Kinematic analysis and singularity loci of spatial four-degree-of-freedom parallel manipulators using a vector formulation

The kinematic analysis and the determination of the singularity loci of spa tial four-degree-of-freedom parallel manipulators with prismatic or revolut e actuators are discussed in this article. A new method for the derivation of the velocity equations and the corresponding Jacobian matrices is presen ted. The numerical determination of the workspace boundaries is then briefl y discussed. Finally, the determination of the singularity loci is performe d using the velocity equations and examples are given to illustrate the res ults obtained. Spatial four-degree-of-freedom parallel manipulators can be used in several robotic applications as well as in flight simulators. The d etermination of their singularity loci is a very important design issue.