On quartically-solvable robots

© 20xx IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.This paper presents a first attempt at a unified kinematics analysis of all serial and parallel solvable robots, that is, robots whose position analysis can be carried out without relying on numerical methods. The efforts herein are focused on finding a unified formulation for all quartically- solvable robots, as all other solvable robots can be seen as particular cases of them. The first part is centered on the quest for the most general quartically-solvable parallel and serial robots. As a result, representatives of both classes are selected. Then, using Distance Geometry, it is shown how solving the forward kinematics of the parallel representative is equivalent to solve the inverse kinematics of the serial representative, thus providing a unified formulation. Finally, it is shown that the position and singularity analysis of these robots reduces to the analysis of the relative position of two coplanar ellipses.Peer Reviewe