Three different concepts for bi-stable linear mechanisms have been
developed. Prototypes of each concept were manufactured and tested
on an Instron materials testing machine. The experimental results
were then compared to analytical results derived for each model.
4 Bar, 2 Spring Mechanism (4B2S)
The 4B2S mechanism is a two dimensional, 4 bar, 2 spring
mechanism. All the bars are of equal length and connected to each
other by revolute joints with parallel axes. All of the four
joints are connected to the joint opposite with a length of steel
tape spring. At the joints between the tape springs and the bars
the only constrained axis is the one along the tape spring.
The geometry of the linkage makes it impossible for both tape
springs to be straight (unbuckled) at any time. When the tape
springs are buckled, they exert a relatively small force on the
four bar linkage. This force is considerably lower than the force
required to buckle the tape springs. As a result, the mechanism is
stable and stiff when one tape spring or the other is straight.
The mechanism has relatively low stiffness when both tape springs
are buckled.
Using the buckling characteristics and moment-rotation
characteristics of the tape springs, a force deflection plot could
be derived. This can be compared to the plot obtained from the
Instron. The dotted line in the analytical plot.
Having determined that a good correlation was achieved between the analytical and experimental results a design plot was created. The output criteria will typically be Fmax, Fmin, Lmax and Lmin. The design variables in the mechanism are the eccentricity of the loading on the two tape springs, the area and second moment of area of the two tape springs, the number to tape springs and the length of the tape springs and the bars. Given the
number of variables (11) and the number of known parameters (4),
it is not possible to set up a sufficient number of equations to
fix all the variables by solving simultaneous equations.
In order to simplify matters, the following assumptions were made.
The values of A and I are fixed, in this case given the values
of 25.4 mm Sears carpenter's tape. B is set to an arbitrary
value of 0.447*Lmax. Finally, na and nb are set to the minimum value possible in order to achieve the required
forces.
As an example, the design plot for the geometry of the prototype
4B2S mechanism has been included below.