File(s) not publicly available
The forward kinematics of 3-RPR planar robots: a review and a distance-based formulation
journal contribution
posted on 2023-06-09, 00:29 authored by Nicolás Rojas, Federico ThomasThe standard forward-kinematics analysis of 3-RPR planar parallel robots boils down to computation of the roots of a sextic polynomial. There are many different ways to obtain this polynomial, but most of them include exceptions for which the formulation is not valid. Unfortunately, near these exceptions, the corresponding polynomial exhibits numerical instabilities. In this paper, we provide a way around this inconvenience by translating the forward-kinematics problem to be solved into an equivalent problem fully stated in terms of distances. Using constructive geometric arguments, an alternative sextic - which is not linked to a particular reference frame - is straightforwardly obtained with the need for neither variable eliminations nor tangent-half-angle substitutions. The presented formulation is valid, with no modification, for any planar 3-RPR parallel robot, including the special architectures and configurations - which ultimately lead to numerical instabilities - that cannot be directly handled by previous formulations.
History
Publication status
- Published
Journal
IEEE Transactions on RoboticsISSN
1552-3098Publisher
Institute of Electrical and Electronics Engineers (IEEE)External DOI
Issue
1Volume
27Page range
143-150Department affiliated with
- Engineering and Design Publications
Full text available
- No
Peer reviewed?
- Yes
Legacy Posted Date
2016-03-07Usage metrics
Categories
No categories selectedKeywords
Licence
Exports
RefWorks
BibTeX
Ref. manager
Endnote
DataCite
NLM
DC