Line Geometry Tools for the Analysis and synthesis of a Medical Robot

Abstract

This research focuses on the analysis, synthesis and optimization of parallel robot maniplulators, using line geometry and projective geometry tools (The analysis provides both the singular configurations of the robot and its workspace).

A parallel type manipulator can be modeled as dominant lines along its linear actuators. Using this presentation and linear dependence of lines, the robot singular configurations could be found. Those lines expressed in Plucker coordinates are the homogeneous coordinates of a projective five-dimension space . In this space each line is presented as a point, and all screws with the same pitch form a quadric surface. We focus on one specific quadric called “Klein Quadric”, representing all screws with infinite pitch (lines). In this quadric all families form geometric varieties that reflect the singular configuration and the workspace of the manipulator. Using these tools we will examine parallel structured manipulators and optimize their structure for a given workspace. This will be achieved by representing the joint workspace, as a restricted variety of lines, by formulating inequality equations in Plucker coordinates. We will also include a broader family of manipulators where not all actuators are linear, by finding the lines that governs the kinematics of the system.

The design tools presented above will be used to optimize and find best configuration of a parallel robot for a medical application. Our goal is to design a light weighted, highly accurate miniature parallel robot that will guide the physician tools during operation.