Cuspidal Redundant Robots: Classification of Infinitely Many IKS of Special Classes of 7R Robots

Redundant robots, with more degrees of freedom than required for a given task, offer enhanced dexterity but can exhibit complex kinematic behaviour in motion planning. Cuspidal robots, which can change inverse kinematic solutions without crossing singularities, have been reported to pose unique challenges for motion feasibility and repeatability. While cuspidality has been extensively studied for 3R and certain 6R robots, no formal classification exists for redundant architectures. This letter presents a systematic framework for classifying 7R wrist-partitioned redundant robots based on their cuspidal properties. The method reduces the 7R structure to a parameterized 3R equivalent via the redundant joint angle, enabling the application of established theory for cuspidal robots. Using this approach, commercially available robots are analysed and categorized as cuspidal or noncuspidal. Results show that the design offsets in commercial cobots may lead to cuspidality, which can potentially cause a nonsingular change of operation mode in collaborative applications. This classification framework provides a foundation for cuspidality-aware path planning and offers practical guidelines for designing non-cuspidal redundant robots to ensure safer and more predictable operation.