume 34 , Issue 2 , February 2016 , pp. 383 - 402
Copyright
Copyright © Cambridge University Press 2014 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Clavel, R., “DELTA, A Fast Robot with Parallel Geometry,” 18th International Symposium on Industrial Robots, Sydney, Australia 91–100 (1988).Google Scholar
2.Clavel, R., “Device for the Movement and Positioning of an Element in Space,” United States Patent No. 4,976,582 (1990).Google Scholar
3.Tsai, L. W., Walsh, G. C. and Stamper, R. E., “Kinematics of a Novel Three DoF Translational Platform,” IEEE International Conference on Robotics and Automation, Minneapolis, MN3446–3451 (1996).Google Scholar
4.Tsai, L. W. and Joshi, S., “Kinematics and optimization of a spatial 3-UPU parallel manipulator,” ASME, J. Mech. Des. 122, 439–446 (2000).CrossRefGoogle Scholar
5.Siciliano, B., “The tricept robot: inverse kinematics, manipulability analysis and closed-loop direct kinematics algorithm,” Robotica 17, 437–455 (1999).CrossRefGoogle Scholar
6.Zhang, D. and Gosselin, C. M., “Kinetostatic analysis and design optimization of the tricept machine tool family,” ASME J. Manuf. Sci. Eng. 124, 725–733 (2002).CrossRefGoogle Scholar
7.Neumann, K. E., “Next Generation Tricept—A True Revolution in Parallel Kinematics,” Proceedings of the 4th Chemnitz Parallel Kinematics Seminar, Zwickau, Germany (2004) pp. 591–594.Google Scholar
8.Hervé, J. M. and Sparacino, F., “Structural Synthesis of Parallel Robots Generating Spatial Translation,” Proceedings of the 5th International Conference on Advanced Robotics, Pisa, Italy1 (1991) pp. 808–813.Google Scholar
9.Kong, X. and Gosselin, C. M., “Kinematics and singularity analysis of a novel type of 3-CRR 3-DOF translational parallel manipulator,” Int. J. Robot. Res. 21, 791–798 (2002).CrossRefGoogle Scholar
10.Carricato, M. and Parenti-Castelli, V., “Singularity-free fully-isotropic translational parallel mechanisms,” Int. J. Robot. Res. 21, 161–174 (2002).CrossRefGoogle Scholar
11.Kim, H. S. and Tsai, L. W., “Design optimization of a cartesian parallel manipulator,” ASME, J. Mech. Des. 125, 43–51 (2003).CrossRefGoogle Scholar
12.Lee, C. C. and Hervé, J. M., “Cartesian parallel manipulators with pseudoplanar limbs,” ASME, J. Mech. Des. 129, 1256–1264 (2007).CrossRefGoogle Scholar
13.Gogu, G., “Structural synthesis of fully-isotropic translational parallel robots via theory of linear transformations,” Eur. J. Mech. 23, 1021–1039 (2004).CrossRefGoogle Scholar
14.Kong, X. and Gosselin, C. M., “Type synthesis of 3-DOF translational parallel manipulators based on screw theory,” J. Mech. Des. 126, 83–92 (2004).CrossRefGoogle Scholar
15.Gosselin, C. M., “Stiffness mapping for a parallel manipulators,” IEEE Trans. Robot. Autom. 6, 377–382 (1990).CrossRefGoogle Scholar
16.Gosselin, C. M. and Zhang, D., “Stiffness analysis of parallel mechanisms using a lumped model,” Int. J. Robot. Autom. 17, 17–27 (2002).Google Scholar
17.El-Khasawneh, B. S. and Ferreira, P. M., “Computation of stiffness and stiffness bounds for parallel link manipulators,” Int. J. Mach. Tools Manuf. 39, 321–342 (1999).CrossRefGoogle Scholar
18.Ceccarelli, M. and Carbone, G., “A stiffness analysis for CaPaMan (Cassino Parallel Manipulator),” Mech. Mach. Theory 37, 427–439 (2002).CrossRefGoogle Scholar
19.Huang, T., Zhao, X. and Whitehouse, D. J., “Stiffness estimation of a tripod-based parallel kinematic machine,” IEEE Transactions on Robotics and Automation 18, 50–58 (2002).CrossRefGoogle Scholar
20.Xi, F., Zhang, D., Mechefske, C. M. and Lang, S. Y. T., “Global kinetostatic modeling of tripod-based parallel kinematic machine,” Mech. Mach. Theory 39, 357–377 (2004).CrossRefGoogle Scholar
21.Zhang, D. and Lang, S. Y. T., “Stiffness modeling for a class of reconfigurable PKMs with three to five degrees of freedom,” J. Manuf. Syst. 23, 316–327 (2004).CrossRefGoogle Scholar
22.Pham, H. H. and Chen, I. M., “Stiffness modeling of flexure parallel mechanism,” Precis. Eng. 29, 467–478 (2005).CrossRefGoogle Scholar
23.Majou, F., Gosselin, C. M., Wenger, P. and Chablat, D., “Parametric stiffness analysis of the Orthoglide,” Mech. Mach. Theory 42, 296–311 (2007).CrossRefGoogle Scholar
24.Chen, J. and Lan, F., “Instantaneous stiffness analysis and simulation for hexapod machines,” Simul. Modelling Pract. Theory 16, 419–428 (2008).CrossRefGoogle Scholar
25.Jung, H. K., Crane, C. D. III and Roberts, R. G., “Stiffness mapping of compliant parallel mechanisms in a serial arrangement,” Mech. Mach. Theory 43, 271–284 (2008).CrossRefGoogle Scholar
26.Pashkevich, A., Chablat, D. and Wenger, P., “Stiffness analysis of overconstrained parallel manipulators,” Mech. Mach. Theory 44, 966–982 (2009).CrossRefGoogle Scholar
27.Wu, J., Wang, J., Wang, L., Li, T. and You, Z., “Study on the stiffness of a 5-DOF hybrid machine tool with actuation redundancy,” Mech. Mach. Theory 44, 289–305 (2009).CrossRefGoogle Scholar
28.Shneor, Y. and Portman, V. T., “Stiffness of 5-axis machines with serial, parallel, and hybrid kinematics: Evaluation and comparison,” CIRP Ann. - Manuf. Technol. 59, 409–412 (2010).CrossRefGoogle Scholar
29.Pashkevich, A., Klimchik, A. and Chablat, D., “Enhanced stiffness modeling of manipulators with passive joints,” Mech. Mach. Theory 46, 662–679 (2011).CrossRefGoogle Scholar
30.Hua, B., Lu, Y., Tan, Q., Yu, J. and Han, J., “Analysis of stiffness and elastic deformation of a 2(SP+SPR+SPU) serial–parallel manipulator,” Robot. Comput.-Integr. Manuf. 27, 418–25 (2011).CrossRefGoogle Scholar
31.Rezaei, A., Akbarzadeh, A. and Akbarzadeh-T, M. R., “An investigation on stiffness of a 3-PSP spatial parallel mechanism with flexible moving platform using invariant form,” Mech. Mach. Theory 51, 195–216 (2012).CrossRefGoogle Scholar
32.Aginaga, J., Zabalza, I., Altuzarra, O. and Najera, J., “Improving static stiffness of the 6-RUS parallel manipulator using inverse singularities,” Robot. Comput.-Integr. Manuf. 28, 458–471 (2012).CrossRefGoogle Scholar
33.Portman, V. T., Chapsky, V. S. and Shneor, Y., “Workspace of parallel kinematics machines with minimum stiffness limits: Collinear stiffness value based approach,” Mech. Mach. Theory 49, 67–86 (2012).CrossRefGoogle Scholar
34.Gan, D. M., Dai, J. S., Dias, J. and Seneviratne, L. D., “Unified Kinematics and Singularity Analysis of A Metamorphic Parallel Mechanism with Bifurcated Motion,” Unified Kinematics and Singularity Analysis of A Metamorphic Parallel Mechanism with Bifurcated Motion 5, 041104 (2013).Google Scholar
35.Gan, D. M., Liao, Q. Z., Dai, J. S. and Wei, S. M., “Design and kinematics analysis of a new 3CCC parallel mechanism,” Robotica 28, 1065–1072 (2010).CrossRefGoogle Scholar
36.Hosseini, M. A. and Daniali, H. M., “Weighted local conditioning index of a positioning and orienting parallel manipulator,” Scientica Iranica B 18, 115–120 (2011).CrossRefGoogle Scholar
37.Li, Y. and Xu, Q., “Stiffness analysis for a 3-PUU parallel kinematic machine,” Mech. Mach. Theory 43, 186–200 (2008).CrossRefGoogle Scholar
38.Xu, Q. and Li, Y., “An investigation on mobility and stiffness of a 3-DOF translational parallel manipulator via screw theory,” Robot. Comput.-Integr. Manuf. 24, 402–414 (2008).CrossRefGoogle Scholar
39.Wang, Y., Liu, H., Huang, T. and Chetwynd, D. G., “Stiffness modeling of the tricept robot using the overall jacobian matrix,” Stiffness modeling of the tricept robot using the overall jacobian matrix 1, 021002 (2009).Google Scholar
40.Joshi, S. A. and Tsai, L. W., “Jacobian analysis of limited-DOF parallel manipulators,” ASME, J. Mech. Des. 124, 254–258 (2002).CrossRefGoogle Scholar
41.Ball, R. S., A Treatise on the Theory of Screws (Cambridge University Press, Cambridge, 1900).Google Scholar
42.Hunt, K. H., Kinematic Geometry of Mechanisms (Clarendon Press, Oxford, 1978).Google Scholar
43.Hervé, J. M., “The Lie group of rigid body displacements, a fundamental tool for mechanism design,” Mech. Mach. Theory 34, 719–730 (1999).CrossRefGoogle Scholar
44.Fanghella, P. and Galletti, C., “Metric relations and displacement groups in mechanism and robot kinematics,” ASME, J. Mech. Des. 117, 470–478 (1995).CrossRefGoogle Scholar