The Dexterous Solid Angle of Robotic Manipulators With a Spherical Wrist

We present an analytical method to calculate the Dexterous Solid Angle (DSA) of manipulators with any number of degrees of freedom, and a spherical wrist. The dexterous solid angle is measured by calculating the area of so-called no-service regions. No-service regions are located on the service sphere which is placed at a point of interest in the reachable workspace of a manipulator. The method is illustrated for a specific manipulator, designed and built by one of us (Abdel-Malek).