| Abstract: | In this article a novel geometrical method is presented to obtain singular points of a parallel manipulator. First, the constrained plain method (CPM) and some of its application in parallel mechanism is introduced. 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. Another theorem is used to achieve the direction of angular velocity of a body having three ICPs. Finally, as an example, using these two theorems, singularities of the 3UPS_PU mechanism are obtained. This method is completely geometrical, involving no complex or massive calculations and yields the answer quickly. 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. It usually needs exhaustive search of the workspace using an accurate analytical model of the mechanism kinematics and may lead to plenty of conditions remained to be pondered in order to obtain the singularity conditions. |
