Modeling and Solving Strategies for the Forward Kinematics Problem of the translation parallel manipulators, application to high speed manufacturing and high accuracy

This article investigates the forward kinematics problem formulation and resolution specifically applied to spatial parallel manipulators which allow only for translationnal displacements of the end-effector. The translation manipulator is usually constituted of three to six kinematics chains with three actuators usually located on the base. These mechanisms are designed to prevent any rotation. This article shall focus on the Delta manipulator, but the analyses can be extrapollated to any other translation manipulators. To acheive FKP computations, it is relevant to ask wheather it is possible to improve computations by proper modeling and algorithms. The goal is to minimize the real solution number along with response times. ' An algebraic method is applied to solve the FKP for parallel robots. It is implementing proven Grobner bases from which an equivalent univariate polynomial system is deduced. This univariate system resolution leads to all the system real solutions which exactly corresponds to the manipulator postures. The Delta manipulator can be described by two equivalent models: the 3-RCC and the 6-6 from which four different kinematics formulations are determined. Finally, using the second formulation, a solution reduction algortithm is introduced. A discussion follows which allows to select the best approach in typical applications such as material handling and high speed milling.