Influence of Joint Offsets on the Elbow Null Space Motions of the  Redundant 7-DOF Franka Robot Arm

Franka Robotics introduced offsets between the joints of their robots which cause some of the adjacent joint axes not to intersect. These offsets have a significant influence on the robot’s null space motions. While the elbow moves on two deformed circles for some end effector poses, a specific combination of end effector position and orientation causes these two circles to break and connect with each other. The connected manifolds require a configuration switch to still support a full elbow rotation. The different types of spherical curvatures are presented and their required properties as well as their effects on the robot’s mobility are explained.