Cuspidal robots: theory and applications

When a new robot is installed on a production site, its kinematic architecture (serial or parallel, number and type of axes, etc.) must be chosen first, and then it must be programmed and controlled so that the tool it is handling can properly follow the set trajectories defined to carry out the required tasks. Most serial robots have the ability to reach a target in their workspace in several postures (e.g. "elbow up" and "elbow down"). A change of posture can be made to avoid a joint limit on an axis or a collision with an obstacle. For a long time, it was assumed that the robot would have to pass through a singular configuration during a change of posture, as is the case with most industrial robots: the singular configuration "arm extended" must always be passed through to move between the "elbow up" and "elbow down" postures. While this property is indeed observed on most robots with geometric features (parallel or intersecting axes), it is not the case for many other robots. This raises a number of crucial questions, both for the user and the designer. How do you know if the robot has this property? If not, how do we know if the robot has changed its posture? Which robots have this property?

This article sets out to answer these questions. A cuspidal robot is defined as a robot that can change posture without crossing a singular configuration. Most of this article deals with serial robots. It proposes a methodology for identifying cuspidal robots and describes in depth their posture change mechanism. Particular attention is paid to a family of robots with three pivot joints with orthogonal axes in pairs. These robots are potentially interesting alternatives to conventional robots. It is therefore important to be able to classify them as cusp and non-cusp robots. Six-joint robots are more difficult to analyze and, at the time of writing, are still the subject of research. They are mainly discussed through a few examples of cuspidal 6R robots, some of which are used in industry as painting robots. The more delicate case of parallel-architecture robots is also discussed. We analyze examples of plane, spherical, parallel robots with 6 degrees of freedom, capable of changing assembly mode without crossing a singularity. Finally, the article discusses the interest of cuspidal robots.