Singularities and Workspace of a Bio-Inspired Positioning Arm with a Rolling Shoulder Joint

This paper presents the singularities and workspace of a 3-degree-of-freedom (3-DoF) bio-inspired positioning arm. It comprises a 2-DoF shoulder joint whose kinematics is equivalent to pure rolling of two identical spheres, followed by a 1-DoF revolute elbow joint. The singularities are computed from the degeneracy of its Jacobian matrix, leading to two non-trivial factors. The first factor represents the fully-stretched and folded-back configurations of the arm, akin to elbow singularities in PUMA-type robots. The second factor represents finite-dwell motion of the manipulator, in which the end-effector (EE) point remains stationary for finite non-zero motion of the joints, akin to the shoulder singularity of PUMA-type robots. These singularities map to nested shells in the Cartesian space, leading to a complex workspace pattern comprising several regions with {0,2,4} inverse kinematic solutions (IKS). Finally, we demonstrate a non-singular change of IKS, indicating the cuspidal nature of this manipulator.