Mathematical modeling of a 3-CUP parallel mechanism using the Fermat point. (July 2021)

• Record Type: Journal Article
• Authors: Martínez, Omar; Soto, Israel; Campa, Ricardo
• Is Part Of: Mechanism and machine theory. Volume 161(2021)
• Publication Date: 2021-07
• Subjects: 3-CUP parallel mechanism -- Pose kinematics -- Velocity kinematics -- Dynamics -- Fermat point; Machine theory -- Periodicals; Machinery -- Periodicals; Machines -- Périodiques; Génie mécanique -- Périodiques; Machine theory; Machinery; Periodicals; 621.81
• DOI: 10.1016/j.mechmachtheory.2021.104326
• Languages: English
• ISSNs: 0094-114X

Abstract

Highlights: The 3-CUP parallel robot is a novel 3-dof mechanism that belongs to the 2R1T type. The Fermat point is the basic concept of the novel proposed approach. The Fermat point is used to compute the equations of motion of the 3-CUP robot. Numerical simulations allow to validate the proposed approach. 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.