Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the determination of cusp points of 3-R\underline{P}R parallel
  manipulators   This paper investigates the cuspidal configurations of 3-RPR parallel
manipulators that may appear on their singular surfaces in the joint space.
Cusp points play an important role in the kinematic behavior of parallel
manipulators since they make possible a non-singular change of assembly mode.
In previous works, the cusp points were calculated in sections of the joint
space by solving a 24th-degree polynomial without any proof that this
polynomial was the only one that gives all solutions. The purpose of this study
is to propose a rigorous methodology to determine the cusp points of
3-R\underline{P}R manipulators and to certify that all cusp points are found.
This methodology uses the notion of discriminant varieties and resorts to
Gr\"obner bases for the solutions of systems of equations.

2
The categories of this paper are: math
33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
21
The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin