Displacement analysis of robotic frames for reliable and versatile use as external fixator

External fixators are widely used in the area of orthopedics to manage deformities and fractures. The historical trend in obtaining a mechanical infrastructure has shifted from simple devices like pins, rods, and hinges to more sophisticated frames involving parallel manipulators. Despite advantages of such robotic frames especially in removing stiffness issues, there are still problems associated with the reliable deployment of these modern devices. Problems like singularity, possibilities of guiding fragments along many different trajectories have been handled in this paper. A method has been shown how to detect singularity in displaced, aligned, and intermediate positions of the fragments. How the robotic system could be actuated according to different functions have been investigated, in addition to their effects on trajectories of distal fragment end. These considerations have been demonstrated on numerical examples.