Nowadays, two kinds of suspending devices are used: the pendulum-rod, and the Picavet suspension.
Each kaper has his preference. On my own, I almost always use a pendulum-rod about 0.5m long, equipped with the stabilizer bow and with the Michaël Haugrund's damping device. I also adjusted a Picavet suspension with 3 hanging points and a stabilizer bow.
After long and enduring observations, I realized that the Picavet' suspension was combining both the pendulum function, and the damping function. This is why it has the favor of many kapers because of its lightness, and its small size when fold.
The pendulum is easy to built. It doesn't have spinning movement. It performs well in all conditions. It seems more appropriate for very light rigs and for all high angle flying kites. It needs to be dampened.
The Picavet suspension fits well the kites with a smaller line angle, as the flowform. It is less efficient with the higher line angle kites, such as Delta, Rokkaku, Dopero, Crico, or Waco kites. The length of lines and the dimension of the cross must be fitted to the mass.
Other pages described devices as I make them. Consider that as a guidance; feel free to make your own devices in accordance with techniques and materials you prefer.
During KAPiNed in May 2010, I have presented a topic on Pendulum and Picavet or more exactly on the motions and absorptions of the suspensions. A "silent" presentation, P & P, is available here.
This left picture is the Picavet III with dihedral or saddle sail. It is very efficient, more than my ability to make a page here to describe it.
Tell me how you fly, I will tell you how you suspend rig!