Assisted analyze of the Extenics dependent functions theory is necessary to study easily all influences of the current point in to the space of nR dimensions. The Extenics theory was defined by prof. Cai Wen in 1983 and his collaborators in the mathematical, philosophy and logical models [1-. This paper inspired from the Extenics theory try to transfer the mathematical formalism in to the virtual LabVIEW instrumentation what can be easily establish, by on-line calculus of the dependent functions, the affiliation of one class or interval in the nR dimensions and validate all Extenics conditions. The research established the complex field of the dependent functions, when the work point is inside, outside, symmetrical or asymmetrical position versus the optimal area. In the Extenics theory wasnt defined in this new form the nR dimensions. It is defined also in this paper the attraction field instead of the attraction point defined in [. The paper show the study case of the 2D and 3D dependent on-line functions with define finally the attraction field like the optimized place of the working point.

Finding the better solution of the inverse kinematics problem, with the minimum of the trajectory errors, is very difficult because there are many variable parameters and many redundant solutions. The presented paper show the assisted solving of the inverse kinematics with the goal to minimize the final end-effector trajectory errors, by optimizing the distance between the and-effector final position and the target. All obtained results were been verified by applying the proper forward kinematics virtual LabVIEW instrumentation. The paper tries to answer at the inverse kinematics problem for one known mathematical trajectory and identifying the cinematic errors after the establishing and applying the proper assisted solving method using the Cycle Coordinate Descent Method coupled to the proper Neural Network Sigmoid Bipolar Hyperbolic Tangent (CCDM-SBHTNN). We were shown one complete study case to obtain one circle space trajectory using one arm type robot fixed on the ceiling. The presented method is general and can be used in all other robots types and in all other conventional and unconventional space curves.

In the control of the position of the robots systems one of the more important is to assure the minimum errors between the output and the target. All advanced researches in the word propose to use the neural network (NN) and the learning algorithm like Widrow and Hoff, or Levenberg-Marquard by using the least mean square (LMS) of errors and Delta rule, or back propagation training algorithm. Present paper is showing the mathematical model and numerical simulation of some important neurons types used in many applications that require extreme precision and neural network. All assisted researches were made with the owner LabVIEW virtual instrumentation. The research results and virtual LabVIEW instrumentation can be used in many other mechatronics applications.

The purpose of this paper is not to elaborate the bionic pattern of walking robot, but to elaborate our own simple idea of a 4 degree of freedom (DOF) walking robot with the ability to walk on flat surfaces, rotate and climbing upstairs, which is composed of vertical moved legs with a rotary foot and a controlled mass for stabilizing. In this paper, based on the former idea, a prototype model of a 3-DOF walking robot is presented for walking only on flat surfaces. This walking robot is actuated by servo motors. The paper covers the kinematics, centre of gravity analysis, description of the robot and its control system made using Pololu controller. Experiments confirmed the feasibility of the proposed design.

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