Combined Inverse Kinematic and Static Analysis and Optimal Design of a Cable-Driven Mechanism with a Spring Spine

A special humanoid neck with low motion noise requirements yields a cable-driven parallel mechanism to imitate the rotational motion of a human neck. The fixed base and moving platform of the mechanism are connected by four cables and a column compression spring. The four cables are actuated separately, while the spring can support weight on the moving platform. Although similar mechanisms exist in the literature, the analysis of them is scarce because a flexible spring instead of a rigid kinematic chain is used as the spine. With the spring's lateral buckling motion, a new approach must be adopted to solve the kinematics. In this paper, we propose a method that combines the kinematics with the statics to solve them simultaneously. The configuration of the moving platform is parameterized with four parameters, one of which is considered as parasitic motion. Using the spring's lateral buckling equation, we can obtain the parasitic motion and solve the inverse position problem. The optimal design for cable placements is then performed to minimize the actuation force. The method in this paper provides a novel way to analyze parallel mechanisms with a spring spine and it can be applied to other mechanisms with flexible spines. (C) Koninklijke Brill NV, Leiden and The Robotics Society of Japan, 2012