Model 20: Stephenson-2 mechanism
Kinematic scheme:
Dimensions:
|
|
Dimensions [m] |
|
a |
0.090 |
|
b |
0.10817 |
|
c |
0.12369 |
|
d |
0.300 |
|
e |
0.18974 |
|
f |
0.18248 |
|
g |
0.21213 |
|
p |
0.12369 |
|
q |
0.180 |
|
r |
0.24187 |
Explanation:
This six-bar
mechanism, in which the two ternary links (blue and green) are hinged with binary
links, is known as the Stephenson mechanism. It has 3 variants, distinguished
by the choice for the frame link. Variant 2, as in this model, has a binary
link (d) of the five-bar loop as the frame link. In practice this type of
mechanism finds hardly application. One reason is that the transfer quality of
motion cannot be understood easily.
The model
allows measure d, the frame length, to be varied between 0.295 and 0.35m. For the bigger values of d the crank
cannot make a full revolution. Starting with the mechanism of the upper
picture, it is possible now to enlarge d, branch to a new configuration and
then restore the frame length. The lower picture shows the new configuration,
which is just a different assembly mode.
In this way the
model is able to show the problem of motion transfer quality. In the upper
picture the crank (red) can be rotated without problems. The lower picture has
obviously some positions with very bad motion quality, apparently without any
reason.
In general
transfer quality can be expressed with the determinant of the “characteristic
matrix” according the FEM-method, as used in the program Runmec.
This determinant should not be zero. The calculation of the determinant values,
for both branches, shows the difference (see picture with graphs).
Literature:
Klein Breteler,
A.J. : Movability and Transfer quality of arbitrary mechanisms, an application
of the FEM-Theory. Proceedings of 6th IFToMM
world congress,
Remarks:
The motion
analysis has been performed with the program Runmec