Snappability and singularity-distance of pin-jointed body-bar frameworks

Abstract

It is well-known that there exist rigid frameworks whose physical models can snap between different realizations due to non-destructive elastic deformations of material. We present a method to measure these snapping capability based on the total elastic strain energy density of the framework by using the physical concept of Green-Lagrange strain. As this so-called snappability only depends on the intrinsic framework geometry, it enables a fair comparison of pin-jointed body-bar frameworks, thus it can serve engineers as a criterion within the design process either to avoid snapping phenomena (e.g. truss structures) or to utilize them (e.g. multistable materials).Moreover, it turns out that the value obtained from this intrinsic pseudometric also gives the distance to the closest shaky configuration in the case of isostatic frameworks. Therefore it is also of use for the kinematics community, which is highly interested in the computation of these singularity-distances for diverse mechanical devices. In more detail we study this problem for parallel manipulators of Stewart-Gough type.

On origami-like quasi-mechanisms with an antiprismatic skeleton

“…, 6 and check if this value implies a pair of snapping sandglass realizations. To do so, we compute the realizations and check in a first step if they are free of self-intersections, and in a second step if they can snap into each other by the methods presented by the author in [9,10]. It turns out that only the branch of Eq.…”

“…(i) Snapping quasi-mechanism: The shape variation results from the snap (caused by deformation) of a given realization into another one. An example for this is the Siamese dipyramid, which even snaps between three realizations [2,10]. (ii) Shaky quasi-mechanism: Now the deformed states originate from a given shaky (also known as singular or infinitesimal flexible) realization.…”

“…2a). Note that shakiness can be seen as the limit of snapping when the related realizations converge to coincidence [12,10].…”

“…There are also examples, like the four-horn [16,10], which use both functional principles (i & ii) at the same time.…”

“…Moreover, in these two sections we also evaluate the capability of these snapping/shaky quasimechanisms to flex on base of the snappability index (cf. [9,10]) and the novel shakeability index, respectively. The paper is concluded in Section 5.…”