COMPUTER VIZUALIZATION OF MULTY-LINK MECHANISMS WITH TWO DEGREES OF FREEDOM

COMPUTER VIZUALIZATION OF MULTY-LINK

MECHANISMS WITH TWO DEGREES OF FREEDOM

Georgian Technical University

PhD Student Marina Razmadze

Mechanisms used in technological machines

Four link slider - crank mechanism

Four link mechanism with rotating kinematic pairs

Six link gear mechanism

Five link mechanism with gear pair, reducing number degrees of freedom of the mechanical system

Here are given the traditional mechanisms with one degree of freedom. These mechanisms were the basis of all machines ,because in the past there not existed the controllable actuators.

The formulation of task of kinematics of five link mechanism is done in the following way: the location of point C of mechanism, i.e. its coordinates in the base coordinate system, are given and it’s necessary to find generalized coordinates of the mechanism, which provides the location of C point.

The design diagram of five link mechanism.

Based on previous works devoting to this task the generalized coordinates as angles between the links are determined as follows.

2 2 2 21 2

121 2

arccos2

C CX Y l l

l l

43

24

23

220

34 2arccos

ll

llYlX CC

34

223

24343

4343034340

sincos

cossinarccos

lll

llXlYl CC

2 12 2 12 101 2 2 2

2 12 1 2 12

sin cosarccos

cos sinC Cl Y X l l

l l l

(2)

This expressions are determining CDO kinematic chain location. In order to find generalized velocities and accelerations, that are very important for calculation dynamic parameters of the given mechanical system obtaining by taking derivatives of given expressions.

Variation of the angels during the motion of the mechanism were calculated by means of MATLAB computer standard program. This program allows to carry out data analysis, visualization, and numerical computation as well.

In order to examine capabilities of the program MATLAB to solve the problem of visualization of displacements of five-link mechanism, has been utilized calculations done above and investigated facilities of program components as Simulink as well as SimMechanics. The mentioned programs will help for modeling the multibody system using the system blocks that would describe state of known parts of mechanism as bodies (levers, cranks, floating links and others), joints, constraints, and force elements. Particularly, has been used SimMechanics program, which would parameterized reusable components of the mechanical system with taking in account type of coupling of each link of the mechanism and in order to achieve our goal, the said parts, with their characterized parameters are gradually modeling for several different stages.

From the very beginning each link has to be given with following parameters – width, length and thickness.

Thickness

parameters of the link

This is the model of our link witch drown in Simulink program. From this picture we see that the model contains a single link of our mechanism and in case of necessary amendments of the link it is easily can be changed key parameters with Matlab variables. For this purposes we add a Simulink Mask, define the variables and set up a custom Dialog Box for parameters of the examined link.

The model of our link

Here, two variables Length (L) in Dimensions Tab, variable Density of Material or Thickness are defined manually in Tab section of the Mask.

The conducted operations allow us by means of block Refined Link to assign desirable values of parameters of concerning link, which is indicated on the dialog block named Block Parameters. So we conditionally set up the length of the link 240 cm. and thinkness 10 cm.

Mask Editor for manage defined variables.

Block Parameters.

After this transformations by clicking on Refined Block of our model of link we can see the subsystem block-diagram of the link broken up on four sections. In order to describe motion of the links with known homogenous shape the link can be divided on different sections.

Link’s subsystem block diagram

So in each of this sections we simply use variable L(length) that we defined and divided it on 4 for all the transforms that defines the distance between the coordinate systems there are used to define the link.

Division of the link in four sections allows to obtain the links with different configuration. So after this transformations we can use already known block named “Block Parameters” of the model of our link and conditionally cut this link on half (240/2). The appropriate diagram will have the following state indicated bellow - diagram B.

A.B.

Configuration of the link.

Block Parameters

The scheme of full mechanism with facilities of visualization of complete mechanism .

On the basis of described operations, by means of assembling of determined links the block diagram for full mechanism with facilities of visualization of complete mechanism is given by the diagram that is depicted on the Figure.

Here in the block-scheme the values of calculated angles will supply by block named “angles”, which is connected with different links of examined mechanism. Here is not shown the block, which assigned for calculation of meanings of angles during mechanisms motion. This block scheme is experimental type and during the subsequent researches the full visualized model will be obtained, where is intended to receive model ,which will depict the traces of planed and real trajectories of output link motion. The said will allow to designer make appropriate amendments in real mechanical system in order to achieve minimum value of inaccuracy of intending trajectory passing of kinematic chain.

Thereby we received the conceptual block-scheme for description of movement of full mechanism and on the basis of solution of kinematic analysis of planar five link linkage with two degrees of freedom is shown that the visualization of displacement of links of multi-bar mechanisms will be achieved.This method also would be used for study purposes for students of mechanical engineering and other specialties .

Thank You for Attention