Numerical Kinematical Analysis of the Shaping Mechanism

AbstractThe paper deals with the complete kinematical analysis of the mechanism that enters the machine tool structure designed to generate, in particular, plane surfaces. A machine tool of this kind is called shaping machine. For this purpose, Euler’s relations concerning the velocities distribution, written in projections on the fix reference system axes will be used. Starting from these relations we will get to a system of the first order linear differential equations whose unknowns are the kinematical parameters of the mechanism elements. The variation in time of these parameters will be obtained by solving the differential equations system the differential equations system using numerical integration methods.

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Numerical Kinematical Analysis of the Articulated Quadrilateral Mechanism

Scientific Bulletin of Valahia University - Materials and Mechanics ◽

10.2478/bsmm-2019-0019 ◽

2019 ◽

Vol 17 (17) ◽

pp. 52-62

Author(s):

Mircea Bogdan Tătaru ◽

Vladimir Dragoş Tătaru

Keyword(s):

Differential Equations ◽

Numerical Method ◽

Reference System ◽

Electronic Computer ◽

System Of Differential Equations ◽

First Order ◽

Kinematical Analysis ◽

Fixed Reference ◽

Numerical Integration Methods ◽

Kinematical Parameters

AbstractThe paper presents a numerical method of kinematical analysis of the articulated quadrilateral mechanism. Starting from Euler’s relation concerning the distribution of speeds written in projections on the fixed reference system axes, a system of differential equations describing the movement of the mechanism was obtained. This system of differential equations was then solved using numerical integration methods and the variation with respect to time of the position kinematical parameters, of the velocities (the first order kinematical parameters), and of the accelerations (the second order kinematical parameters), was obtained. Matrix writing of the differential equations was used in order to make the differential equations set out in the paper easier to solve using the electronic computer.

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The Wave Theory of the Electron

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004100014638 ◽

1928 ◽

Vol 24 (4) ◽

pp. 501-505 ◽

Cited By ~ 3

Author(s):

J. M. Whittaker

Keyword(s):

Wave Function ◽

Differential Equations ◽

Fourth Order ◽

Commutative Algebra ◽

Wave Theory ◽

Wave Functions ◽

Linear Differential Equations ◽

Wave Mechanics ◽

First Order ◽

Linear Differential

In two recent papers Dirac has shown how the “duplexity” phenomena of the atom can be accounted for without recourse to the hypothesis of the spinning electron. The investigation is carried out by the methods of non-commutative algebra, the wave function ψ being a matrix of the fourth order. An alternative presentation of the theory, using the methods of wave mechanics, has been given by Darwin. The four-rowed matrix ψ is replaced by four wave functions ψ1, ψ2, ψ3, ψ4 satisfying four linear differential equations of the first order. These functions are related to one particular direction, and the work can only be given invariance of form at the expense of much additional complication, the four wave functions being replaced by sixteen.

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