The kinematic design of spatial, hybrid closed chains including planar parallelograms

It is presented an integral approach for the kinematic design of spatial, hybrid closed chains which include planar parallelograms into their kinematic structure. It is based on a systematic application of recursive formulae intended for describing the evolution of screws through time. Due to the particular nature of the proposed approach, it can be closely related with Lie algebras and allows to overcome the lacking of group structure offered by a parallelogram when it is going to be considered as a component of a hybrid closed chain. Several application examples are presented in order to show the potential of the proposed approach.