In this article singular points of a parallel manipulator are obtained based on a novel geometrical method. Here we introduce the constrained plain method (CPM) and some of its application in parallel mechanism. Given the definition of constraint plane (CP) and infinite constraint plane (ICP) the dependency conditions of constraints is achieved with the use of a new theorem based on the Ceva geometrical theorem. The direction of angular velocity of a body is achieved by having three ICPs with the use of another theorem. Finally, with the use of the above two novel theorems singularities of the 3UPF_PU mechanism are obtained. It should be emphasized that this method is completely geometrical, involving no complex or massive calculations. In the previous methods based on the Grassmann Geometry, the mechanism needs to be statically analyzed at first, so that the Inverse Jacobian Matrix is achieved, and then the Plucker-Vector is derived. This task is somewhat inconvenient and in the end there are plenty of conditions remained to be pondered in order to obtain the singularity conditions, while the novel method introduced here, involves no tiring calculations neither the analysis of numerous conditions and yields the answer quickly.

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