COMPUTER VIZUALIZATION OF MULTY-LINK

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Georgian Technical University
COMPUTER VIZUALIZATION OF MULTY-LINK MECHANISMS
WITH TWO DEGREES OF FREEDOM
PhD Student Marina Razmadze
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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.

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Four link slider - crank mechanism
Four link mechanism with
rotating kinematic pairs
Five link mechanism with gear pair, reducing
number degrees of freedom of the mechanical
system
Six link gear mechanism
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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 its necessary to find generalized
coordinates of the mechanism, which provides the
location of C point.
The design diagram of five link mechanism.
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Based on previous works devoting to this task the
generalized coordinates as angles between the
links are determined as follows.
(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.
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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.
parameters of the link
From the very beginning each link has to be given
with following parameters width, length and
thickness.
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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
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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.
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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.
Links subsystem block diagram
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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.
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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
B.
A.
Configuration of the link.
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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.
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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 .
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Thank You for Attention