Shaking Force and Shaking Moment Balancing of Robot Manipulators

  • Vigen ArakelianEmail author
  • Sébastien Briot
Part of the Mechanisms and Machine Science book series (Mechan. Machine Science, volume 27)


This Chapter is devoted to the shaking force and shaking moment balancing of robot manipulators.

The Sect. 7.1 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 is 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.

Section 7.2 deals with the complete shaking force and shaking moment balancing of planar parallel manipulators with prismatic pairs. The cancellation of the dynamic loads transmitted to the ground is a challenge for these types of manipulators. It is obvious that the classical methods based on the optimal redistribution of movable masses and additional counter-rotations can be used to cancel shaking force and shaking moment. However, such a balancing of parallel manipulators with prismatic pairs is only attained via a considerably complicated design. This study shows that it is possible to balance planar parallel mechanisms using Scott-Russell mechanisms. Such an approach enables a division of the number of counter-rotations by two.

Then we consider in Sect. 7.3 a simple and effective balancing method, which allows the considerable reduction of the shaking force of non-redundant manipulators without adding counterweights. It is based on the optimal control of the acceleration of the total com of moving links. The full shaking force and shaking moment balancing of robots using an optimal motion control is also used in last Section (Sect. 7.4) of this Chapter. This strategy takes advantage of the particularities of position/orientation decoupled robots for which the motion of the wrist is decoupled from the motion of the position finder device. Such an approach is illustrated via two applicative examples: the SCARA serial robot and the position/orientation decoupled PAMINSA parallel manipulator.


Parallel Manipulator Revolute Joint Input Torque Motion Profile Axial Moment 
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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Institut National des Sciences Appliquées (INSA), Rennes, France, and Institut de Recherche en Communications et Cybernétique de Nantes (IRCCyN), Nantes, FranceRennesFrance
  2. 2.Institut de Recherche en Com. et Cybernétique de NantesCNRSNantesFrance

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