**1. Introduction**

358 Serial and Parallel Robot Manipulators – Kinematics, Dynamics, Control and Optimization

Oliveira, L.S. and Saramago, S.F.P., 2010, "Multiobjective Optimization Techniques Applied

Price, K., Storn, R. and Lampinen, J., 2005, "Differential Evolution - A Practical Approach to

Sakawa, Y., Matsuno, F. and Fukushima, F., 1985, "Modelling and feedback control of a flexible arm", Journal of Robotic Systems, Vol. 2, No. 4, pp. 453–472. Santos, R. R., Steffen Jr., V. and Saramago, S.F.P., 2005, "Solving the inverse kinematics

Shi, J.X., Albu-Schaffer, A. and Hirzinger, G., 1998, "Key issues in the dynamic control of

International Conference on Robotics and Automation, Vol. 1, pp. 490–497. Tomei, P. and Tornambe, A., "Approximate modeling of robots having elastic links", IEEE Transactions on Systems, Man and Cybernetics, Vol. 18, No. 5, pp. 831–840. Tso, S.K., Yang, T.W., Xu, W.L. and Sun, Z.Q., 2003, "Vibration control for a flexible link

Tsujita, K., Tsuchiya, K., Urakubo, T., Sugawara, Z., 2004, "Trajectory and Force Control of a

Uchiyama, M., Konno, A., Uchiyama, T. and Kanda, S., 1990, "Development of flexible dual-

Vanderplaats, G. N, 1999, "Numerical Optimization Techniques for Engineering Design",3rd

Vose, M. D., 1999, "The Simple Genetic Algorithm: Foundations and Theory", MIT Press,

Yoshikawa, T., Harada, K., and Matsumoto, A., 1996, "Hybrid position/force control of

Zhu, G., Ge, S.S. and Lee, T.H., 1999, "Simulation studies of tip tracking control of a singlelink flexible robot based on a lumped model", Robotica, Vol. 17, pp. 71–78.

Workshop on Intelligent Robots and System, pp. 375–381.

and Automation, Vol. 12, No. 4, pp. 633–640.

214, and pp. 215–224.

and Engineering, Vol. XXXII, p.94 - 104.

Global Optimization", Springer.

Mechanical Engineering.

Mechanics, Vol. 38, pp. 51–62.

1271–1289.

edition, VR&D Inc.

Cambridge, MA.

motions, Part 1: Element level equations, and Part II: System equations", ASME Journal of Dynamic Systems, Measurement, and Control, Vol. 112, No. 2, pp. 203–

to Engineering Problems", Journal of the Brazilian Society of Mechanical Sciences

problem through performance index optimization".XXVI Iberian Latin American Congress on Computational Methods in Engineering, Guarapari-ES.CILAMCE. Santos, R. R., Steffen Jr., V. and Saramago, S.F.P., 2007, "Optimal path planning and task

adjustment for cooperative flexible manipulators". 19th International Congress of

lightweight robots for space and terrestrial applications", Proceedings of the IEEE

robot arm with deflection feedback", International Journal of Non-Linear

Manipulator With Elastic Links", Journal of Vibration and Control, Vol. 10, pp.

arm manipulator tested for space robotics", Proceedings of IEEE International

flexible-macro/rigid-micro manipulator system", IEEE Transactions on Robotics

In recent years, numerous researchers have investigated parallel manipulators and many studies have been done on the kinematics or dynamics analysis. Parallel manipulators has been only mentioned in several books, as in (Merlet, 2006; Ceccarelli, 2004; Kong, & Gosselin, 2007; Glazunov, et al., 1991). Reference (Gosselin, & Angeles, 1990) has established singularity criteria based on Jacobian matrices when describing the various types of singularity. Then, in (Glazunov, et al. 1990) proposed other singularity criteria for consideration of these problems the screw theory based on the approach of the screw calculus, as in (Dimentberg, 1965). Those criteria are determined by the constraints imposed by the kinematic chains, as in (Angeles, 2004; Kraynev, & Glazunov, 1991), taking into account some problems the Plücker coordinates of constraint wrenches can be applied in (Glazunov, 2006; Glazunov, et al. 1999, 2007, 2009; Thanh, et al. 2009, 2010a).

Dynamical decoupling allows increasing the accuracy for the parallel manipulators presented as in (Glazunov, & Kraynev, 2006; Glazunov, & Thanh, 2008). It is necessary to develop optimal structure have combined (Thanh, et al. 2008), as well as algorithms and multi-criteria optimization (Statnikov, 1999; Thanh, et al. 2010b) obtaining the Pareto set. It is very important to taking into account possible singularity configurations, to find out how they influence the characteristics of constraints restricting working space (Bonev, et al. 2003; Huang, 2004; Arakelian, et al. 2007).

The trend towards highly rapid manipulators due to the demand for greater working volume, dexterity, and stiffness has motivated research and development of new types of parallel manipulator (Merlet, 1991). This paper is focused the constraints and criteria existing in known parallel manipulators in form of a parallel manipulator with linear actuators located on the base.
