**8. References**


As a result, no further improvement is achieved by changing the relative importance of the

The numerical experiments conducted during the present research work lead to the following conclusions. The interdependence of the performance indexes is an important aspect that impacts the performance of the numerical method. The evaluation of different objectives that evaluates correlated information increases the computational cost but have no contribution to the optimal design. The use of several weighting factors is recommended. The nonlinear nature of the objective indexes requires a heavy exploration of the design space, aiming at finding a significant improvement for a particular combination of weighing factors. Finally, the use of a global optimization methodology is the most important contribution of this work that will distinguish the proposed methodology as a fast and accurate solver. Few iterations of the tunneling process provided an effective evolution to

From the author's perspective, the effective combination of different techniques is the key to obtain a high performance engineering result. Since this study deals with off-line planning, even a small improvement in the path performed by the robot may lead to expressive economic benefits. This is justified by the fact that the same movement of the robot is

The next step of this research is the evaluation of the effect of uncertainty in the design,

As the proposed methodology is efficient to obtain an improved manipulator trajectory while dealing with the flexibility effect, joint torque and manipulability, the authors believe

Alberts, T. E., Xia, H. and Chen, Y., 1992, "Dynamic analysis to evaluate viscoelastic passive

Bertsekas, D. P., 1995, "Dynamic Programming and Optimal Control", Athena Scientific. Betts, J. T., 2001, "Practical Methods for Optimal Control Using Nonlinear Programming",

Bryson, Jr., A. E., 1999, "Dynamic Optimization", Addison Wesley Longman, Inc.

Book, W. J., 1984, "Recursive Lagrangian dynamics of flexible manipulator arms", The International Journal of Robotics Research, Vol. 3, No. 3, pp. 87–101. Bricout, J.N., Debus, J.C. and Micheau, P., 1990, "A finite element model for the dynamics of

Cannon, R.H. and Schmitz, E., 1984, "Initial experiments on end-point control of a flexible onelink robot", The International Journal of Robotics Research, Vol. 3, No. 3, pp. 62–75. Chang, Y. C. and Chen, B. S., 1998, "Adaptive tracking control design of constrained robot systems," International Journal of Adaptive Control, Vol. 12, No. 6, pp. 495–526. Choi, B. O. and Krishnamurthy, K., 1994, "Unconstrained and constrained motion control of

damping augmentation for the space shuttle remote manipulator system", ASME Journal of Dynamic Systems, Measurement, and Control, Vol. 114, pp. 468–474. Bayo, E., 1986, "Timoshenko versus Bernoulli beam theories for the control of flexible

robots", Proceeding of IASTED International Symposium on Applied Control and

flexible manipulator", Mechanism and Machine Theory, Vol. 25, No. 1, pp. 119–128.

a planar 2-link structurally flexible robotic manipulator", Journal of Robotic

that the present contribution is a useful tool for robotic path planning design.

objectives.

the global minimum.

**8. References** 

through a stochastic approach.

repeated several times during the working cycle.

Identification, pp. 178–182.

SIAM 2001, Philadelphia.

Systems, Vol. 11, No. 6, pp. 557–571.


**18** 

*1,2Vietnam 3Russia* 

**Singularity Analysis, Constraint Wrenches** 

Nguyen Minh Thanh1, Le Hoai Quoc2 and Victor Glazunov3 *1Department of Automation, Hochiminh City University of Transport,* 

**and Optimal Design of Parallel Manipulators** 

*2 Department of Science and Technology, People's Committee of Hochiminh City, 3Mechanical Engineering Research Institute, Russian Academy of Sciences,* 

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

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;

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

In this section, let us consider a 6-DOF parallel manipulator with actuators situated on the

base. The mechanical architecture of the considered robot is illustrated in Fig. 1.

(Glazunov, 2006; Glazunov, et al. 1999, 2007, 2009; Thanh, et al. 2009, 2010a).

**1. Introduction** 

Huang, 2004; Arakelian, et al. 2007).

**2. Kinematic of parallel manipulator** 

actuators located on the base.

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– 214, and pp. 215–224.

