Singularity Distance for Parallel Manipulators of Stewart Gough Type

Nawratil, Georg

doi:10.1007/978-3-030-20131-9_26

Cited by 7 publications

(10 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A detailed literature review on works dealing with the determination of the closest singular configuration to a given nonsingular one, which is of interest for singularity-free path-planning and performance optimization of the robot, was done by the author in [36]. Most of these approaches (also the one presented in [36]) evaluate the closeness extrinsically (i.e. in the 6 dimensional configuration space) and not intrinsically (i.e.…”

Section: Singularity-distance Computation For Stewart-gough Manipulatorsmentioning

confidence: 99%

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

Nawratil¹

2021

Preprint

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Section: Singularity-distance Computation For Stewart-gough Manipulatorsmentioning

confidence: 99%

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

Nawratil¹

2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…Fig. 1) with a pinned base given by k 1 = (0, 0) T , k 2 = (9, 0) T , k 3 = (7, 4) T which is equipped with the intrinsic metric (L 14 , L 25 , L 36 , L 45 , L 46 , L 56 ) = (11,10,5,8,5,5). The two undeformed realizations G(k) and G(k) snap into each other over G(k ) which was computed based on a framework consisting of (a) six bars using GL/CE strain (cyan/magenta dotted), (b) three bars and one triangular plate using GL strain (blue dashed).…”

Section: Singularity-distancementioning

confidence: 99%

“…Especially for these mechanical devices also the proposed singularity-distance is of interest (e.g. for path planning), which can be seen as an alternative to the extrinsic metrics presented by the author in [8]. Therefore we demonstrate our methods on the basis of a 3-legged planar parallel manipulator (cf.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

On the Snappability and Singularity-Distance of Frameworks with Bars and Triangular Plates

Nawratil

2021

Springer Proceedings in Advanced Robotics

View full text Add to dashboard Cite

In a recent article the author presented a method to measure the snapping capability -shortly called snappability -of bar-joint frameworks based on the total elastic strain energy by computing the deformation of all bars using Hooke's law and the definition of Cauchy/Engineering strain. Within the paper at hand, we extend this approach to isostatic frameworks composed of bars and triangular plates by using the physical concept of Green-Lagrange strain. An intrinsic pseudometric based on the resulting total elastic strain energy density cannot only be used for evaluating the snappability but also for measuring the distance to the closest singular configuration. The presented methods are demonstrated on the basis of the 3-legged planar parallel manipulator.

show abstract

“…( 8). In the following we present the procedure for determining G(k ), which is similar 8 to the one given in [9]. As preparatory work for this algorithm we define the quotient set R := S /SE(n) where SE(n) denotes the group of direct isometries of E n and S the set of real saddle points of U(k ), which can be selected from the critical points via the second derivative test.…”

Section: If Triangular Plates Are Involved We Considermentioning

confidence: 99%

On the snappability and singularity-distance of frameworks with bars and triangular plates

Nawratil¹

2020

Preprint

Self Cite

View full text Add to dashboard Cite

In a recent article the author presented a method to measure the snapping capability -shortly called snappability -of bar-joint frameworks based on the total elastic strain energy by computing the deformation of all bars using Hooke's law and the definition of Cauchy/Engineering strain. Within the paper at hand, we extend this approach to frameworks composed of bars and triangular plates by using the physical concept of Green-Lagrange strain. An intrinsic pseudometric based on the resulting total elastic strain energy density cannot only be used for evaluating the snappability but also for measuring the distance to the closest singular configuration. The presented methods are demonstrated on the basis of the 3-legged planar parallel manipulator.

show abstract

Singularity Distance for Parallel Manipulators of Stewart Gough Type

Cited by 7 publications

References 16 publications

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

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

On the Snappability and Singularity-Distance of Frameworks with Bars and Triangular Plates

On the snappability and singularity-distance of frameworks with bars and triangular plates

Contact Info

Product

Resources

About