Abstract
The subject of this paper is the elastostatics of a novel three-limb, full-mobility parallel-kinematics machine (PKM) with flexible links, dubbed the SDelta robot. Due to the inherent flexibility of the light-weight limb rods under fast operations, they are modeled as identical linearly elastic beams. The moving platform of the PKM is assumed to be elastically attached to the base platform via a six-dof generalized spring. Because of the symmetric design of the SDelta robot, the constant generalized stiffness matrix becomes isotropic. Moreover, the posture-dependent Cartesian stiffness matrix is derived. Based on the preliminary design of a prototype at the desktop scale, its stiffness matrix is numerically evaluated.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
C, P and S stand for cylindrical, prismatic and spherical joints, respectively, the actuated joint being underlined.
- 2.
The moment is defined w.r.t. the MP c.o.m.
- 3.
A small-amplitude rotation reduces to a vector [13].
- 4.
At this posture the Jacobian matrix of the SDelta robot, mapping the twist of the MP into the actuated joint rates, attains its minimum condition number.
References
Merlet, J.P.: Parallel Robots. Springer, Netherlands (2006). https://doi.org/10.1007/1-4020-4133-0
Briot, S., Khalil, W.: Dynamics of Parallel Robots. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-19788-3
Podhorodeski, R.P.: A class of parallel manipulators based on kinematically simple branches. J. Mech. Des. 116, 908–914 (1994). https://doi.org/10.1115/1.2919468
Li, W., Angeles, J.: A novel three-loop parallel robot with full mobility: kinematics, singularity, workspace, and dexterity analysis. J. Mech. Rob. 9, 051003 (2017). https://doi.org/10.1115/1.4037112
Harada, T., Friedlaender, T., Angeles, J.: The development of an innovative two-DOF cylindrical drive: design, analysis and preliminary tests. In: 2014 IEEE International Conference on Robotics and Automation (ICRA), pp. 6338–6344. IEEE, New York (2014). https://doi.org/10.1109/ICRA.2014.6907794
Eskandary, P.K., Angeles, J.: The translating \(\varPi \)-joint: design and applications. Mech. Mach. Theory 122, 361–370 (2018). https://doi.org/10.1016/j.mechmachtheory.2018.01.011
Azulay, H., Mahmoodi, M., Zhao, R., Mills, J.K., Benhabib, B.: Comparative analysis of a new 3\(\times \) PPRS parallel kinematic mechanism. Rob. Comput.-Integr. Manuf. 30, 369–378 (2014). https://doi.org/10.1016/j.rcim.2013.12.003
Yang, G., Chen, I.M., Chen, W., Lin, W.: Kinematic design of a six-DOF parallel-kinematics machine with decoupled-motion architecture. IEEE Trans. Rob. Autom. 20, 876–887 (2004). https://doi.org/10.1109/TRO.2004.829485
Klein, C.A., Blaho, B.E.: Dexterity measures for the design and control of kinematically redundant manipulators. Int. J. Rob. Res. 6, 72–83 (1987). https://doi.org/10.1177/027836498700600206
Yoshikawa, T.: Manipulability of robotic mechanisms. Int. J. Rob. Res. 4, 3–9 (1985). https://doi.org/10.1177/027836498500400201
Lončarić, J.: Normal forms of stiffness and compliance matrices. IEEE J. Rob. Autom. 3, 567–572 (1987). https://doi.org/10.1109/JRA.1987.1087148
Li, W., Angeles, J.: The design of a 3-CPS parallel robot for maximum dexterity. Mech. Mach. Theory 122, 279–291 (2018). https://doi.org/10.1016/j.mechmachtheory.2018.01.003
Li, W., Angeles, J.: On the use of the dual Euler-Rodrigues parameters in the numerical solution of the inverse-displacement problem. Mech. Mach. Theory (2017, in press). https://doi.org/10.1016/j.mechmachtheory.2017.12.006
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 CISM International Centre for Mechanical Sciences
About this paper
Cite this paper
Sun, Q., Angeles, J., Forbes, J.R. (2019). Elastostatics of a Full-Mobility PKM with Flexible Links. In: Arakelian, V., Wenger, P. (eds) ROMANSY 22 – Robot Design, Dynamics and Control. CISM International Centre for Mechanical Sciences, vol 584. Springer, Cham. https://doi.org/10.1007/978-3-319-78963-7_6
Download citation
DOI: https://doi.org/10.1007/978-3-319-78963-7_6
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-78962-0
Online ISBN: 978-3-319-78963-7
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)