This work presents a method based on spherical trigonometry for computing all joint angles of the spherical metamorphic palm. The spherical palm is segmented into spherical triangles which are then solved and combined to fully solve the palm configuration. Further, singularity analysis is investigated with the analysis of each spherical triangle the palm is decomposed. Singularity-avoidance-based design criteria are then presented. Finally, point clouds are generated that represent the joint space of the palm as well as the workspace of the hand with the advantage of an articulated palm is shown.

A non-overconstrained three-DOF parallel orientation mechanism that is kinematically equivalent to the Agile Eye is presented in this paper. The output link (end-effector) of the mechanism is connected to the base by one spherical joint and by another three identical legs. Each leg comprises of, in turns from base, a revolute joint, a universal joint, and three prismatic joints. The three lower revolute joints are active joints, while all other joints are passive ones. Based on a special configuration, some three projective angles of the end-effector coordinates are fully decoupled with respect to the input actuated joints, that is, by actuating any revolute joint the end-effector rotates in such a way that the corresponding projective angle changes with the same angular displacement. The fully decoupled motion is analyzed geometrically and proved theoretically. Besides, the inverse and direct kinematics solutions of the mechanism are provided based on the geometric reasoning and theoretical proof.