Static balancing of parallel robots

doi:10.1016/j.mechmachtheory.2004.06.011

Mechanism and Machine Theory

Volume 40, Issue 2, February 2005, Pages 191-202

https://doi.org/10.1016/j.mechmachtheory.2004.06.011 Get rights and content

Abstract

In this paper, the static balancing of spatial parallel manipulator is addressed. Static balancing is defined as that the weight of the links does not produce any force at actuators for any configuration of the manipulator. In order to obtain the balancing condition, the position vector of the global center of the mass is expressed as a function of the position and orientation of the platform and of the six actuated prismatic joint. Then, the conditions for balancing are derived from the expressions obtained. Two methods lead to static balancing, namely using counterweight and using springs. In both methods, the resulting mechanism is fully balanced for gravity. In this study the first method is implemented, leading to the manipulator with a stationary global center of mass.

Introduction

The static and dynamic balancing is a classic problem in the theory of machines and mechanisms. In particular, when a mechanism is not statically balanced, the weight of linkage produces force or torque at actuators under static conditions and actuators have to contribute to support the weight of the moving links for any configurations. The problem becomes more serious for the parallel manipulator applied as flight simulator where the weight of the moving platform is very large with respect to the masses of the links. Static balancing also called gravity compensation is important. If the forces/toques exerted by joint actuators are reduced, the full potential of machine will be improved.

A great deal of work has been carried out and reported in the literature for the static balancing problem. For example, in the case of serial manipulator, Nathan [1] and Hervé [2] applied the counterweight for gravity compensations. Streit et al. [3], [4] proposed an approach to static balanced rotary bodies and two degrees of freedom of the revolute links using springs. Streit and Shin [5] presented a general approach for the static balancing of planar linkages using springs. Ulrich and Kumar [6] presented a method of passive mechanical gravity compensation using appropriate pulley profiles. Kazerooni and Kim [7] presented a method for statically balanced direct drive arm.

For the parallel manipulator much work was done by Gosselin et al. Research reported in [8] was focused on the design of gravity-compensated of a six-degree-of-freedom parallel manipulator with revolute joints. Each leg with two links is connected by an actuated revolute joint to the base platform and by a spherical joints the moving platform. Two methods are used, one approach using the counterweight and the other using springs. In the former method, if the center of mass of a mechanism can be made stationary, the static balancing is obtained in any direction of the Cartesian space. In the second approach, if the total energy is kept constant, the mechanism is statically balanced only in the direction of gravity vector. In [9] the static balancing conditions are derived for the three-degree-of-freedom spatial parallel manipulator and in [10] similar conditions are obtained for spatial four-degree-of-freedom parallel manipulator using two common methods, namely, counterweights and springs.

In this paper, following the same approach presented in [8], [9] and [10] by Gosselin, the static balancing of the six-degree-of-freedom platform type parallel manipulator with the fixed-length legs shown in Fig. 1 is studied. This system consists of a moving platform (MP) to which a tool is attached, and six legs sliding along the guideways that are mounted on the support structure including the base platform (BP). Each leg is connected at one end to the guideway by a universal joint and at another end to the moving platform by a spherical joint. While the kinematics and dynamics model of this type of the manipulator were derived in [11], static balancing was not studied. In this paper, a method is proposed to solve this problem. Based on the proposed method, the mechanism can be balanced using the counterweight with a smart design of pantograph. With this design, it is possible to obtain a constant global center of mass for any configurations of the manipulator.

Section snippets

Static balancing using counterweight

In this section, the static balancing of the parallel manipulator under study is investigated using counterweights. The base coordinate frame designated by the Oxyz frame as shown in Fig. 2, is fixed to the base with Z-axis pointing vertically upward. The moving coordinate frame O′x′y′z′ is attached to the moving platform. The Cartesian coordinates used to describe the pose of the platform are given by the position of O′ with respect to the fixed frame and the orientation of the platform

Static balancing using a pantograph counterweight

Since it is shown that the static balancing of the examined mechanism is impossible with the help of counterweights, we propose a method to add a pantograph connecting the moving platform O′ to the fixed platform O, as shown in Fig. 4. The pantograph is a device that allows to keep two end points on the same line and keep their distance at the center with a constant ratio. In this application it is possible to use a pantographs with two or more mesh as shown in Fig. 4 and Fig. 5, respectively.

Concluding remarks

The static balancing of hexapods is addressed in this paper. The expression of the global center of mass is derived, based on which a set of static balancing equations has been obtained. It is shown that this type of parallel mechanism cannot be statically balanced by counterweights because prismatic joints do not have a fixed point to pivot as revolute joints. A new design is proposed to connect the center of the moving platform to that of the fixed platform by a pantograph. The conditions for

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Static balancing of parallel robots☆

Abstract

Introduction

Section snippets

Static balancing using counterweight

Static balancing using a pantograph counterweight

Concluding remarks

Mechanism and Machine Theory

Mechanism and Machine Theory

Mechanism and Machine Theory

Journal of Manufacturing Systems

A constant force generation mechanism

ASME Journal of Mechanism, Transmissions, and Automation in Design