Kinematic, singularity and stiffness analysis of the hydraulic shoulder: a 3-d.o.f. redundant parallel manipulator

In this paper, kinematic modeling and singularity and stiffness analysis of a 3-d.o.f. redundant parallel manipulator have been elaborated in detail. It is known that, contrary to series manipulators, the forward kinematic map of parallel manipulators involves highly coupled non-linear equations, whose closed-form solution derivation is a real challenge. This issue is of great importance noting that the forward kinematics solution is a key element in closed-loop position control of parallel manipulators. Using the idea of inherent kinematic chains formed in parallel manipulators, both inverse and forward kinematics of the redundant parallel manipulator are fully developed, and a closed-form solution for the forward kinematic map of the parallel manipulator is derived. The closedform solution is also obtained in detail for the Jacobian of the mechanism and singularity analysis of the manipulator is performed based on the computed Jacobian. Finally, as the first step to develop a control topology based on the overall stiffness property of the manipulator, the stiffness mapping of the manipulator is derived and its configuration dependence is analyzed. It is observed that the actuator redundancy in the mechanism is the major element to improve the Cartesian stiffness and, hence, the dexterity of the hydraulic shoulder. Moreover, loosing one limb actuation reduces the stiffness of the manipulator significantly.