Cable Path Analysis and Kinematic Control of a Cable-Driven Parallel Robot Allowing Cables to Wrap on Cylinders or Spheres

Scholars have proposed to allow cables to wrap on the base, the end-effector, or obstacles to expand the workspace of a cable-driven parallel robot (CDPR) in recent years. However, it is not entirely clear whether the path of a cable wrapped on the surface of different rigid bodies can or cannot be solved analytically. To this end, this paper analyzes the statics of a cable wrapped on a general surface and proposes necessary conditions for a path of a cable wrapped on a general frictionless surface. This paper shows that only the path of a cable wrapped on a frictionless surface included in a handful of surfaces, including cylinders and spheres, can be solved analytically. Then, the cable path and inverse velocity kinematics of a CDPR with cables, every of which wraps on a frictionless cylinder or a frictionless sphere, are solved. A CDPR demonstrator with cables wrapped on cylinders fixed to the base and a CDPR demonstrator with cables wrapped on a spherical end-effector are established. The kinematics-based control of the CDPR demonstrators is achieved.