Joint-Space Characterization of a Medical Parallel Robot Based on a Dual Quaternion Representation of SE(3)

The paper proposes a mathematical method for redefining motion parameterizations based on the joint-space representation of parallel robots. The study parameters of SE(3) are used to describe the robot kinematic chains, but, rather than directly analyzing the mobile platform motion, the joint-space of the mechanism is studied by eliminating the Study parameters. From the loop equations of the joint-space characterization, new parameterizations are defined, which enable the placement of a mobile frame on any mechanical element within the parallel robot. A case study is presented for a medical parallel robotic system in which the joint-space characterization is achieved and based on a new defined parameterization, the kinematics for displacement, velocities, and accelerations are studied. A numerical simulation is presented for the derived kinematic models, showing how the medical robot guides the medical tool (ultrasound probe) on an imposed trajectory.