A Class of Kinematically Simple 7-Revolute Jointed Serial Manipulators and their Velocity-Degenerate (Singular) Configurations

摘要

The velocity degeneracies (singularities) for a class of 7-revolute jointed manipulators are found. Within the class, unnecessary lengths and 4-jointed spherical groups of joints are avoided; successive joints are perpendicular or parallel. The concept of screw reciprocity is used to find the velocity-degenerate configurations. For manipulators based on a spherical-revolute-spherical (shoulder-elbow-wrist) joint arrangement, it is confirmed that four condition-sets lead to velocity degeneracies. Of these four condition-sets, one requires the satisfaction of only one joint-displacement condition, and three require the satisfaction of two joint-displacement conditions. Depending on the specific layout of the manipulators based on pointer-pointer-spherical joint arrangements, it is found that five or six condition-sets, all requiring the satisfaction of two conditions, lead to velocity degeneracies. Reciprocal screw quantities characterizing the lost instantaneous motions are derived. Using a point on the end effector coincident with the origin of frame 4 and the orientation of frame 4 as the reference frame is found to lead to simpler derivation of the degeneracy conditions.