Georgian Technical University
COMPUTER VIZUALIZATION
OF MULTY-LINK
MECHANISMS WITH TWO
DEGREES OF FREEDOM
PhD Student
Marina Razmadze
Mechanisms used in technological machines
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.
Four link mechanism with
rotating kinematic pairs
Six link gear mechanism
Four link slider - crank
mechanism
Five link mechanism with gear pair, reducing
number degrees of freedom of the mechanical
system
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.
X C2  YC2  l12  l22
12   arccos
2l1l2
01  arccos
l2YC sin 12  X C  l2 cos 12  l1 
 l2 cos 12  l1 
2
 l22 sin 2 12
 X C  l0 2  YC2  l32  l42
34   arccos
2l3l 4
 l3YC sin 34  l0  X C l3 cos34  l4 
 40  arccos
l3 cos34  l4 2  l32 sin 2 34
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.
Thickness
parameters of the link
From the very beginning each link has to be given with following parameters –
width, length and thickness.
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
Mask Editor for manage defined
variables.
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.
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.
Block Parameters
A.
Configuration of the link.
B.
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.
The scheme of full mechanism with facilities of visualization of complete mechanism .
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