An Integrated Kinematic Mapping and Fourier Method to Design Spherical Coupled Serial Chain Mechanisms for Single-Joint Rehabilitation

Abstract Robotic devices are capable of reducing the physical burden on rehabilitation therapists and providing training programs of good repeatability, high efficiency and high precision. When designing the kinematic structure for rehabilitation robots, there has been a growing interest towards 1-degree-of-freedom (DOF) end-effector mechanisms due to their simpler structure and less complicated control algorithms. Compared with current 1-DOF mechanism designs that are mainly customized for multi-joint robotic training, spherical coupled serial chain (SCSC) mechanisms are proposed in this paper to specifically deliver the single-joint robotic training, which is of equal importance to the effective physical recovery. Using kinematic mapping theory, the end-effector motion of SCSC mechanisms can be naturally transformed to two trigonometric curves composed of finite Fourier series in two separate planes of the image space. This novel formulation helps to establish an analytical and direct relationship between the design parameters of SCSC mechanism and the harmonic parameters of the image-space representation of the task rehabilitation motion. The result is a simple and effective method to kinematic synthesis of SCSC mechanisms for generation of single-joint motion with an arbitrary number of spherical poses. An example of designing SCSC mechanisms for shoulder-joint rehabilitation is presented at the end of this paper to illustrate the feasibility of the proposed method.