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On quartically-solvable robots

posted on 2023-06-09, 00:28 authored by Nicolas Rojas, Julia Borras, Federico Thomas
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.


Publication status

  • Published

Page range


Presentation Type

  • paper

Event name

2015 IEEE International Conference on Robotics and Automation (ICRA)

Event location

Seattle, WA

Event type


Event date

26 to 30 May 2015

Book title

2015 IEEE International Conference on Robotics and Automation (ICRA)

Department affiliated with

  • Engineering and Design Publications

Full text available

  • No

Peer reviewed?

  • Yes

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