Solution of the forward kinematics of parallel robots based on constraint curves
A. Peidró, L. Payá, S. Cebollada, V. Román, O. Reinoso
Lecture Notes in Electrical Engineering. Informatics in Control, Automation and Robotics  (2022)
Ed. Springer  ISBN:978-3-030-92441-6  ISSN:1876-1100  DOI:  - 793 (386-409)


This paper presents a method to solve the forward kinematic problem of parallel robots, obtaining all real solutions. The method is illustrated with the 3UPS-PU parallel robot, and consists in eliminating one unknown to obtain an equation that constrains the admissible values of the remaining unknowns. This constraint defines a curve in the plane of the remaining unknowns, which contains all real solutions. The proposed method samples and scans this constraint curve in order to find all real solutions, using only analytical operations and kdimensional trees. This method is able to find all real solutions and performs at least one order of magnitude faster than other numerical methods, while avoiding the complicated and lengthy symbolic expressions that traditional elimination procedures involve. The proposed method is also extended to the complex domain and another parallel robot (the 3RRR robot).