Design and kinematic analysis of 3PSS-1S wrist for needle insertion guidance

In this work it is presented a complete kinematic analysis of the 3PSS-1S parallel mechanism for its implementation as a spherical wrist for a needle insertion guidance robot. The spherical 3PSS-1S mechanism is a low weight and reduced dimension parallel mechanism that allows spherical movements providing the requirements needed for the serial–parallel robotic arm for needle insertion guidance. The solution of its direct kinematic is computed with a numerical method based on the Newton–Raphson formulation and a constraint function of the mechanism. The input–output velocity equation is obtained with the use of screw theory. Three types of singular postures are identified during simulations and verified in the real prototype. The 3PSS-1S can perform pure rotations of ±45°±45°, ±40°±40°, ±60°±60° along the View the MathML sourcex, View the MathML sourcey, View the MathML sourcez axes respectively.