On the Comprehensive Kinematics Analysis of a Humanoid Parallel Ankle Mechanism

In this paper, we present a thorough kinematics analysis of a humanoid two degrees-of-freedom (DoF) ankle module based on a parallel kinematics mechanism. Compared with the conventional serial configuration, the parallel kinematics ankle permits the distribution of the torque/power of the actuators to the two DoF of the ankle taking full advantage of available power/torque capacity of the two actuators. However, it complicates the kinematics study in return. In this work, a complete study of a parallel ankle mechanism is performed that permits the full characterization of the ankle module for the purpose of its design study, control, and performance evaluation. Screw theory is employed for mobility analysis to first determine the number and properties of the mechanism's DoFs. Then the inverse kinematics is solved analytically and the Jacobian matrix for describing the velocity relation between the ankle joints and motors is found. Based on these results, the forward kinematics of the parallel mechanism can be numerically computed using the Newton–Raphson method. The workspace of the ankle is also analyzed and the motor limits are decided accordingly. Finally, an experimental demonstration consisting of four tests is carried out to evaluate the proposed methods and ankle module.