scholarly journals Method for analytical description and modeling of the working space of a manipulation robot

2021 ◽  
Vol 6 (7 (114)) ◽  
Author(s):  
Akambay Beisembayev ◽  
Anargul Yerbossynova ◽  
Petro Pavlenko ◽  
Mukhit Baibatshayev
Keyword(s):  
Normal Form ◽  
Analytical Description ◽  
Disjunctive Normal Form ◽  
Necessary Condition ◽  
Logic Function ◽  
Working Space ◽  
Graphic Image ◽  
Logic Functions ◽  
Manipulation Robot ◽  
Boundary Surfaces

This paper reports a method, built in the form of a logic function, for describing the working spaces of manipulation robots analytically. A working space is defined as a work area or reachable area by a manipulation robot. An example of describing the working space of a manipulation robot with seven rotational degrees of mobility has been considered. Technological processes in robotic industries can be associated with the positioning of the grip, at the required points, in the predefined coordinates, or with the execution of the movement of a working body along the predefined trajectories, which can also be determined using the required points in the predefined coordinates. A necessary condition for a manipulation robot to execute a specified process is that all the required positioning points should be within a working space. To solve this task, a method is proposed that involves the analysis of the kinematic scheme of a manipulation robot in order to acquire a graphic image of the working space to identify boundary surfaces, as well as identify additional surfaces. The working space is limited by a set of boundary surfaces where additional surfaces are needed to highlight parts of the working space. Specifying each surface as a logic function, the working space is described piece by piece. Next, the resulting parts are combined with a logical expression, which is a disjunctive normal form of logic functions, which is an analytical description of the working space. The correspondence of the obtained analytical description to the original graphic image of working space is verified by simulating the disjunctive normal form of logic functions using MATLAB (USA).

DESIGN AND APPLICATION OF AN INTERACTIVE WHEELCHAIR TRAINING SYSTEM

2008 ◽  
Vol 20 (06) ◽  
pp. 377-385 ◽  
Author(s):  
Chern-Sheng Lin ◽  
Chia-Chang Chang ◽  
Wei-Lung Chen
Keyword(s):  
Control Function ◽  
Training System ◽  
Digital Logic ◽  
3D Simulation ◽  
Initial Time ◽  
Logic Function ◽  
Wheelchair Users ◽  
Rehabilitation Training ◽  
Direction Control ◽  
Logic Functions

In this paper we constructed an interactive wheelchair rehabilitation training platform. The roller wheel on the platform is driven mainly by turning the wheelchair, and then the relative position of wheelchair on the screen can be adjusted based on the rotation speed of left and right wheels on the platform. Comparing the digital logic function when two wheels rotate at the same time and judging the variance in digital logic, the steering direction of wheels can be known and be controlled forward or backward. Additionally, the standard digital logic function could be individually judged when left wheel rotates and vice versa, so as to control the steering. Through judging three digital logic functions, the initial time of left wheel, next signal selecting time of left wheel, initial time of right wheel, and next signal selecting time of right wheel could be obtained, then the system can achieve the required direction control function through the judgment formula. The direction control function is indicated by standard digital logic function, so that the user can operate smoothly in the interactive situation software and make an interaction with the computer 3D simulation scene, the patient would have rehabilitation training through various 3D simulation real exteriors. This study not only provides basic trainings but also records the service behavior of wheelchair users, so that the rehabilitation consultant would have reference for the future diagnosis.

3D Visualization Model and Sample Implementation of 0-1 Function on Variant Logic

2013 ◽  
Vol 718-720 ◽  
pp. 480-483
Author(s):  
Huan Wang ◽  
Jie Ao Zhu ◽  
Xue Liu ◽  
Jeffrey Zheng
Keyword(s):  
Data Visualization ◽  
3D Visualization ◽  
Random Sequence ◽  
Relevant Logic ◽  
Complex Data ◽  
Paper Sample ◽  
Logic Function ◽  
Visual Model ◽  
Logic Functions ◽  
Visual Results

Random sequences generated by different logic functions play an important role in cryptography. The structure and the special properties of the logic function has been one of the most active areas of research. In order to study the random sequence and its related logic functions, many models have been established, and different advanced tools are applied to make complex data visualization. In this paper, sample logic functions are transferred into variant logic expressions to form a set of measurements. Using selected measurements, a 3D visual model is proposed. Selected 3D visual results are shown their intrinsic 3D spatial characteristics of relevant logic functions respectively.

On closure under direct product

1958 ◽  
Vol 23 (2) ◽  
pp. 149-154 ◽  
Author(s):  
C. C. Chang ◽  
Anne C. Morel
Keyword(s):  
Normal Form ◽  
Direct Product ◽  
Disjunctive Normal Form ◽  
Negative Answer ◽  
Sufficient Condition ◽  
Natural Question ◽  
Existential Quantifier ◽  
Relational Systems ◽  
Image Position

In 1951, Horn obtained a sufficient condition for an arithmetical class to be closed under direct product. A natural question which arose was whether Horn's condition is also necessary. We obtain a negative answer to that question.We shall discuss relational systems of the formwhere A and R are non-empty sets; each element of R is an ordered triple 〈a, b, c〉, with a, b, c ∈ A.1 If the triple 〈a, b, c〉 belongs to the relation R, we write R(a, b, c); if 〈a, b, c〉 ∉ R, we write (a, b, c). If x0, x1 and x2 are variables, then R(x0, x1, x2) and x0 = x1 are predicates. The expressions (x0, x1, x2) and x0 ≠ x1 will be referred to as negations of predicates.We speak of α1, …, αn as terms of the disjunction α1 ∨ … ∨ αn and as factors of the conjunction α1 ∧ … ∧ αn. A sentence (open, closed or neither) of the formwhere each Qi (if there be any) is either the universal or the existential quantifier and each αi, l is either a predicate or a negation of a predicate, is said to be in prenex disjunctive normal form.

scholarly journals On the learnability of disjunctive normal form formulas

1995 ◽  
Vol 19 (3) ◽  
pp. 183-208 ◽  
Author(s):  
Howard Aizenstein ◽  
Leonard Pitt
Keyword(s):  
Normal Form ◽  
Disjunctive Normal Form

scholarly journals Study of T-norms and Quantum Logic Functions on BL-algebra and Their Relationships to the Classical Probability Structures

2020 ◽  
pp. 591-599
Author(s):  
Ahmed AL-Adilee ◽  
Habeeb Kareem Abdullah ◽  
Hawraa A. AL-Challabi
Keyword(s):  
Quantum Logic ◽  
Probability Space ◽  
Binary Operation ◽  
The Other ◽  
Symmetric Difference ◽  
Logic Function ◽  
Classical Probability ◽  
Binary Operations ◽  
Basic Probability ◽  
Logic Functions

This paper is concerned with the study of the T-norms and the quantum logic functions on BL-algebra, respectively, along with their association with the classical probability space. The proposed constructions depend on demonstrating each type of the T-norms with respect to the basic probability of binary operation. On the other hand, we showed each quantum logic function with respect to some binary operations in probability space, such as intersection, union, and symmetric difference. Finally, we demonstrated the main results that explain the relationships among the T-norms and quantum logic functions. In order to show those relations and their related properties, different examples were built.

scholarly journals Foundations for Applications of Gibbs Derivatives in Logic Design and VLSI

VLSI Design ◽  
2002 ◽  
Vol 14 (1) ◽  
pp. 65-81 ◽  
Author(s):  
Radomir S. Stanković ◽  
Milena Stanković ◽  
Reiner Creutzburg
Keyword(s):  
New Technologies ◽  
Differential Operators ◽  
Rate Of Change ◽  
Logic Design ◽  
Logic Function ◽  
Spectral Techniques ◽  
Cad Systems ◽  
Vlsi Cad ◽  
Efficient Calculation ◽  
Logic Functions

New technologies and increased requirements for performances of digital systems require new mathematical theories and tools as a basis for future VLSI CAD systems. New or alternative mathematical approaches and concepts must be suitable to solve some concrete problems in VLSI and efficient algorithms for their efficient application should be provided. This paper is an attempt in this direction and relates with the recently renewed interest in arithmetic expressions for switching functions, instead representations in Boolean structures, and spectral techniques and differential operators in switching theory and applications. Logic derivatives are efficiently used in solving different tasks in logic design, as for example, fault detection, functional decomposition, detection of symmetries and co-symmetries of logic functions, etc. Their application is based on the property that by differential operators, we can measure the rate of change of a logic function. However, by logic derivatives, we can hardly distinguish the direction of the change of the function, since they are defined in finite algebraic structures. Gibbs derivatives are a class of differential operators on groups, which applied to logic functions, permit to overcome this disadvantage of logic derivatives. Therefore, they may be useful in logic design in the same areas where the logic derivatives have been already using. For such applications, it is important to provide fast algorithms for calculation of Gibbs derivatives on finite groups efficiently in terms of space and time. In this paper, we discuss the methods for efficient calculation of Gibbs derivatives. These methods should represent a basis for further applications of these and related operators in VLSI CAD systems.

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