Mathematical modeling of a 3-CUP parallel mechanism using the Fermat point

Abstract

This document is devoted to the analysis of the pose and velocity kinematics, as well as of the dynamics, for a parallel mechanism with three degrees of freedom, of the type known as 3-CUP. This mechanism is constituted by two triangular rigid bodies, one fixed (base) and other mobile (platform), connected to each other by three kinematic chains, each with a cylindrical (C), a universal (U), and a prismatic (P) joint. A novel approach is used for kinematic analysis, as well as for obtaining the dynamic equations of motion of the system. In such approach, tools of geometry, vector analysis, and mainly the Fermat point are employed to obtain a closed solution for the forward kinematics problem for this kind of parallel robot with variable geometry triangular mobile platform. At the end, the analytical kinematics and dynamics models obtained are compared, via simulations, with the corresponding models computed using commercial software; the results allow to validate the approach.