Plataforma De Stewart

Functional Analysis And Position Control Of a Stewart’s Platform

Nina Gorie and Alí Barrera
Department of XXXX
Faculty of Mechanical


Abstract
The study of the architecture, the geometrical structures and the mechanical linkages of a parallel manipulator allows knowing its physical limits. This paper discusses the current state of the Stewart’s Platform that is considered as a parallelrobot with 6 degrees of freedom. Due of the advantages and drawbacks of the parallel manipulators make it useful for specific applications. The simulation-control software is not intended simply to operate the platform as quickly as possible. This is a teaching program in automated mechanics. At each step of calculating a “movement”, the elements necessary to control position are worked out, andalso various mechanical calculations are performed.
Keywords: Stewart’s Platform; Parallel manipulator; Inverse Kinematics; Forward; Kinematics;


1. INTRODUCTION

A parallel robot is defined as:
“Those robots in which the tail end is attached to the base for more than a kinematic chain independent” (Waldron, 1991).

Compared with serial manipulators, parallel manipulators have a highrigidity in its structure and therefore have a high load-carrying capacity, moreover since there is no accumulation of errors on the mobile platform is possible to obtain a better accuracy. In exchange for these advantages, parallel manipulators have a very limited workspace. Despite their poor dexterity, parallel manipulators have interesting applications such as flight and vehicle simulators,high-precision machining centers, mining machines, and so on.
In 1965, Stewart (1965) proposed the use of a parallel structure with six degrees of freedom to generate motion in the space, as the most practical solution in the constructions of flight simulators. The choice of this type of mechanism is justified by the good relationship load capacity/weight of its own.
Stewart’s mechanism consisting ofa triangular platform connected by ball joints to three linear actuators adjustable in length, which is connected in turn to a fixed base by means of universal joints.

Over time, the architecture of the Stewart’s Platform was undergoing modifications. Stewart’s Platform as it is known today, consists of two platforms (the base and mobile platform) linked via six extendable actuators throughball joints on both sides, or with ball joints to one side and the other universal.
Until the mid-80’s, more designs are focused in two configurations. One with the base and the end effector with triangular shape, and the actuators coinciding two by two at the vertices of each triangle, and another, with the mobile platform in triangular shape and the actuators coinciding two to two vertices in atriangle and with six different points contained in the plane of the hexagonal shaped base. These configurations are denoted as 3-3 Stewart’s Platform (See figure 1a) and 3-6 Stewart’s Platform (See figure 1b), respectively. Soon it was noted that the coincidence of the ball joints of severely restricted mobility of the manipulator, setting 3-6 however still remained popular for some time. Anotherconfiguration which became popular is the one with semiregular hexagons as connection points on both the base and the end effector (6-6 Stewart’s Platform) (See figure 1c).





Figure 1. Stewart’s Platform: (a) 3-3, (b) 3-6, (c) 6-6.


There are a variety of mechanical configurations for this type of robots, depending on the structures of the kinematic chains which connect the basewith the end effector. Kinematic structure with ball joints on both sides for each actuator (See figure 2a), denoted as Stewart’s Platform 6-SPS, where 6 is the number of degrees of freedom of the robot and SPS comes from Spherical – Prismatic – Spherical. Similarly the structure with universal joints at the base and ball in the end effector is denoted Stewart’s Platform 6-UPS (Universal –...