Geometric Design of Spatial PRR Manipulators Using Polynomial Elimination Techniques

This paper studies the geometric design of spatial open loop prismatic-revolute-revolute (PRR) robot manipulators. Four spatial positions and orientations are defined and the dimensions of the geometric parameters of the PRR manipulator are computed so that the manipulator will be able to place its end-effector at these four pre-specified locations. Denavit and Hartenberg parameters and 4×4 homogeneous matrices are used to formulate the design equations. Polynomial Elimination techniques are used to solve these equations and twelve geometrically different solutions are found.