Kinematics of an overconstrained mechanism in practice

In 1939 Paul Schatz, a Swiss anthroposophist and geometrician had invented a mechanism which with few links generates spatial motions. Mixing machine based on this Schatz mechanism uses a highly ordered form of three dimensional motion that brings centrifugal and centripetal forces to dynamic balance. This results in ideal mixing environment. While exploring this mechanism, it was then clear that this mechanism is a six link spatial mechanism which does not satisfy the Kutzbach criterion of full cycle mobility. Such practical application of overconstrained mechanism has very interesting characteristics. Without the use of cams or gears it performs spatial motion. The work described in this paper is an attempt to describe general kinematics of this six link mechanism involving only revolutes, using matrix method. As discussed here, a spatial mechanism containing only revolutes is derived from the seven link kinematics chain. However mechanism described here has only six links including the fixed base. If the link lengths are selected arbitrary, then the mechanism will result in immobility with no degrees of freedom. Mobility of the mechanism is because of specific linear dimensions only. The mobility of the mechanism is proved with this kinematics description.