Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-13T10:20:39.461Z Has data issue: false hasContentIssue false
  • English
  • Français

Angularity and axiality of a Schönflies parallel manipulator

Published online by Cambridge University Press:  24 February 2015

J. Jesús Cervantes-Sánchez ,
José M. Rico-Martínez  and
Víctor H. Pérez-Muñoz
J. Jesús Cervantes-Sánchez*
Affiliation:
Universidad de Guanajuato, DICIS, Departamento de Ingeniería Mecánica 36885, Salamanca, Guanajuato, México. E-mails: jrico@ugto.mx, vperez@ugto.mx
José M. Rico-Martínez
Affiliation:
Universidad de Guanajuato, DICIS, Departamento de Ingeniería Mecánica 36885, Salamanca, Guanajuato, México. E-mails: jrico@ugto.mx, vperez@ugto.mx
Víctor H. Pérez-Muñoz
Affiliation:
Universidad de Guanajuato, DICIS, Departamento de Ingeniería Mecánica 36885, Salamanca, Guanajuato, México. E-mails: jrico@ugto.mx, vperez@ugto.mx
*
*Corresponding author. E-mail: jecer@ugto.mx
Get access Rights & Permissions [Opens in a new window]

Summary

This paper presents a systematic approach to compute the angularity and the axiality indices for a Schönflies parallel manipulator. Angularity index may be considered as a measure of the sensitivity of the mobile platform to changes in rotation, while axiality index can be used to measure the sensitivity of the OP of the mobile platform to changes in translation. Since both indices were inspired by very fundamental concepts of classical kinematics (angular velocity vector and helicoidal velocity field), they offer a clear and simple physical meaning, which may be useful to the designer of parallel manipulators. Moreover, both dexterity indices do not require obtaining a dimensionally homogeneous Jacobian matrix, nor do they depend on having similar types of actuators in each manipulator's leg. Detailed numerical examples are given in order to illustrate the computation of the dexterity indices.

Keywords

Schönflies parallel manipulatordexterity indicesangularityaxiality
Type
Articles
Information
Robotica , Volume 34 , Issue 11 , November 2016 , pp. 2415 - 2439
Copyright
Copyright © Cambridge University Press 2015 

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. Gosselin, C. M., “Dexterity Indices for Planar and Spatial Robotic Manipulators,” Proceedings of the IEEE International Conference on Robotics and Automation, Cincinnati, OH, USA (1990) pp. 650–655.Google Scholar
2. Klein, C. A. and Miklos, T. A., “Spatial Robotic Isotropy,” Int. J. Robot. Res. 10 (4), 426–437 (1991).CrossRefGoogle Scholar
3. Pittens, K. H. and Podhorodeski, R. P., “A family of Stewart platforms with optimal dexterity,” J. Robot. Syst. 10 (4), 463–479 (1993).Google Scholar
4. Zanganeh, K. E. and Angeles, J., “Kinematic isotropy and the optimum design of parallel manipulators,” Int. J. Robot. Res. 16 (2), 185–197 (1997).Google Scholar
5. Yoshikawa, T., “Manipulability of robotic mechanisms,” Int. J. Robot. Res. 4 (2), 3–9 (1985).Google Scholar
6. Tsai, K. Y. and Huang, K. D., “The manipulability and transmissivity of manipulators,” Int. J. Robot. Autom. 13 (4), 132–136 (1998).Google Scholar
7. Merlet, J. P., “Jacobian, manipulability, condition number, and accuracy of parallel robots,” ASME J. Mech. Des. 128, 199–206 (2006).Google Scholar
8. Pond, G. and Carretero, J. A., “Quantitative dexterous workspace comparison of parallel manipulators,” Mech. Mach. Theory 42 (12), 1388–1400.Google Scholar
9. Cardou, P., Bouchard, S. and Gosselin, C., “Kinematic-sensitivity indices for dimensionally nonhomogeneous Jacobian matrices,” IEEE Trans. Robot. 26 (1), 166–173 (2010).Google Scholar
10. Kim, S. G. and Ryu, J., “New dimensionally nonhomogeneous Jacobian matrix formulation by three end-effector points for optimal design of parallel manipulators,” IEEE Trans. Robot. Autom. 19 (4), 731–737 (2003).Google Scholar
11. Kong, M., Zhang, Y., Du, Z. and Sun, L., “A Novel Approach to Deriving the Unit-Homogeneous Jacobian Matrices of Mechanisms,” Proceedings of the IEEE International Conference on Mechatronics and Automation, Harbin, China (August 5–8 2007) pp. 3051–3055.Google Scholar
12. Liu, H., Huang, T. and Chetwynd, D. G., “A method to formulate a dimensionally homogeneous Jacobian of parallel manipulators,” IEEE Trans. Robot. 27 (1), 150–156 (2011).Google Scholar
13. Jesús Cervantes-Sánchez, J., Rico-Martínez, J. M. and Pérez-Muñoz, V. H., “Two natural dexterity indices for parallel manipulators: Angularity and axiality,” ASME J. Mech. Robot. 6, Paper No. 041007 (2014).Google Scholar
14. Pérez-Soto, G. I., Rico, J. M., Cervantes-Sánchez, J. J., López-Custodio, P. C., Gallardo-Mosqueda, L. A. and Camarillo-Gómez, K. A., “A New Method for the Kinematic Synthesis of Parallel Platforms,” Proceedings of the ASME DETC 2014, Buffalo, N. Y., USA (August 17–20, 2014) pp. 1–14.Google Scholar
15. Kong, X. and Gosselin, C. M., Type Synthesis of Parallel Mechanisms (Springer, New York, 2007) pp. 154–156.Google Scholar
16. Brand, L., Vector and Tensor Analysis, vol. 46 (John Wiley and Sons, New York, 1947).Google Scholar
17. Angeles, J., Fundamentals of Robotic Mechanical Systems: Theory, Methods and Algorithms, vol. 82 (Springer, New York, 2014).Google Scholar
18. Phillips, J., Freedom in Machinery: Introducing Screw Theory, vol. 1 (Cambridge University Press, New York, 1984) pp. 69–72.Google Scholar
19. Angeles, J., Rational Kinematics (Springer-Verlag, New York, 1989) pp. 49–50.Google Scholar