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