Singularity and kinematics analysis for a class of PPUU mobile parallel robots

Abstract

In this paper a class of mobile parallel robots with the structural configuration of PPUU (Prismatic-Prismatic- Universal-Universal) is investigated in detail. Firstly a singularity analysis corresponding to different configured cases of the revolute axes of the robot's U-joint based on the screw theory is developed and a brief comparison of the four cases is carried out. Of all four configuration schemes, only P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</sub> P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">y</sub> U <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">xE</sub> U <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">FG</sub> can avoid a singularity by mechanism design rather than complicated trajectory control. Then the inverse kinematics to the P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</sub> P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">y</sub> U <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">xE</sub> U <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">FG</sub> mobile parallel robot is developed. By a numerical approach, the orientation workspace envelope is mapped. This work provides an analytical basis for the design of an MPR prototype.