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.

We evaluate the measure of kinematic flexibility as an index that quantifies the manipulator's redundancy. Initially, we propose a general algorithm for its calculation, then present two illustrative numerical examples of redundant mechanisms and discuss the obtained results. We show that the distribution of the kinematic flexibility throughout the workspace can be a discontinuous function. There exist different sub-domains of joint angles corresponding to the same primary task. In some poses, the manipulator is able to pass from one sub-domain to another continuously, while in other cases the manipulator cannot change the current sub-domain without violating the primary task constraints. This fact may have important implications in robot control.

The fundamental concept of the paper is to divide the inverse kinematics problem of a non-redundant robot manipulator into two sub-problems of different priorities, one associated with the position and one with the orientation of the end effector. We apply a standard weighted-pseudoinverse-based scheme which is normally utilised to resolve the inverse kinematics of a redundant manipulator. We show that the proposed approach is advantageous when the secondary task (orienting of the end effector) cannot entirely be executed.

The paper introduces a simplified mathematical model of the human arm kinematics which is used to determine the workspace related to the reachability of the wrist. The model contains six revolute degrees of freedom, five in the shoulder complex and one in the elbow joint. It is not directly associated to the anatomical structure of the arm, but represents the spatial motion of two characteristic points, epicondylus lateralis and proc. styloideus. Use of this simplified model for the determination of reachable workspace offers several advantages versus direct measurement: (i) the workspace can be obtained in few minutes on a micro VAX II computer, (ii) patients with various injuries in various stages of recovery can be treated since only a few brief and simple measurements of the model's parameters are needed, and (iii) the calculated workspace includes complete information of the envelope, as well as inside characteristics.>