This paper deals with the survey of kinematic structures adapted to specific medical robots: minimally invasive surgery (MIS) and tele-echography. The large diversity of kinematic architectures that can be found in medical robotics leads us to perform a statistical analysis to inform and guide design of medical robots. Safety constraints and some considerations in design evolution of medical robots are presented in this paper. First, we describe the spectrum of medical robots in minimally invasive surgery and tele-echography applications and particularly the variety of kinematic architectures used. We present the robots and their kinematic architectures and highlight differences that occur in each medical application. We perform a statistical analysis which can serve as a resource in topological synthesis for each specific medical application. Safety is an important specification in medical robotics, and for that reason we show the means used to take into account this constraint. This study demonstrates that the nature of medical robots implies specific requirements leading to different kinematic structures. The statistical analysis gives information on choice of kinematic structures for medical applications (minimally invasive surgery and echography). The safety constraint as well as the interaction between doctor and robot leads to investigate new mechanical solutions to enhance medical robot safety and compliance. We expect that this paper will serve as a significant resource and help the design of future medical robots.