Software Platform for the Assisted Research of the Kinematics and Dynamics of Industrial Robots

The paper presents a software platform made with LabVIEWTM for the assisted research of the kinematic and dynamic behavior of industrial robots. The platform comprises a series of virtual instrumentation LabVIEWTM programs (subVI-s) with: the input data modules in the form of several clusters with the parameters of the trapezoidal velocity characteristics of each joint, the axes of movement and the type of each joints, the dimensions of each body, the graph associated to the robot’s structure, the incidence matrices bodies - joints and joints- bodies, as well as the control buttons for movement up or down with or without object in the end- effecter, some modules with 2D characteristics of positions, velocities, accelerations, forces and moments in each joints and also the 3D characteristics of them. The research of the current stage shows that such a complex platform like this was not realized, the current research being limited to the animation of motion trajectories, determining the characteristics of positions, velocities, accelerations, forces and moments without the possibility of changing all motion parameters and robot’s dimensions and without show how these parameters change the behavior. The paper studies the case of an articulated arm type robot, but the platform can be used for any type of robot with four degrees of freedom (DOF).

UNION AND INTERSECTION OF CHAOTIC GRAPHS WITH DENSITY VARIATION

The aim of the present study is to discuss the union and intersection operations on chaotic graphs with density variation; the adjacency and incidence matrices representing the chaotic graphs induced from these operations will be introduced when physical characters of chaotic graphs have the same properties. There are several applications that have been utilized on chaotic graphs with density variation. The most practical applications of these kinds of operations on chaotic graphs with density variation are the internet signal speeds and the variation of green color for different parts of the plant. For example, in botany, in some cases, several plants suffer from a lack of chlorophyll in the damaged parts of the plant. In this case, the plant is represented by a chaotic graph, and the proportion of chlorophyll is represented by the density property, then the appropriate process is applied to increase the chlorophyll percentage in the appropriate place, so these operations help us to choose the suitable operator that satisfies our desires and requests. Keywords: adjacency matrix, incidence matrix, chaotic graph, density, union, intersection.

Evaluating Popular Statistical Properties of Incomplete Block Designs: A MATLAB Program Approach

Evaluating the statistical properties of a semi-Latin square, and in general, an incomplete block design, is vital in determining the usefulness of the design for experimentation. Improving the procedures for obtaining these statistical properties has been the subject of some research studies and software developments. Many available statistical software that evaluate incomplete block designs do so at the level of analysis of variance but not for the popular A-, D-, E-, and MV-efficiency properties of these designs to determine their adequacy for experimentation. This study presents a program written in the MATLAB environment using MATLAB codes and syntaxes which is capable of computing the A-, D-, E-, and MV-efficiency properties of any n×n/k semi-Latin square and any incomplete block design via their incidence matrices, where N is the number of rows and columns and k is the number of plots. The only input required for the program to compute the four efficiency criteria is the incidence matrix of the incomplete block design. The incidence matrix is the binary representation of an incomplete block design. The program automatically generates the efficiency values of the design once the incidence matrix has been provided, as shown in the examples.

Lattice Bounded Distance Equivalence for 1D Delone Sets with Finite Local Complexity

Spectra of suitably chosen Pisot-Vijayaraghavan numbers represent non-trivial examples of self-similar Delone point sets of finite local complexity, indispensable in quasicrystal modeling. For the case of quadratic Pisot units we characterize, dependingly on digits in the corresponding numeration systems, the spectra which are bounded distance to an average lattice. Our method stems in interpretation of the spectra in the frame of the cut-and-project method. Such structures are coded by an infinite word over a finite alphabet which enables us to exploit combinatorial notions such as balancedness, substitutions and the spectrum of associated incidence matrices.

RETRACTING 1-SIMPLICIAL CHAOTIC GRAPHS WITH DENSITY VARIATION

In this paper we will discuss retraction transformation on chaotic graphs for different cases of density variation, Two types of retraction will be discussed, geometric retraction and chaotic edges retraction, We shall study and discuss the effects of retraction on the shape and density degree of chaotic graphs shown on figures, the adjacent and incidence matrices with be presented. The density character may present many applications in life such as degree of green color in plants, net perturbation resonance, signals in the nerve system and so many, we focus our study on plants, how retraction effects of the degree of green color of plants leaves and shape of the leave its self. The variation of the density character shows the variation of the degree of green color of plant (i.e. Chlorophyll), so we divided in three cases, the first case when the leave of plant is unit and constant everywhere, or varied from level to level or varied even in the same level line of a plant leave, each case will be discussed for two types of retraction and deduce results for both types.

Observability analysis of combined finite automata based upon semi-tensor product of matrices approach

As a fundamental subject, the state estimation of deterministic finite automata has received considerable attention. Especially, it is increasingly necessary to study various problems based on more complex systems. In this paper, the observability of three kinds of combining automata, structured in parallel, serial and feedback manners, are investigated based on an algebraic state space approach. Compared with the formal language method, the matrix approach has great advantages in problem description and solution. Because of inconsistent frameworks of these combined automata, we optimize structure matrices by pseudo-commutation of semi-tensor product and power-reducing matrix. In addition, we construct corresponding incidence matrices by labelling to avoid superfluous null elements in the logical matrix occupying storage space. It follows that the observability analysis could be carried out under two polynomial matrices, established from the above algebraic form. Meanwhile, two algorithms, judging whether a combined automaton is initial state observable or current state observable, are presented. Finally, there are two representative examples to actualize our approach.

Constructing non-orthogonal split-split-plot designs using some resolvable block designs

SummaryWe consider a new method of constructing non-orthogonal (incomplete) split-split-plot designs (SSPDs) for three (A, B, C) factor experiments. The final design is generated by some resolvable incomplete block design (for the factor A) and by square lattice designs for factors B and C using a modified Kronecker product of those designs (incidence matrices). Statistical properties of the constructed designs are investigated under a randomized-derived linear model. This model is strictly connected with a four-step randomization of units (blocks, whole plots, subplots, sub-subplots inside each block). The final SSPD has orthogonal block structure (OBS) and satisfies the general balance (GB) property. The statistical analysis of experiments performed in the SSPD is based on the analysis of variance often used for multistratum experiments. We characterize the SSPD with respect to the stratum efficiency factors for the basic estimable treatment contrasts. The structures of the vectors defining treatment contrasts are also given.