טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
Ph.D Thesis
Ph.D StudentWolf Alon
SubjectLine Geometry Tools for the Analysis and Synthesis of a
Medical Robot
DepartmentDepartment of Mechanical Engineering
Supervisor Professor Moshe Shoham


Abstract

Parallel robots are a relatively new trend in the field of robotics, yet they are already becoming a niche product in several robotics research areas, such as in machine tools, assembly lines, medical applications, and others.

Numerous works investigating parallel mechanisms stress out the various advantages of these mechanisms, however one of their major drawbacks is their performance while in, or close to singular configurations. In these configurations, the mechanism tends to lose its stiffness while gaining extra degrees of freedom. Physically, when the mechanism is in a singular configuration, the structure cannot resist or balance an external wrench applied at the mobile platform.

In this investigation, drawing principally upon tools from line geometry and screw theory, we introduce new analysis and synthesis tools for the investigation of singular configurations and rigidity of parallel robots. As a first step, the 6X6 transformation matrix mapping external wrenches acting on the moving platform to the internal forces/moments of the moving platform’s joints is derived, the rows of which are the Plücker line coordinate of a set of six governing lines of the structure. The closest linear complex to these six governing lines is then obtained. The linear complex’s axis and its pitch not only provide insight of the type and location of the robots’ singularities, but also on the nature of any instantaneous motions arising from manufacturing tolerances and low rigidity.

In addition, we investigated the optimal design and positioning of a parallel robot by deriving a parametric objective function which describes the robots’ performance in sense of its rigidity, with respect to a given task. These analysis and synthesis tools were used to investigate a new concept of a medical parallel robot.