Swivel Angle

For a 7-DoF arm holding a fixed hand pose, the angle the elbow can still rotate through around the shoulder-wrist line.

The swivel angle is a scalar parameter describing the redundancy of a 7-DoF arm. Kreutz-Delgado and colleagues parameterized this redundancy in a 1992 IJRR paper using the angle between the 'arm plane' — defined by the shoulder, elbow, and wrist — and a reference plane. Reaching a given end-effector pose only requires 6 degrees of freedom, so the extra one shows up as self-motion: with the hand held fixed, the elbow can still trace out a circle around the shoulder-wrist line, a joint motion that leaves the end effector unmoved. Fixing the swivel angle turns inverse kinematics into a problem with a unique closed-form solution; building on this, Shimizu and colleagues gave an analytical 7-DoF inverse-kinematics solution that accounts for joint limits in 2008. The human arm has the same redundancy, and exoskeleton and teleoperation research commonly calls this the swivel angle.

ExampleWhen teleoperating a 7-DoF arm, motion capture first measures the human operator's own swivel angle, which is then fed into the arm's inverse kinematics together with the target hand pose, so the robot's elbow matches the human's posture; this has been demonstrated on a teleoperated KUKA LWR4+ using the human arm's swivel angle.

Also called

Arm Angle, Elbow Swivel Angle, Arm Plane Angle

Related

7-DoF Robot Arm · Kinematic Redundancy · Null Space · Analytical Inverse Kinematics · Inverse Kinematics (IK) · Motion Retargeting

Sources

Kreutz-Delgado, Long, Seraji: Kinematic Analysis of 7-DOF Manipulators (IJRR, 1992)
Shimizu et al.: Analytical Inverse Kinematic Computation for 7-DOF Redundant Manipulators With Joint Limits (IEEE T-RO, 2008)
Kim & Rosen: Redundancy Resolution of the Human Arm and an Upper Limb Exoskeleton (IEEE TBME, 2012)