This paper presents a humanoid robotic shoulder complex and the kinematics of humanoid humeral pointing as performed by this complex. The humanoid shoulder complex is composed of two subsystems, a parallel mechanism which serves as the innermost shoulder girdle and a serial mechanism which serves as the outermost spherical glenohumeral joint. These two subsystems are separated by an offset distance and a twist angle. The subsystems operate cooperatively as an offset double pointing system. Humanoid humeral pointing is defined as a configuration in which the displacement of the shoulder girdle and the humerus are coplanar, and in which a ratio between an inclination angle in each subsystem achieves a constant value consistent with human humeral pointing. One redundant degree of freedom remains in the humanoid shoulder girdle, and it can be used to optimize system configuration and operating criteria, such as avoiding the singular cones of the humanoid glenohumeral joint.

We present a mechanical design for a humanoid robotic shoulder complex. The aim of the mechanism is to support the load of the arm and to copy four principal motions of the human shoulder in order to furnish the desired arm mobility and reachability. We utilize a fully parallel mechanism with four driven legs that provide to the movable platform (on which the arm is to be attached) three rotations and one translation. These three rotations represent the shoulder's flexion-extension (about the vertical axis), the shoulder's abduction-adduction (about the anterior-posterior axis), and the shoulder's rotation (about the medial-lateral axis). The fourth degree of freedom is controlled depending on the angles of the first two rotations and represents the shoulder contraction and enlargement along the medial-lateral axis.

Previously a reduced Jacobian method was used to constrain a redundant articulated arm-subassembly resulting in a complete workspace without singularities. This paper presents a purely geometric solution to the same problem, and shows that a geometric analysis of singular configurations quickly provides necessary conditions which any singularity elimination algorithm must meet. Sufficiency of the candidate algorithm is established by direct analysis.>

Adding a redundant degree of freedom to the shoulder pointing system complex of an articulated arm subassembly makes it possible to achieve a maximal workspace that is free of singularities. This paper derives a functional constraint between three of the four joints of this new type of arm, achieving a singularity-free workspace encompassing the entire reachable volume between the maximal- and minimal-reach surfaces. The large volume of dexterous workspace is verified by animation of the resulting arm design. Graphical results from the animation are presented comparing the dexterous workspace of this new arm to that of the standard nonredundant articulated arm subassembly found in the Puma manipulator.>

An analysis is conducted of symmetrically actuated double pointing systems, which are two spherical pointing systems connected serially with a common center. The double pointing systems have four degrees of freedom interrelated by two constraint functions, reducing the systems to two independent degrees of freedom. Together, these constraint functions result in a symmetry in the motion of corresponding links in each pointing system of the double system. A singularity analysis is presented of a generalized symmetrically actuated double pointing system in order to prove that it and the systems derived from it have maximal singularity-free workspaces. Closed-form solutions to the inverse position and velocity problems are presented along with different types of kinematic arrangements. Any of the double pointing systems presented can serve as the basis of a singularity-free wrist.>

In this paper a non-degenerate orientation solution is developed for a Four-Jointed Wrist. The solution will guarantee that the wrist is capable of continuously orienting an end-effector without ever finding itself in a degenerate configuration. The solution is in closed-form and is developed from well-known methods and results in spherical kinematics.