The analysis of modern development trends and methods of construction of collaborative medical robotic systems is carried out. An approach is proposed for the design of medical collaborative robotics, which is aimed at a purposeful scientific and technical search for new robotic and mechatronic technologies. The goal of developing new technologies is a significant excess of the capabilities of natural human systems in the performance of medical operations. In the following work, the state and development trends of medical robotics such as autonomous robotic surgery and recently found application in a medical field additive manufacturing are studied. Design approach applicable to the relatively new medical collaborative robotics is proposed. Several mathematical criteria with respect to both engineering and medical aspects are developed. Based on the analysis of typical movements and trajectories of the medical instrument, the following functional criteria were used in the design: - the standard deviation from a linear (semilunar, scalloped) trajectory is the deviation value at each point from its projection to the midline; - the error in the magnitude of the air gap between the laser tip and the treated biological tissue; - accuracy of the average speed of movement of a medical instrument; - standard deviation from the average speed of movement of a medical instrument. Components of efficient surgery robot are described. Results of the development of two experimental setups for the maxil-lofacial laser surgery robotic system and robotic based 3D bio-printing 'in situ', respectively, are given. Proposed systems exceed the capabilities of human in the performance of medical operations, and can be a basis for the development of principally new maxillofacial laser surgery and 3D bio-printing robotic based systems. This work accomplished by collaboration of Moscow State Technological University "STANKIN" and Moscow State University of Medicine and Dentistry named after A I. Evdokimov.