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 only 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 (assembly mode).

In this way the model is able to show the problem of transfer of motion 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, apperently without any reason.

In general transfer quality can 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 below).

 

Literature:

Klein Breteler, A.J. : Movability and Transfer quality of arbitrary mechanisms, an application of the FEM-Theory. Proceedings of 6th IFToMM world congress, New Delhi, 1083.

 

Remarks:

The motion analysis has been performed with the program Runmec

 

 

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