Hinge Force in Kangaroo

The new Hinge Force in Kangaroo is perfect for simulating bent developable surfaces!

In these examples, Kangaroo wants to flatten the meshes by trying to set the angle between each neighbouring triangles to zero. Springs make sure the surfaces don't deform. Thanks to Daniel Piker for this great force! More reading about the Hinge concept here.

Kangaroo Curvature Graphs

I used Kangaroo to generate these bending curves and plotted their Curvature Graphs above.

Comparing 5 curves

This diagram shows five different versions of a bending curve.

1. Elastica curve, curvature varies with Sine (0-180°)

2. Clothoid curve, linear increase / linear decrease of curvature

3. The original traced saw blade (it was difficult to meassure the curvature of the scanned line)

4. Curve from Daniel Pikers Kangaroo (see previous post)

5. A curve with curvature made up of two different Sine curves.

The last curve is based on a diagram by Maarten Kuijvenhoven, see image below from his thesis. The curve is a combination of two sine waves, the first one with aplitude 1 (0-180°) and the other one with amplitude -0.1 (0-540°). The amplitude relation was something I had to experiment with, but the one used above seemed to work quite well. In the illustration below, both sine waves have amplitude 1.

Image: Maarten Kuijvenhoven

Kangaroo Curvature Analysis

Daniel Pikers KANGAROO

(As reported earlier in this previous post) Daniel Piker is developing ways to accurately simulate physical behavior in his Grasshopper component "Kangaroo".

In the latest release there are tools for simulating bending geometry.

This is nothing but a revolution for this investigation!

Never before have I been able to recreate bending geometry so accurately in an "artificial way". At the moment Kangaroo works very accurately for 2d-bending with both fixed and hinged ends and also in 3d for rods.

3d-bending of developable surfaces is a little more tricky and requires a careful setup to make sure the surfaces stay developable.

Kangaroo works in an iterative way by letting some predefined forces (like springs, bending resistance, pressure and gravity) affect the geometry, step by step, until (usually) a stable solution is reached. The beautiful thing is that all this is done in real-time, so you can play around with different constraints and setting and see the result instantly.
Of course, this investigation is not only about mimicking bending geometry, but also about understanding it. Kangaroo brings my understanding to a new level!

For more reading on how Kangaroo deals with bending, Daniel Piker has recommended a paper written in 1998 by S.M.L. Adriaenssens and M.R. Barnes called Tensegrity spline beam and grid shell structures, published in Engineering Structures 23 (2001), pages 29–36.

Many thanks to Daniel Piker for making and sharing the Kangaroo!

Kangaroo Bending + Reactivision

A video response to these photos by Amir Gazit. Thanks to Daniel Piker for this setup: Also thanks to Andy Payne and Jason K Johnson for including the Reactivision stuff in the latest FireFly. It's a lot of fun!

Realtime curvature analysis of a Kangaroo bending curve

Some more testing with bending in Daniel Pikers Kangaroo.
Kangaroo is a component for Grasshopper (Rhino).

Kangaroo Physics "Drop shape"

This is the closest approximation I have found so far in my quest for finding the Geometry of Bending. It's a fairly simple setup in Kangaroo. Pretty amazing how well it works! Thanks Daniel...

Bending simulation in Kangaroo

A very simple test in Kangaroo (only 8 control points) turned out to be very realistic in the way it moves. View it at Vimeo.

Kangaroo Physics by Daniel Piker

The Kangaroo by Daniel Piker brings live 3D Physics into Rhino/Grasshopper (see some videos explaining what Kangaroo can do here). Kangaroo is installed like a subcomponent in Grasshopper for Rhino (a lot of animals...) Daniel kindly let me try an unofficial version which can simulate bending geometry (!) Below are images from Kangaroo in action and verification with a guitar string. Thanks Daniel!