Schematic concept of the LaCoste linkage consisting of a zero length spring and flexure pivoted arm.
Force-displacement diagram of different types of spring with initial physical length L 0. The dots represent the force applied to the springs. The slopes of the lines are the spring rate of these different springs, respectively. Note that the stretching of the spring Δl is different from the physical length change of the spring ΔL = L − L 0.
Schematic of tunable LaCoste system.
Force-angular displacement characteristic of a LaCosta Linkage with non-zero length spring or non-zero x offset.
Effect of x offset tuning on the slope of the force-angular displacement curve. It can be seen that at small angle the force-angular displacement is quite linear and by tuning the x offset, it is possible to achieve a low spring rate and thus low resonant frequency. Here, x < 0 means the top mount is at the left side relative to the pivot.
Euler buckling spring in different boundary conditions: (a) hinged-hinged elastic column in buckled mode; (b) clamped-clamped elastic column in buckled mode.
Force-displacement characteristic of typical Euler springs.
Principle of the tensile Euler springs arrangement which uses tension wires pulling from opposite ends. This structure is normally unstable.
Stable tensile Euler spring unit able to work as a “zero length spring” in a LaCoste frame. (a) Four pairs of blades are clamped and attached to two rigid rings with non-conflicting wire structures for tension. (b) A monolithic Euler spring unit with three pairs of blades constructed by electric discharge machining. Similar sets of non-conflicting extension wires as the ring design are attached to the two triangular frames of the spring module to form a tension spring module.
Prototype Euler-LaCoste linkage as a very low frequency oscillator. (a) Schematic diagram; (b) Photo of the apparatus. The Euler spring blades are 2 cm wide, 0.5 mm thick, and 260 mm long between the clamps. The distance between the top and bottom mount of the Euler spring unit L ∼ 300 mm.
Force-displacement characteristic of the Euler spring unit. The unit under test is arranged as shown in Fig. 9(a) so that it operates under tension. The original spring unit length is 260 mm. The force was applied by directly adding weight under the unit, which buckled under the weight about 21 kg.
Tuning of the Euler-LaCoste linkage with x offset. Here, Δx is the change of the offset value.
Euler-LaCoste linkage period of oscillation with height adjustment. Each curve represents different final length L indicated in the legend.
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