A Complete Kinematic Analysis of the SNU 3-UPU Parallel Robot

Dominic Walter

Several articles have been published about the SNU 3-UPU parallel robot, since the prototype built at the Seoul National University (SNU) showed a rather unexpected behavior, being completely mobile although none of the prismatic joints was actuated. In this talk a brief introduction is given how to describe all possible poses of the robot by a system of algebraic equations using Study parameters, such that theoretical questions concerning assembly modes and mobility can be answered on the basis of the solutions of this system. A complete analysis of the forward kinematics is given showing that the manipulator
has theoretically up to 78 assembly modes, most of them being always complex. Investigating the system's Jacobian it can be shown that for equal limb lengths the manipulator has some highly singular poses. Furthermore possible operation modes of the manipulator are discussed. To obtain these modes methods from algebraic geometry prove to be very useful. Moreover it is examined for which fixed design and joint parameters the mechanism allows self-motion and it is shown that there are only two such mobile robots.