Geometric support of algorithms for solving Problems of higher mathematics

2020 ◽  
Author(s):  
Ilzina Dmitrieva ◽  
Gennadiy Ivanov ◽  
Alexey Mineev
Keyword(s):  
Linear Algebra ◽  
Computer Aided Design ◽  
Analytical Approach ◽  
Constructive Approach ◽  
Source Data ◽  
Computer Aided ◽  
Multidimensional Geometry ◽  
Linear And Nonlinear ◽  
Aided Design ◽  
Modern Technologies

The need to improve the level of mathematical in particular geometric training of students of technical universities is due to modern technologies of computer-aided design. They are based on mathematical models of designed products, technological processes, etc., taking into account a large variety of source data. Therefore, from the first years of technical universities, when studying the cycle of mathematical disciplines, it is advisable to interpret a number of issues in terms and concepts of multidimensional geometry. At the same time, the combination of constructive (graphical) algorithms for solving problems in descriptive geometry with analytical algorithms in linear algebra and matanalysis allows us to summarize their advantages: the constructive approach provides the imagery inherent in engineering thinking, and the analytical approach provides the final result. The article shows the effectiveness of combining constructive and analytical algorithms for solving problems involving linear and nonlinear forms of many variables using specific examples.

Analyses of kinematics, statics, and workspace of a 3-RRPRR parallel manipulator and its three isomeric mechanisms

2008 ◽  
Vol 222 (9) ◽  
pp. 1829-1837 ◽  
Author(s):  
B Hu ◽  
Y Lu
Keyword(s):  
Computer Aided Design ◽  
Parallel Manipulator ◽  
Analytical Approach ◽  
Displacement Velocity ◽  
Active Force ◽  
Kinematic Characteristics ◽  
Computer Aided ◽  
Analytical Formulae ◽  
The Common ◽  
Aided Design

A novel 3-RRPRR parallel manipulator with three pure translational movements and a relative larger workspace is proposed. Its three isomeric mechanisms 3-RR PU, 3-R PRU, and 3-U PU with three pure translational movements are constructed by varying dimensions of some links. Their common kinematic characteristics, workspace, and singularity are analysed, the active force and the constrained torque are solved. First, a simulation mechanism of the 3-RR PRR manipulator is created, and its kinematics, singularity, and workspace are analysed by using an analytical approach and a computer-aided design (CAD) variation geometry approach. Second, the common analytical formulae for solving the displacement, velocity, and acceleration of the four manipulators are derived. Third, the formulae for solving the active forces and constrained torques of the 3-RR PRR manipulator are derived. The analytic-solved results are verified by their simulation mechanisms.

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