6. Conclusion

This article takes a look at so-called "cuspidal" robots, which have the property of being able to change the solution of the inverse geometric model (serial robots) or the direct geometric model (parallel robots) without passing through a singularity. This property is little discussed in the literature. A serial (resp. parallel) robot with at least one cusp point in its workspace (resp. in its joint space) is cuspidal, but the converse is not always true. Particularly difficult to study due to the complexity of the equations involved, cuspidity analysis requires the use of sophisticated algebraic tools. These tools are based in particular on Gröbner bases and the algebraic cylindrical decomposition