Design of planar 3-DOF 3-RRR reactionless parallel manipulators

Abstract

This paper discusses the development of reactionless 3-RRR planar parallel manipulators, which apply no reaction forces or moments to the mounting base during motion. Design equations and techniques are proposed which allow for the dynamic substitution of the mass of the moving platform of a parallel manipulator by three concentrated masses. The dynamic model of the moving platform consequently represents a weightless link with three concentrated masses. This allows for the transformation of the problem of the design of a reactionless manipulator into a problem of balancing pivoted legs carrying concentrated masses. The total angular momentum of the manipulator can be reduced to zero using two approaches: (i) on the basis of counter-rotations and (ii) using an inertia flywheel rotating with a prescribed angular velocity. The suggested solutions are illustrated through computer simulations and the results verified by showing that the manipulator is indeed reactionless, there being no forces or moments transmitted to the base during motion of the moving platform.

Introduction

In high-speed mechanical systems, mass balancing of the moving links brings about a reduction of the variable dynamic loads on the frame and, as a result, a reduction of vibrations. Different approaches and solutions have been developed and documented [1], [2], [3] but, despite its long history, mechanism balancing theory continues to develop and new approaches and solutions are constantly being reported. A new field for their application is the design of fast parallel manipulators, which are very efficient for advanced robotic applications. Previous work on the problem of balancing of parallel manipulators may be arranged in the following groups:

• Shaking force balancing by counterweights mounted on the movable links of the parallel manipulator [4], [5], [6], [7], [8]. The aim of these balancing methods is the redistribution of movable masses by adding counterweights to the links, which allows the fixation of the common centre of mass of the moving links of the manipulator. After such a redistribution of the masses, the gravitational and inertia forces are cancelled.

• Gravitational force balancing by springs mounted on the movable links of the parallel manipulator [7], [8], [9], [10]. Such a balancing can be defined as when the weights of the links do not produce any force on the actuators for any configuration of the manipulator, i.e. potential energy of the parallel manipulator is constant for all possible configurations. It should be noted that many results in the field of balancing of robotic arms and linkages [11], [12], [13], [14], [15], [16], [17] can be successfully applied to the balancing problems of parallel manipulators.

• Gravitational force balancing by secondary mechanisms coupled with the parallel manipulator [18], [19], [20], [21], [22]. In this case the balancing element, which can be a spring [18], a counterweight [19] or an actuating power cylinder [20], [21], [22], is mounted on the links of the secondary mechanism. In these studies the added system is a pantograph linkage which allows the gravitational forces to be balanced.

These approaches have been developed for inertia or gravitational force balancing of parallel manipulators. In the case of shaking force balancing the mentioned methods allow the cancellation of the resultant of all reaction forces at the frame. However, the unbalanced angular moments create a moment on the frame, which can also be significant.

Among several works on this subject, studies devoted to the design of reactionless parallel manipulators [23], [24] should be highlighted. These manipulators are of interest because the inertia forces are cancelled together with the total angular momentum of the manipulator. Such a design enables the cancellation of the reaction forces and torques at the frame of the parallel manipulator.

In this paper, the design of reactionless 3-DOF 3-RRR planar parallel manipulators is considered and design equations and techniques are developed.