Mobility properties of a Schoenflies-type parallel manipulator

This paper addresses the mobility properties of a novel Schoenflies-type parallel manipulator. By analyzing the degree of freedom (DoF) of the manipulator, we select a set of independent variables to describe the pose relationship of the manipulator and the fixed base, which is the least in number compared with others. Through coordinate transformation, we can obtain the geometric relationship in the absolute coordinate system via a set of parametric equations. As a result, the least order's Jacobian matrix will be gained and the singularity of the manipulator can be expressed as the determinate of the Jacobian matrix is zero. The distinctive merit of this methodology is that the order of Jacobian matrix is the least compared with others.