Combined kinematic and static analysis of a cable-driven manipulator with a spring spine

A humanoid neck design with low motion noise yields a cable-driven parallel manipulator to imitate two axis rotational motion of a human neck. The fixed base and moving platform of the manipulator 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 manipulators exist in literature, the analysis for them is scarce. The difficulty is that while traditional parallel manipulator usually has a rigid kinematic chain as the spine, this manipulator has a flexible spring. With the spring's lateral bending motion, new approach must be adopted to solve the kinematics. In this paper, we propose a method which combines the kinematics with the statics to solve them simultaneously. We parameterize the posture of the moving platform with four parameters and consider one of them as parasitic motion. Using the spring bending equation, we can obtain the parasitic motion and solve the inverse position problem. The analysis in this paper provides a novel way to analyze parallel manipulator with a spring spine, and it can be applied to other manipulators with flexible spines.